@article{havner_2020, title={Analytical solutions for material line and plane in triple slip, with inverse solutions for the slips from a finite deformation experiment on iron crystals}, volume={125}, ISSN={["1879-2154"]}, DOI={10.1016/j.ijplas.2019.08.018}, abstractNote={Triple-slip analytical solutions are derived for rotation and extension of crystal material lines and planes relative to the underlying lattice, applicable to any crystal class. An algebraic inverse solution is then developed for the amounts of slip on the three systems (two collinear) in terms of initial and final positions of material line and plane. The solutions are applied to a finite deformation experiment (from the recent literature) on a bcc iron crystal in uniaxial compression, considering both {110} and {112} slip-planes. The respective slips and areal and length changes are determined from the initial and final experimental positions of the compression plane and an edge line. Such analyses can assist in assessment of relative hardening rates of the slip systems.}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={Havner, Kerry S.}, year={2020}, month={Feb}, pages={280–293} }
 @article{havner_franciosi_2018, title={Finite deformation analysis of slip-induced crystalline rotations during tensile and compressive tests on bcc iron crystals}, volume={98}, ISSN={["1478-6443"]}, DOI={10.1080/14786435.2018.1506177}, abstractNote={ABSTRACT This work compares slip-induced lattice rotations calculated from double-slip, finite-deformation analytical solutions to electron-back-scattering-diffraction (EBSD) rotation measurements from SEM in situ, room temperature straining of bcc iron crystals. The finite-deformation modelling assumes slip proportionality between the two dominant active systems. Four experimental cases from a recently published work (2015) are examined, two in axial tension and two in axial compression. They correspond to mixed double-slip on {110} and {112} planes, with slip on the latter in both ‘easy’ and ‘hard’ orientations. In the experiments, EBSD rotation measurements were made on three faces of the iron samples and the dominant active systems were identified from slip traces. Here the relative contributions of the two systems for the best match with available rotation data are determined for each case, and the results discussed in relation to initial shear stress and (probable) critical shear-strength ratios. The analyses provide insight into achievable accuracy in crystal-slip quantification, based on slip-trace observations and rotation measurements of a sample’s load and lateral axes, and some assessment of the relative hardening of active slip systems.}, number={31}, journal={PHILOSOPHICAL MAGAZINE}, author={Havner, Kerry S. and Franciosi, Patrick}, year={2018}, month={Nov}, pages={2797–2825} }
 @article{havner_2014, title={On crystal shear, lattice rotation and constraint stress in (110) channel die compression: rate-independent and viscoplastic analyses and predictions compared}, volume={94}, ISSN={["1478-6443"]}, DOI={10.1080/14786435.2014.899441}, abstractNote={Rate-independent crystal plasticity theory and a classic viscoplastic power-law are investigated, contrasted and compared for finite deformation analysis of fcc crystals in channel die compression, including full consideration of lattice straining. Both experiment-based anisotropic and isotropic (Taylor) hardenings are evaluated in rate-independent theory; and an unlimited range of power-law exponent n is considered in viscoplasticity. The focus is on predictions of lateral constraint stress, lattice rotation and crystal shear, and their comparison with experiment. General elastic-plastic equations (for both theories) are given for the range of unstable lattice orientations in (1 1 0) compression (‘range I’) and evaluated before and after a finite rotation of the lattice about the load axis. Equations also are given and evaluated for the ‘Brass’ orientation. It is shown that the theories can be in close agreement at the onset of finite deformation in range I, but that viscoplasticity gives results (for any n) after finite rotation that are in sharp contrast to rate-independent theory. The latter’s predictions for crystal shear and lattice rotation are in good to very good agreement with finite deformation experiments on aluminium and copper. The inclusion of lattice elasticity is found to have a negligible effect in range I. In contrast, for finite deformation in the stable Brass orientation, elastic-viscoplastic theory can be made to agree very closely with rate-independent theory and with experiment.}, number={17}, journal={PHILOSOPHICAL MAGAZINE}, author={Havner, Kerry S.}, year={2014}, pages={1924–1955} }
 @article{havner_2013, title={Comparative evaluation of a viscoplastic power-law and rate-independent crystal plasticity in channel die compression}, volume={59}, ISSN={["0167-6636"]}, DOI={10.1016/j.mechmat.2012.09.004}, abstractNote={General equations in (1 1 0) channel die compression are derived for a viscoplastic power-law, and comparative evaluations made with rate-independent theory and experiment. The latter theory has been shown in a series of papers (2007–2012) to predict well the finite-deformation experimental behavior (1966–2007) of fcc crystals in this family of orientations, and to give a rational basis for the elastoplastic transition that precedes the onset of finite multiple-slip. It is established analytically that, during this elastoplastic transition, the power-law equations in the limit of unbounded exponent n are identical with the rate-independent equations for lateral stress-rate and (very small) lattice rotation-rate. Moreover, results for aluminum and copper agree very closely for large n in four initial orientations investigated numerically. At the onset of finite deformation (in general when four or more systems are equally stressed) the respective results for stress-rate differ sharply, with the exception of the experimentally stable Brass orientation. When lattice elasticity is included in the power-law in this orientation (with an n of 100 or greater), it predicts results essentially indistinguishable from rate-independent theory for both aluminum and copper, in good agreement with experiment. In two orientations near the ends of the range, the power-law lattice rotation-rates at the onset of finite deformation for large n also agree closely with the rate-independent results. However, in the specific orientation from which there is large lattice rotation, the power-law significantly under-predicts rate-independent and experimental results after large strains, whatever the value of exponent n.}, journal={MECHANICS OF MATERIALS}, author={Havner, Kerry S.}, year={2013}, month={Apr}, pages={126–141} }
 @article{havner_2012, title={The elastoplastic transition in channel die compression of fcc crystals}, volume={35}, ISSN={["0749-6419"]}, DOI={10.1016/j.ijplas.2012.02.002}, abstractNote={A comprehensive analysis of the elastoplastic transition in fcc crystals in (110) channel die compression is presented. This range of very small crystal deformations and lattice rotations, of order 10−3 or less (typically with only two equally-stressed slip systems significantly active), precedes the 4-fold (or higher) large multiple-slip deformations that have been studied extensively, both experimentally and theoretically. General equations are derived for the strains, rotations, and crystal shearing in the elastoplastic transition, including a predictive equation for the compressive strain at the onset of finite deformation. From crystal elastic properties and experimental stress data for aluminum and copper in various lattice orientations, these very small elastoplastic strains, rotations, and shears are calculated over the range of possible lateral constraint directions. The results are contrasted with experimental and theoretical values of finite shears and lattice rotations in the same initial orientations, and a justification for the disregard of lattice straining in the finite deformation realm is given.}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={Havner, Kerry S.}, year={2012}, month={Aug}, pages={31–43} }
 @article{havner_2011, title={Perspectives on (110) channel die compression and analysis of the Goss orientation}, volume={27}, ISSN={["0749-6419"]}, DOI={10.1016/j.ijplas.2010.08.007}, abstractNote={Abstract The set of geometrically based slip-systems hardening inequalities introduced in Havner [Havner, K.S., 2005. Philos. Mag. 85, 2861–2894] is applied to the analysis and prediction of experimental response of fcc crystals in the singular ‘Goss’ orientation of the channel die test – loading direction (1 1 0), lateral constraint direction ( 1 ¯ 1 0 ) . In addition, perspectives from my previous analyses of (1 1 0) channel die compression (2007–10) are presented and relationships between hardening moduli and compressive stress–strain curves evaluated for aluminum and copper in each lattice-orientation range. In the Goss orientation and for all orientation ranges in (1 1 0) compression, theoretical results for active slip planes, principal slip-rates, lattice rotation or stability, and finite crystal shearing are fully consistent with the gross-scale, finite-deformation experimental response of aluminum and copper crystals.}, number={10}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={Havner, Kerry S.}, year={2011}, month={Oct}, pages={1512–1526} }
 @article{havner_2010, title={Analysis of fcc crystals in two singular orientations in (110) channel die compression}, volume={42}, ISSN={["0167-6636"]}, DOI={10.1016/j.mechmat.2010.04.003}, abstractNote={Analyses of fcc crystals in two singular orientations in (1 1 0) channel die compression – lateral constraint directions (11¯2¯)and(11¯1¯) (the ‘Brass’ orientation) – based upon rigorous multi-slip kinematics and a set of slip-systems hardening inequalities (Havner, 2005) are presented. Previous analyses of three orientation ranges in (1 1 0) compression, also based on these hardening inequalities, are briefly reviewed. Both the earlier results (2007–2008) and the current predictions, as regard (i) load-axis stability, (ii) finite crystal shear in the horizontal channel plane, (iii) either lattice stability or lattice rotation about the (1 1 0) load axis (dependent upon orientation), and (iv) lateral constraint stress, are compared with available experiment. The theoretical results are consistent with the gross scale, finite deformation behavior of fcc crystals (aluminum, copper, and Permalloy) in various orientations.}, number={6}, journal={MECHANICS OF MATERIALS}, author={Havner, Kerry S.}, year={2010}, month={Jun}, pages={657–672} }
 @book{havner_2008, title={Finite plastic deformation of crystalline solids (paperback re-issue)}, publisher={Cambridge: Cambridge University Press}, author={Havner, K. S.}, year={2008} }
 @article{havner_2008, title={Further investigation of crystal hardening inequalities in (110) channel die compression}, volume={464}, ISSN={["1364-5021"]}, DOI={10.1098/rspa.2007.0272}, abstractNote={A set of geometrically based FCC crystal slip-systems hardening inequalities is analytically investigated in (110) channel die compression for all lateral constraint directions betweenand, following previous analyses of the other two distinct orientation ranges in (110) compression. With all critical slip systems active, it is proved that these inequalities uniquely predict initial lattice stability and finite crystal shearing only in the horizontal channel plane, consistent with experiments for this range of orientations. (The earlier analyses had predicted load-axis stability in both orientation ranges, and lattice stability in one, also commonly found experimentally.) Moreover, it is established that the lateral constraint stress predicted by the hardening inequalities will be less than that given by classic Taylor hardening as this stress evolves with deformation. It is further shown, taking into account experimental stress–strain curves and latent hardening experiments for aluminium and copper, that lattice stability generally can be expected to very large deformations, except perhaps for lateral constraint orientations near theend of the range, which result is consistent with experiment. In appendix A, the possibilities of solutions with a critical slip system inactive are investigated, and predictions of a power law rate-dependent plasticity model are analysed for comparison with the results based on the hardening inequalities.}, number={2096}, journal={PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}, author={Havner, Kerry S.}, year={2008}, month={Aug}, pages={1955–1982} }
 @article{havner_2008, title={Investigation of basic crystal hardening inequalities in a range of stable lattice orientations in (110) channel die compression}, volume={24}, ISSN={["0749-6419"]}, DOI={10.1016/j.ijplas.2007.02.002}, abstractNote={Abstract The fcc slip-systems hardening inequalities given in [Havner, K.S., 2005. On lattice and material-frame rotations and crystal hardening in high-symmetry axial loading. Philos. Mag. 85 (25), 2861–2894] are investigated in (1 1 0) channel die compression for the 35.26° range of lateral constraint directions from ( 1 1 ¯ 1 ¯ ) (the ‘brass’ orientation) to ( 1 1 ¯ 0 ) (the ‘Goss’ orientation). It is established analytically that the inequalities uniquely predict lattice stability and finite shearing about the (1 1 0) load axis, consistent with experiments in this range. An analysis of the continuation of lattice stability to large deformations leads to a critical strain at which the lattice could theoretically, but not necessarily, lose stability.}, number={1}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={Havner, Kerry S.}, year={2008}, pages={74–88} }
 @article{havner_2007, title={"Channel die compression revisited: Application of a set of basic crystal hardening inequalities to (110) loading" (vol 39, pg 610, 2007)}, volume={39}, ISSN={["0167-6636"]}, DOI={10.1016/j.mechmat.2007.03.001}, abstractNote={An error in the uniqueness proof of load-axis stability in the subject paper [Havner, K.S., 2007. Channel die compression revisited: application of a set of basic crystal hardening inequalities to (1 1 0) loading. Mech. Mater. (39), 610–622] is acknowledged and another argument for axis stability is given.}, number={9}, journal={MECHANICS OF MATERIALS}, author={Havner, Kerry S.}, year={2007}, month={Sep}, pages={893–895} }
 @article{havner_2007, title={Channel die compression revisited: Application of a set of basic crystal hardening inequalities to (110) loading}, volume={39}, ISSN={["0167-6636"]}, DOI={10.1016/j.mechmat.2006.09.004}, abstractNote={A rigorous analytical investigation of (1 1 0) compression of fcc crystals in a channel die is carried-out for all lattice orientations between lateral constraint directions (channel-wall normals) (001¯) and (11¯2¯). It is proved that a set of basic slip-system hardening inequalities, that are consistent with experiments on fcc crystals in high symmetry, multiple-slip orientations in tension [Havner, K.S., 2005. On lattice and material-frame rotations and crystal hardening in high-symmetry axial loading. Philos. Mag. 85 (25), 2861–2894.], uniquely predict load-axis stability in (1 1 0) channel die compression, with lattice rotation and finite shearing about the loading direction as found experimentally for this range of orientations. It also is established from the inequalities that the evolving lateral constraint stress will be less than that predicted by classic (isotropic) Taylor hardening.}, number={6}, journal={MECHANICS OF MATERIALS}, author={Havner, Kerry S.}, year={2007}, month={Jun}, pages={610–622} }
 @article{havner_yu_2005, title={Kinematic, stress, and hardening analysis in finite double slip}, volume={21}, ISSN={["0749-6419"]}, DOI={10.1016/j.ijplas.2004.04.008}, abstractNote={A kinematic, stress, and hardening analysis of finite double slip in fcc crystals under axial loading is presented. The relative amounts of slip in classic 1925 experiments by Taylor and Elam (determined analytically in [Int. J. Plasticity 9 (1993) 159–179] by comparing theoretical and experimental cones of unextended directions), together with load-extension data and other measurements, are used to calculate resolved shear stress vs. slip curves and assess predictions of several finite distortional hardening theories. In particular, a new hardening rule is introduced that gives very close agreement with the anisotropic experimental results in double slip yet is consistent with the axisymmetric deformation, lattice stability, and isotropic hardening that are characteristic of fcc and bcc crystals in high symmetry axial-load orientations involving 6- and 8-fold slip.}, number={1}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={Havner, KS and Yu, PG}, year={2005}, pages={83–99} }
 @article{havner_2005, title={On lattice and material-frame rotations and crystal hardening in high-symmetry axial loading}, volume={85}, ISSN={["1478-6435"]}, DOI={10.1080/14786430500154315}, abstractNote={A diverse range of experimental behaviour in high-symmetry tensile loading of fcc crystals has been reported in a number of classic papers in the literature (1960–1982). This behaviour includes: (i) axis stability and axisymmetric deformation in ⟨111⟩ and ⟨100⟩ load orientations; (ii) axis rotation toward a ⟨111⟩ orientation in coplanar double-slip in ⟨110⟩ loading; and (iii) axis rotations toward (from an initial misalignment) or away from precise ⟨111⟩ and ⟨100⟩ load orientations, with a reduced number of active slip planes. In this paper extensive kinematic analyses of coincident and relative rotations among material, lattice, and loading frames in each of these orientations, together with additional kinematic solutions for load-axis rotations, are combined with experimental information and perspectives connecting relative hardening and geometric slip-system interactions to determine probable active systems and slip rates in this diverse set of experiments. It is found that a set of basic hardening inequalities, which follow from classic latent hardening experiments in single slip, is consistent with the full range of experimental behaviour in high-symmetry axial-load orientations.}, number={25}, journal={PHILOSOPHICAL MAGAZINE}, author={Havner, KS}, year={2005}, month={Sep}, pages={2861–2894} }
 @article{havner_2004, title={On the onset of necking in the tensile test}, volume={20}, ISSN={["0749-6419"]}, DOI={10.1016/j.ijplas.2003.05.004}, abstractNote={A very small inhomogeneity in macroscopic material properties is considered for the investigation of necking of a (polycrystalline) bar in the tensile test. A simple, one-dimensional model is adopted (i.e. spatial variation only along the bar's length), corresponding to which the evolving nonuniformity of cross-sectional area with increasing load, up to the maximum, also is small. The inhomogeneity is represented by a single modulus varying slightly with position, but with the same dimensionless form of the stress–strain curve throughout. A transcendental equation is derived that relates the strains at the weakest and strongest sections to their respective material strengths. It is shown that, at the well known Considère strain (corresponding to the maximum load), the decrease in area at the minimum section is only a little greater than at the strongest, but its rate of change with the latter strain is infinite. The analysis thus gives an idealized representation of the rapid increase in necking that typically ensues from the maximum load in experiments. In an extended Appendix the traditional case of a bar of theoretically homogeneous material is reviewed and reanalyzed, including consideration of rate-dependence.}, number={4-5}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={Havner, KS}, year={2004}, pages={965–978} }
 @article{yu_havner_2001, title={Numerical studies of nonuniform deformation, stress state evolution, and subgrain formation in bicrystals in (110) channel die compression}, volume={49}, ISSN={["1873-4782"]}, DOI={10.1016/s0022-5096(00)00021-1}, abstractNote={Abstract An elastoplastic numerical model for f.c.c. bicrystals in (110) channel die compression is investigated to a logarithmic strain of 10% and compared with the analytical rigid-plastic solution at the yield point. Three lattice orientations of an aluminum bicrystal are calculated between constraint directions [00 1 ] and [1 1 2 ] . It is found that the elastoplastic results for each of stress state, velocity field and lattice-rotation rate (indicating subgrain formation) pass very close to the analytical solution at 0.2% strain for two of the orientations. This is in spite of small tangential velocity discontinuities along characteristic directions of that solution which are not permitted in the numerical (finite element) modeling. The results are never as close in the third orientation, for which there are much greater tangential velocity discontinuities in the rigid-plastic model. It is suggested that the elastoplastic comparisons with the rigid-plastic model may provide insight into realistic strain levels at the beginning of fully plastic response. However, it also is concluded that a deeper analytical representation of the tangential velocity discontinuities is needed.}, number={1}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={Yu, PG and Havner, KS}, year={2001}, month={Jan}, pages={173–208} }
 @article{havner_yu_1998, title={On the stress state at the yield point in symmetric bicrystals in (110) channel die compression}, volume={27}, ISSN={["0167-6636"]}, DOI={10.1016/S0167-6636(97)00049-5}, abstractNote={The stress state at the yield point in symmetric fcc bicrystals is analytically investigated for a range of crystal lattice orientations in (110) channel die compression. Although strain-rates and lattice-rotation rates necessarily are nonuniform, it is proved that the stress field satisfying both equilibrium and yield-locus constraints must lie on an edge of the locus and is thereby uniform.}, number={4}, journal={MECHANICS OF MATERIALS}, author={Havner, KS and Yu, PG}, year={1998}, month={Apr}, pages={211–227} }
 @article{havner_1998, title={On velocity discontinuities in elastoplastic bicrystals in channel die compression}, volume={14}, ISSN={["0749-6419"]}, DOI={10.1016/S0749-6419(97)00040-5}, abstractNote={Possible consequences of including lattice straining in f.c.c. bicrystal models in channel die compression are investigated. It is determined that the tangential velocity discontinuities which emanate from the interface edges in rigid/plastic models are not eliminated by taking crystal elasticity into account.}, number={1-3}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={Havner, KS}, year={1998}, pages={61–74} }
 @article{wu_havner_1997, title={Analytical and numerical investigation of non-uniform straining and subgrain initiation in bicrystals in channel die compression}, volume={355}, ISSN={["1364-503X"]}, DOI={10.1098/rsta.1997.0095}, abstractNote={Effects of the grain boundary (i.e. interface plane) on deformation and stress state in symmetric FCC bicrystals are investigated. The full range of lattice constraint directions for crystals compressed in a (110) direction within a rigid channel die is considered. The spatial non–uniformity is only two dimensional and in the plane transverse to the loading direction. Principal analytical results are that subgrains begin to form within each crystal and tangential velocity discontinuities extend from interface edges in characteristic directions which depend on crystal orientation. Numerical (finite element) results for several orientations at the end of the elastoplastic transition form purely elastic to fully plastic (multiple–slip) response are compared with the analytical rigid–plastic solutions. Both analytical and numerical results predict subranges of lattice orientations in which there is separation of crystal and channel wall.}, number={1730}, journal={PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}, author={Wu, SC and Havner, KS}, year={1997}, month={Sep}, pages={1905–1943} }
 @article{lin_havner_1996, title={A comparative study of hardening theories in torsion using the Taylor polycrystal model}, volume={12}, ISSN={["0749-6419"]}, DOI={10.1016/S0749-6419(96)00025-3}, abstractNote={A study of five rate-independent hardening rules (from Taylor and Elam (“The Distortion of an Aluminium Crystal during a Tensile Test”, Proc. R. Soc. Lond. (1923), A102, 643) to Bassani and Wu (“Latent Hardening in Single Crystals II. Analytical Characterization and Predictions,” Proc. R. Soc. Lond. (1991), A435, 21)) is presented based upon the classic Taylor polycrystal model in finite strain torsion. Comparisons of aggregate shear stress-strain curves, evolving crystallographic textures, yield loci, and axial stresses among the theories are made; and results are assessed against experiments on polycrystalline copper from the literature.}, number={5}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={Lin, G and Havner, KS}, year={1996}, pages={695–718} }
 @inproceedings{havner_wu_1995, title={An analytical investigation of inhomogeneous straining, subgrain formation, and the initiation of microshear bands in bicrystals}, ISBN={0792335945}, booktitle={IUTAM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics: Proceedings of the IUTAM-ISIMM symposium held in Nottingham, U.K., 30 August-3 September 1994}, publisher={Dordrecht; Boston: Kluwer Academic}, author={Havner, K. S. and Wu, S.-C.}, editor={D. F. Parker and England, A. H.Editors}, year={1995}, pages={211–216} }
 @article{wu_havner_1995, title={Exact stress states and velocity fields in bicrystals at the yield point in channel die compression}, volume={46}, journal={Zeitschrift fur Angewandte Mathematik und Physik}, author={Wu, S.-C. and Havner, K. S.}, year={1995}, pages={446–465} }
 @inbook{havner_1994, title={A statical interpretation of the stress work-conjugate to Lagrangian-based Almansi strain}, ISBN={0444899189}, DOI={10.1016/b978-0-444-89918-7.50019-8}, abstractNote={A complete statical interpretation of the stress conjugate to (Lagrangian-based) Almansi strain is presented. This is accomplished through the process of force resolution on a reciprocal element constructed upon the inverse spacing-stretch vectors of an embedded material parallelepiped (deformed from an initial unit cube). Connection is made with a basic contribution of R. Hill.}, booktitle={Mechanics of materials and structures (Studies in applied mechanics, 35)}, publisher={Amsterdam; New York: Elsevier}, author={Havner, Kerry}, editor={Voyiadjis, L. C. Bank G. Z. and Jacobs, L. J.Editors}, year={1994}, pages={241–252} }
 @article{havner_wu_fuh_1994, title={ON SYMMETRICAL BICRYSTALS AT THE YIELD-POINT IN (110) CHANNEL DIE COMPRESSION}, volume={42}, ISSN={["0022-5096"]}, DOI={10.1016/0022-5096(94)90014-0}, abstractNote={The general problem of symmetric fee bicrystals in (110) channel die compression is formulated. For crystals at the yield point, corresponding to the beginning of finite multiple-slip and a rigid-plastic model, analytical bounds on the yield-point load are established for all lattice orientations. The upper bound analyses incorporate a deformation field that is motivated by observations from experiment. The bounds are generally good, and are highly satisfactory over approximately two-thirds of the range of possible orientations of the channel constraint direction relative to the lattice axes.}, number={2}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={HAVNER, KS and WU, SC and FUH, S}, year={1994}, month={Feb}, pages={361–379} }
 @article{lin_havner_1994, title={ON THE EVOLUTION OF TEXTURE AND YIELD LOCI IN AXISYMMETRICAL DEFORMATION OF FCC POLYCRYSTALS}, volume={10}, ISSN={["0749-6419"]}, DOI={10.1016/0749-6419(94)90010-8}, abstractNote={A comprehensive analysis of texture formation and the evolution of macroscopic yield loci in face-centered cubic polycrystalline metals is presented for each of axisymmetric tension and compression, based upon the classic aggregate model of Taylor [1938a]. The nonuniqueness of slip rates corresponding to rate-independent hardening theories is resolved in two alternative ways: the average slip method (Bunge [1970]) and minimum plastic spin (Fuh & Havner [1989]). Calculations to logarithmic strains of 1.61 in tension and compression are carried out for each of four hardening rules: the “simple theory” (Havner & Shalby [1977]), Taylor hardening (Taylor & Elam [1923]), the “P.A.N. tule” (Peirce, Asaro, & Needleman [1982]), and a two-parameter rule (Nakada & Keh [1966]). The results compared with each other, with other computational studies (for both rate-independent theories), and with experimental information on texture.}, number={5}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={LIN, G and HAVNER, KS}, year={1994}, pages={471–498} }
 @article{havner_1993, title={TAYLOR,G.I., REVISITED - THE CONE OF UNEXTENDED DIRECTIONS IN DOUBLE SLIP}, volume={9}, ISSN={["0749-6419"]}, DOI={10.1016/0749-6419(93)90027-N}, abstractNote={Recently developed general equations for the cone of unextended directions in arbitrary d double slip in f.c.c. crystals, in each of uniaxial tension and compression, are applied to the interpretation of finite deformation measurements from the classic series of papers (1923–27) by G. I. Taylor on cubic metal crystals. Measurements of comparable completeness are not found readilu elsewhere in the literature. From the equations and the experimental data (including lattice positions from X-ray diffraction analysis), the respective amounts of finite double slip are calculated for several cases from comparisons of theoretical and experimentally determined cones in stereographic projection. Apparent misconceptions in the literature about the subsequent deformations of Taylor's crystals after the loading axis reached a crystallographic symmetry line are addressed.}, number={2}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={HAVNER, KS}, year={1993}, pages={159–179} }
 @article{al-gadhib_havner_1992, title={Comparative evaluation of plasticity theories against tension- torsion test at finite strain}, volume={118}, DOI={10.1061/(ASCE)0733-9399(1992)118:10(2104)}, abstractNote={Classical isotropic hardening, nonlinear kinematic hardening, and a combined linear‐isotropic/nonlinear‐kinematic hardening theory are compared and contrasted with experimental results from nonproportional loading of thin‐walled tubes of annealed copper (published by Bell and Khan in 1980) and mild steel (published by Bell in 1983) in tension and torsion. Comparisons are made for principal direction paths of Eulerian strain rate and for individual axial and shear strain components. In addition, experimentally determined ratios of principal strain‐rates and principal stresses are compared. Because of the near coaxiality and proportionality of the strain‐rate and deviatoric stress tensors in the moderate finite‐deformation range of the experiments (for a variety of nonproportional loading paths), isotropic hardening theory provides the most satisfactory predictions overall. A simple means of further improving those predictions is suggested.}, journal={Journal of Engineering Mechanics}, author={Al-Gadhib, A. H. and Havner, Kerry}, year={1992}, pages={2104–2126} }
 @book{havner_1992, title={Finite plastic deformation of crystalline solids}, ISBN={0521392454}, publisher={Cambridge: Cambridge University Press}, author={Havner, K. S.}, year={1992} }
 @article{khedro_havner_1991, title={INVESTIGATION OF A ONE-PARAMETER FAMILY OF HARDENING RULES IN SINGLE SLIP IN FCC CRYSTALS}, volume={7}, ISSN={["0749-6419"]}, DOI={10.1016/0749-6419(91)90041-V}, abstractNote={A one-parameter, strain-measure dependent family of hardening rules is presented and investigated regarding predictions of latent hardening of slip systems in f.c.c. crystals in single slip. The family belongs to the general class of hardening theories given by Hill and Havner and includes as a special case (the logarithmic measure) the “simple theory” of plastic-spin dependent anisotropic hardening introduced in Havner and Shalaby. Both tensile and compressive axial loading are considered (to shears of order one) for a range of initial axis positions that span the standard stereographic triangle of the active system. The hardening of all latent systems and the issue of “overshooting” of the loading axis (beyond a crystallographic symmetry line) are investigated for each of the Green and Almansi strain measures and the simple theory. Assessments with respect to other measures also are made. It is found that among standard measures in the one-parameter family of hardening rules, taking into account both tension and compression, the simple theory gives the best overall predictions as compared with experimental observations and measurements at finite strain.}, number={6}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={KHEDRO, T and HAVNER, KS}, year={1991}, pages={477–503} }
 @article{al-gadhib_havner_1990, title={Principal direction paths in tension-torsion test at finite strain}, volume={116}, DOI={10.1061/(ASCE)0733-9399(1990)116:5(1002)}, abstractNote={General equations are presented for the determination of principal direction paths of each of the Lagrangian strain ellipsoid, Eulerian strain ellipsoid, strain rate, and Cauchy stress for uniform finite deformation of thin‐walled tubes in combined tension and torsion. Specific paths are evaluated from experimental results for nonproportional loading of tubes of annealed copper (Bell and Khan 1980) and mild steel (Bell 1983a). It is found that the principal directions of Cauchy stress are not correlated with either of the strain ellipsoids, but that Cauchy stress and Eulerian strain rate are very nearly coaxial throughout the moderate finite‐deformation range of the experiments.}, journal={Journal of Engineering Mechanics}, author={Al-Gadhib, A. H. and Havner, Kerry}, year={1990}, pages={1002–1019} }
 @article{fuh_havner_1989, title={A THEORY OF MINIMUM PLASTIC SPIN IN CRYSTAL MECHANICS}, volume={422}, ISSN={["0080-4630"]}, DOI={10.1098/rspa.1989.0025}, abstractNote={A theory of minimum plastic spin (i. e. minimum relative rate-of-rotation of gross crystalline material and underlying atomic lattice) is proposed for the finite deformation of crystals, consistent with loading conditions and constraints. Three families of multiple-slip configurations of f. c. c. crystals are comprehensively investigated: (i) pure plane strain compression with a [100] axis of free extension; (ii) (110) loading in channel die compression; and (iii) all multiple-slip orientations in uniaxial tension. It is established that, in each case, minimum plastic spin uniquely predicts the experimentally observed behaviour.}, number={1862}, journal={PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES}, author={FUH, S and HAVNER, KS}, year={1989}, month={Mar}, pages={193–239} }
 @article{chidambarrao_havner_1988, title={FINITE DEFORMATION ANALYSIS OF FCC CRYSTALS IN (110)(112)(111) CHANNEL DIE COMPRESSION}, volume={4}, ISSN={["0749-6419"]}, DOI={10.1016/0749-6419(88)90002-2}, abstractNote={A comprehensive analysis of f.c.c. crystals in initial orientation (110)(112)(111) (loading, constraint, and channel axis directions, respectively) in the channel die compression test is presented, to strains of order 1. Three hardening theories are investigated: Taylor's rule, the “simple theory,” and the “P.A.N. rule.” The predictions of these theories are found to be kinematically distinct for this orientation, with only the P.A.N. rule predicting lattice rotation about the loading axis. Comparisons with an experimental study are included.}, number={1}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={CHIDAMBARRAO, D and HAVNER, KS}, year={1988}, pages={1–27} }
 @article{chidambarrao_havner_1988, title={ON FINITE DEFORMATION OF FCC CRYSTALS IN (110) CHANNEL DIE COMPRESSION}, volume={36}, ISSN={["0022-5096"]}, DOI={10.1016/0022-5096(88)90013-0}, abstractNote={The characteristic behavior of f.c.c. crystals in the (110) channel die compression test is loading-axis stability. The lattice either rotates about the (110) loading direction or is stable relative to the channel axes, dependent upon constraint direction and active slip systems. Herein we establish a general theoretical basis for the initial finite deformation behavior that encompasses the full range of crystal orientations under (110) loading. We also make detailed analyses of crystal shearing, lattice rotation, slip-systems hardening, and constraint stress for orientations near a nominal (110) (112) (111) experimental orientation, based upon three specific hardening theories, and make comparisons with the experimental data to a compressive strain of one.}, number={3}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={CHIDAMBARRAO, D and HAVNER, KS}, year={1988}, pages={285–315} }
 @article{havner_chidambarrao_1987, title={ANALYSIS OF A FAMILY OF UNSTABLE LATTICE ORIENTATIONS IN (110) CHANNEL DIE COMPRESSION}, volume={69}, ISSN={["0001-5970"]}, DOI={10.1007/BF01175724}, number={1-4}, journal={ACTA MECHANICA}, author={HAVNER, KS and CHIDAMBARRAO, D}, year={1987}, month={Dec}, pages={243–269} }
 @inproceedings{havner_1987, title={On the continuum mechanics of crystal slip}, ISBN={9061916828}, booktitle={Continuum models of discrete systems: Proceedings of the Fifth International Symposium on Continuum Models of Discrete Systems, Nottingham, 14-20 July, 1985}, publisher={Rotterdam; Boston: A.A. Balkema}, author={Havner, K. S.}, year={1987}, pages={47–59} }
 @inbook{havner_1986, title={Fundamental considerations in micromechanical modeling of polycrystalline metals at finite strain}, ISBN={185166016X}, DOI={10.1007/978-94-009-3407-8_15}, booktitle={Large deformations of solids: Physical basis and mathematical modelling}, publisher={London; New York: Elsevier Applied Science}, author={Havner, Kerry}, editor={Gittus, J. Zarka J. and Nemat-Nasser, S.Editors}, year={1986}, pages={243–265} }
 @article{fuh_havner_1986, title={ON UNIQUENESS OF MULTIPLE-SLIP SOLUTIONS IN CONSTRAINED AND UNCONSTRAINED FCC CRYSTAL DEFORMATION PROBLEMS}, volume={2}, ISSN={["0749-6419"]}, DOI={10.1016/0749-6419(86)90021-5}, abstractNote={Abstract A modification of the simple theory of rotation-dependent anisotropy is applied to the analysis of f.c.c. crystals, in both constrained and unconstrained multiple-slip orientations, with the object of resolving the question of uniqueness of solution. Specifically, tensile loading in each of 4-, 6- and 8-fold symmetry and [110] loading in channel die compression for each of [ 1 10] and [00 1 ] lateral constraint are investigated. It is established that the modified simple theory, augmented by the postulate of minimum plastic work, uniquely predicts equal multiple-slip and lattice stability (relative to the force axis or axes) in all cases.}, number={4}, journal={INTERNATIONAL JOURNAL OF PLASTICITY}, author={FUH, S and HAVNER, KS}, year={1986}, pages={329–345} }
 @article{le_havner_1985, title={ANALYSIS OF TENSILE LOADED FCC CRYSTALS IN 4-FOLD AND 8-FOLD SYMMETRY}, volume={4}, ISSN={["0167-6636"]}, DOI={10.1016/0167-6636(85)90005-5}, abstractNote={A unifying result for the second derivative of axial stretch with tensile load, previously established for f.c.c. crystals in 6-fold symmetry, is proved also to hold in 4 and 8-fold symmetry. This result, a consequence of a postulate of minimum plastic work, encompasses axis stability and applies to each of four hardening theories, including Taylor's classical isotropic rule and the ‘simple theory’ of anisotropic latent hardening. When minimum work is not imposed, the latter theory (uniquely among the four) permits a collinear double-slip mode as a possibly transient phenomenon in initial 8-fold symmetry. The various theoretical results are discussed in light of observations from the experimental literature.}, number={1}, journal={MECHANICS OF MATERIALS}, author={LE, NT and HAVNER, KS}, year={1985}, pages={33–50} }
 @article{havner_1985, title={Comparisons of crystal hardening laws in multiple slip}, volume={1}, DOI={10.1016/0749-6419(85)90023-3}, abstractNote={This paper brings together and concisely reviews results from recent analytical investigations on single crystals (variously done alone or with students) in which predictions from different theoretical hardening laws are contrasted and compared with experimental studies. Finitely deforming f.c.c. crystals in both constrained and unconstrained multiple-slip configurations are considered. Four crystal hardening laws are given prominence. Two of these belong to a class of theories in which the physical hardening moduli relating rates-of-change of critical strengths (in the 24 crystallographically equivalent slip systems) to slip-rates are taken as symmetric. These are G.I. Taylor's classic isotropic hardening rule (proposed in 1923), which is almost universally adopted in the metallurgical literature for various approximate analyses of single and poly-crystal deformation, and a 2-parameter modification of Taylor's rule that has an empirical basis in the qualitative features of experimentally determined latent hardening in single slip. The other two hardening laws featured here belong to a class of theories that were introduced in 1977 by this author. This class requires the above moduli to be nonsymmetric and explicity dependent upon the current stress state in such a manner that the following consequences are assured. (1) The deformation-dependent hardening of latent slip systems necessarily develops anisotropically if there is relative rotation of gross material and underlying crystal lattice. (2) The theories admit self-adjoint boundary value problems for crystalline aggregates, hence a variational formulation. (The fact that symmetric physical hardening moduli do not permit variational formulations of polycrystalline problems was shown at the 1972 Warsaw Symposium.) The two members of this class considered here are the original (and simplest p possible) theory of rotation-dependent anisotropy, which was proposed by this author in 1977 and commonly has been referred to as the “simple theory,” and a modification of this theory introduced in 1982 by Peirce, Asaro and Needleman that lies between Taylor's rule and the simple theory in its predictions for finitely deforming f.c.c. crystals. (In a series of five papers during 1977–1979, the simple theory was shown to universally account for the experimental phenomenon of “overshooting” in single slip in both f.c.c. and b.c.c. crystals.) Theoretical results from the various hardening rules are contrasted and compared with finite strain experiments in the metallurgical literature. Both tensile-loaded crystals in 4, 6 and 8-fold symmetry orientations and compressively loaded crystals under conditions of channel die constraint are treated. A postulate of minimum plastic work introduced in 1981 plays a prominent role in the theoretical analyses, in many cases providing a unique solution to the slip system inequalities and deformation constraints (where applicable). The rather remarkable ability of the simple theory to reconcile diverse qualitative features of both constrained and unconstrained finited deformation of f.c.c. crystals is demonstrated. Finally, conditions for total loading (all systems active) in 6-fold symmetry are investigated, and certain concepts regarding the selection of active systems under prescribed straining are critically assessed.}, journal={International Journal of Plasticity}, author={Havner, Kerry}, year={1985}, pages={111–124} }
 @article{havner_sue_1985, title={THEORETICAL-ANALYSIS OF THE CHANNEL DIE COMPRESSION TEST .2. 1ST-ORDER AND 2ND-ORDER ANALYSIS OF ORIENTATION [110][001][110] IN FCC CRYSTALS}, volume={33}, ISSN={["0022-5096"]}, DOI={10.1016/0022-5096(85)90016-X}, abstractNote={In this paper we present a general formulation of the analysis of the channel die compression test for single crystals, to second order in the applied compressive load increment. Specific first- and second-order analyses of f.c.c. crystals in orientation [110] [001] [110] are carried out for the same four hardening rules considered in Sue and Havner (1984). These are Taylor hardening, a 2-parameter empirical rule, the “simple theory” (Havner and Shalby, 1977), and a modification of the simple theory introduced by Peirce, Asaro and Needleman (1982). In particular, we address the analysis of lattice rotation about the loading axis for each of these theories. Such rotation was a prominent feature of the deformation of a copper crystal in this orientation in experiments by Wonsiewicz and Chin (1970). We establish that all theories permit this rotation consistent with the first- and second-order channel die constraints. Regarding the issue of lattice stability, a fundamental difference between the present orientation and those analyzed in Sue and Havner (1984) is uncovered and discussed. We close with a strong recommendation for a new series of channel die experiments.}, number={3}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={HAVNER, KS and SUE, PL}, year={1985}, pages={285–313} }
 @article{havner_1984, title={1ST-ORDER AND 2ND-ORDER ANALYSIS OF AXIALLY LOADED CRYSTALS IN N-FOLD SYMMETRY}, volume={311}, ISSN={["1364-503X"]}, DOI={10.1098/rsta.1984.0039}, abstractNote={
            A comprehensive theoretical investigation of multiple slip in axially tensile-loaded f.c.c. crystals in
            n
            -fold symmetry positions (
            n
            = 4, 6, 8) is presented. The analysis is complete to second order in terms of series expansions of all variables in the prescribed small load increment. In the first part of the paper, general kinematic relations and slip-system inequalities are given, and several new results discovered that apply independently of hardening rule and degree of symmetry. Subsequent sections contain extensive firsthand second-order analyses corresponding to four specific hardening theories, including Taylor's classical isotropic rule and the ‘ simple theory’ of anisotropic latent hardening. For minimum work, unifying relations are found connecting a generic hardening parameter, its rate of change with load, and the first and second derivatives of axial stretch that hold for all four theories.
          }, number={1518}, journal={PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}, author={HAVNER, KS}, year={1984}, pages={469–493} }
 @article{sue_havner_1984, title={THEORETICAL-ANALYSIS OF THE CHANNEL DIE COMPRESSION TEST .1. GENERAL-CONSIDERATIONS AND FINITE DEFORMATION OF FCC CRYSTALS IN STABLE LATTICE ORIENTATIONS}, volume={32}, ISSN={["0022-5096"]}, DOI={10.1016/0022-5096(84)90029-2}, abstractNote={An extensive theoretical investigation of f.c.c. crystals under [110] loading in the channel die compression test is presented. Two lattice orientations known from experiment to be stable relative to the channel axes, through large deformations, are investigated for each of four hardening laws. These are Taylor's classical isotropic hardening rule, a 2-parameter empirical rule from the metallurgical literature, the “simple theory” of anisotropic latent hardening(Havner and Shalaby, Proc. R. Soc. A 358,47 (1977)), and a modification of the simple theory proposed by pfirce et al., Acta Met.30, 1087 (1982). Predictions of active systems, equal multiple-slip and consequent lattice stability, finite shape change, and lateral constraint stress are the same for all theories, corresponding to minimum rate of plastic work, and are in general agreement with experiments on copper crystals by Wonsiewicz and Chin, Met. Trans.1, 2715 (1970) and Wonsiewiczet al., Met. Trans.2, 2093 (1971). The predictions of latent hardening differ among the theories, however, depending upon whether there is relative rotation of material and lattice. The potential significance of experimental studies of latent hardening in these particular stable lattice orientations is emphasized.}, number={6}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={SUE, PL and HAVNER, KS}, year={1984}, pages={417–442} }
 @article{havner_salpekar_1983, title={THEORETICAL LATENT HARDENING OF CRYSTALS IN DOUBLE-SLIP .2. FCC CRYSTALS SLIPPING ON DISTINCT PLANES}, volume={31}, ISSN={["0022-5096"]}, DOI={10.1016/0022-5096(83)90024-8}, abstractNote={The line of investigation of theoretical latent hardening in axially-loaded cubic crystals initiated by Havner and Shalaby (1977), based upon their “simple theory” of rotation-dependent crystal anisotropy (and continued through various other works), is completed here with the analysis of finite double-slip on distinct planes in f.c.c. crystal lattices. In conjunction with a previous study by the present authors of double-slip on a common plane (Havner and Salpekar, 1982), the general theoretical result is that any f.c.c. crystal which initially deforms homogeneously from the virgin state in double-slip, under either tensile or compressive axial loading, will continue in that mode of deformation to very large shears (γ = 1.5 and beyond). The paper also includes a comparative review of various hardening rules (including the “ldsimple theory”), with regard to both theoretical predictions and mathematical issues, that may be found instructive.}, number={3}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={HAVNER, KS and SALPEKAR, SA}, year={1983}, pages={231–250} }
 @inbook{havner_1982, title={A theory of finite plastic deformation of crystalline solids}, ISBN={0080254438}, DOI={10.1016/b978-0-08-025443-2.50015-x}, abstractNote={The evolution of the continuum theory of crystal plasticity at finite strain is traced with particular reference to advances during the past decade. Included within the exposition are: the general invariance principles of Hill; analytical connections between single crystal and polycrystal deformation; a physical justification for the classical normality postulate; an overall theoretical framework for crystal plasticity, and the recently proposed simple theory of latent hardening which is embedded within that framework. Experimental foundations of the subject are taken into consideration, and the finite deformation experiments on cubic crystals of the 1960s are given prominence. Previous demonstrations of the simple theory's ability to account for significant qualitative and quantitative features of experiment are reviewed.}, booktitle={Mechanics of solids: The Rodney Hill 60th anniversary volume}, publisher={Oxford; New York: Pergamon Press}, author={Havner, Kerry}, editor={Hopkins, H. G. and Sewell, M. J.Editors}, year={1982}, pages={265–302} }
 @inproceedings{havner_1982, title={Aspects of the simple theory of rotation-dependent crystal anisotropy}, ISBN={0960999205}, booktitle={Plasticity of metals at finite strain: Theory, experiment, and computation: Proceedings of research workshop held at Stanford University, July 29, 30, July 1, 1981}, publisher={Stanford, Cal.: Division of Applied Mechanics, Stanford University}, author={Havner, K. S.}, editor={E. H. Lee and Mallett, R. L.Editors}, year={1982}, pages={318–340} }
 @article{havner_1982, title={MINIMUM PLASTIC WORK SELECTS THE HIGHEST SYMMETRY DEFORMATION IN AXIALLY-LOADED FCC CRYSTALS}, volume={1}, ISSN={["0167-6636"]}, DOI={10.1016/0167-6636(82)90038-2}, abstractNote={The assertion of the title is proved, according to each of three hardening theories, for both tensile and compressive loading of f.c.c. crystals in multiple-slip orientations (in particular, for all 2- and 6-fold symmetry positions). The theories are classical Taylor hardening, the writer's ‘simple theory’ of rotation-dependent, anisotropic latent hardening, and a 2-parameter hardening rule introduced in the metallurgical literature. Theoretical latent hardening predictions for tensile loading in 6-fold symmetry are considered in relation to experiment.}, journal={MECHANICS OF MATERIALS}, author={Havner, K. S.}, year={1982}, pages={97–111} }
 @article{hill_havner_1982, title={PERSPECTIVES IN THE MECHANICS OF ELASTOPLASTIC CRYSTALS}, volume={30}, ISSN={["0022-5096"]}, DOI={10.1016/0022-5096(82)90010-2}, abstractNote={The mechanics of metal crystals at finite strain is reappraised, when crystallographic slip is solely responsible for inelastic deformation. Arbitrary work-conjugate variables are used throughout, together with a slip measure that is unaffected by lattice distortion. The pioneering analysis of R. Hill and J.R. Rice (J. Mech. Phys. Solids20, 401. 1972) is amplified and in part recast. The existence of a plastic potential is proved from a new standpoint, which is believed to be more readily understandable and direct. The effect of lattice strain on slip-system geometry is expressed via an influence tensor ; this has the effect of linking apparently disparate elements of the theory. Subsequently the principal formulae are made explicit in terms of Green's measure of strain, supplemented by equations of transformation to other variables. The unique yield criterion that confers a normality structure is formulated in terms of a generalized Schmid stress, and associated rules of hardening in multislip are detailed. The available experimental data are briefly reviewed, more especially in relation to the 'simple theory' of hardening proposed by K.S. Havner and A.H. Shalaby (Proc. R. Soc.A358, 47. 1977).}, number={1-2}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={HILL, R and HAVNER, KS}, year={1982}, pages={5–22} }
 @article{havner_salpekar_1982, title={THEORETICAL LATENT HARDENING OF CRYSTALS IN DOUBLE SLIP .1. FCC CRYSTALS WITH A COMMON SLIP PLANE}, volume={30}, ISSN={["0022-5096"]}, DOI={10.1016/0022-5096(82)90024-2}, abstractNote={Abstract T he hardening of all slip systems in f.c.c. crystals, deforming in finite double-slip on two systems with a common slip plane, is determined according to the “simple theory” of rotation-dependent plastic anisotropy. Both tensile and compressive axial-loading are considered. Of particular interest are predictions of crystal response after the loading axis has rotated into a higher symmetry position (6-fold in tension and 4-fold in compression). In contrast with classical Taylor hardening, the simple theory predicts that the axis will “overshoot” the higher symmetry position. A postulate of minimum plastic work plays a significant role in the theoretical analyses of multiple-slip positions.}, number={6}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={HAVNER, KS and SALPEKAR, SA}, year={1982}, pages={379–398} }
 @article{havner_1981, title={A THEORETICAL-ANALYSIS OF FINITELY DEFORMING FCC CRYSTALS IN THE SIXFOLD SYMMETRY POSITION}, volume={378}, ISSN={["1364-5021"]}, DOI={10.1098/rspa.1981.0155}, abstractNote={An exhaustive analysis of finite plastic straining of f.c.c. crystals in the sixfold, tensile symmetry position is presented. Classical Taylor hardening and the ‘simple theory’ of finite-distortional latent hardening serve, in turn, as a basis for the theoretical studies. For prescribed axial loading, wherein each theory permits a variety of strain-rates and axis rotations, a quasi-energetic postulate is found that constrains (or partially constrains) the solution to that which appears physically most likely: axis stability accompanied by axisymmetric deformation. The two theories are contrasted with one another, with positive-definite hardening rules (which are briefly considered), and with diverse empirical evidence that defines the essential features of finite deformation and latent hardening of f.c.c. crystals in a variety of single- and multiple-slip orientations. It appears that only the simple theory, augmented by a minimumwork postulate, is consistent with this diverse evidence.}, number={1774}, journal={PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}, author={HAVNER, KS}, year={1981}, pages={329–349} }
 @article{havner_1979, title={THE KINEMATICS OF DOUBLE SLIP WITH APPLICATION TO CUBIC-CRYSTALS IN THE COMPRESSION TEST}, volume={27}, ISSN={["0022-5096"]}, DOI={10.1016/0022-5096(79)90023-1}, abstractNote={A generalization and extension of the kinematic analysis of double slip in fcc and bcc crystals by A.H. Shalaby and K.S. Havner (1978) is presented. Particular emphasis is given to equations for areal changes, which are applied to the calculation of loading axis rotations in the compression test. No assumptions are made as to symmetry of slip and/or axis position. Therefore, purely kinematical solutions are obtained which are not limited to the Taylor hardening model and can be used in the interpretation of experimental data from large deformation tests of anisotropic (prestrained) crystals, as well as in theoretical studies.}, number={5-6}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={HAVNER, KS}, year={1979}, pages={415–429} }
 @article{havner_baker_vause_1979, title={THEORETICAL LATENT HARDENING IN CRYSTALS .1. GENERAL EQUATIONS FOR TENSION AND COMPRESSION WITH APPLICATION TO FCC CRYSTALS IN TENSION}, volume={27}, ISSN={["0022-5096"]}, DOI={10.1016/0022-5096(79)90009-7}, abstractNote={Equations for latent strengths in single slip, based upon the simple theory of finite distortional crystal hardening introduced by K.S. Havner and A.H. Shalaby (1977), are derived for both tensile and compression tests without restriction as to crystal class. Detailed comparisons between theoretical results and the experiments of P.J. Jackson and Z.S. Basinski (1967) on copper crystals in tension are presented. There is good qualitative agreement between theory and experiment regarding the diversity of anisotropic hardening among slip systems. Moreover, there is satisfactory quantitative agreement between the theory and the extrapolated experimental data in the stage III, large-strain range. It is suggested that further experimental investigation of latent hardening at large prestrains would be desirable. The simple theory predicts anisotropic hardening and the perpetuation of single slip in axial loading of cubic crystals initially oriented for single slip, but predicts symmetric, isotropic hardening of specimens initially oriented in positions of 4, 6 or 8-fold multiple-slip. These predictions are in general accord with experimental observations from tests of f.c.c. and b.c.c. crystals.}, number={1}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={HAVNER, KS and BAKER, GS and VAUSE, RF}, year={1979}, pages={33–50} }
 @article{vause_havner_1979, title={THEORETICAL LATENT HARDENING IN CRYSTALS .3. FCC CRYSTALS IN COMPRESSION}, volume={27}, ISSN={["0022-5096"]}, DOI={10.1016/0022-5096(79)90022-X}, abstractNote={THE simple theory of finite-distortional latent hardening introduced by havner and shalaby (1977) is applied to an analysis of compressively-activated single slip in f.c.c. crystals. The theory accounts for the observed perpetuation of single slip beyond the crystallographic symmetry line in such cases. As the simple theory has previously been shown to predict this common phenomenon for f.c.c. crystals in the tensile test and b.c.c. crystals in both tension and compression, it stands as a universal theory of "overshooting" in axially-loaded cubic crystals. p]Detailed comparisons are made between theoretical results and the experiments of kocks (1964) and Ramaswami, Kocks and Chalmers (1965) on hardening of latent slip systems in Al and Ag crystals. There is general qualitative agreement as to the diversity of anisotropic hardening among slip systems for these metals and good correlation between theory and experiment for Al crystals to large strains (extending to 70% shear). Finally, aspects of the simple theory are reviewed which suggest its suitability for the calculation of finite plastic deformation of crystalline aggregates.}, number={5-6}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={VAUSE, RF and HAVNER, KS}, year={1979}, pages={393–414} }
 @article{havner_baker_1979, title={Theoretical latent hardening in crystals: II. B.c.c. crystals in tension and compression}, volume={27}, DOI={10.1016/0022-5096(79)90031-0}, abstractNote={The general latent hardening law of single slip derived in the first paper of this series (Havner, Baker and Vause, 1979) is applied to an analysis of "overshooting" phenomena in bcc crystals in tension and compression. This new law, which predicts anisotropic hardening of latent slip systems, is based upon the simple theory of finite distortional crystal hardening introduced by Havner and Shalaby (1977). Because of historical ambiguities regarding identification of the slip plane in bcc metals, parallel analyses are presented corresponding to two separate criteria: (i) slip on {110}, {112} and {123} crystallographic planes only; and (ii) slip on the plane of maximum resolved shear stress containing a 〈111〉 direction. It is established that the new hardening law is a theory of "overshooting" in bcc crystals according to either identification of the slip plane. A qualitative comparison between theoretical results and two experimental papers on Fe crystals is included. The general difficulties in making comparisons with the experimental literature on finite distortional latent hardening are briefly discussed.}, journal={Journal of the Mechanics and Physics of Solids}, author={Havner, Kerry and Baker, G. S.}, year={1979}, pages={285–314} }
 @article{havner_shalaby_1978, title={FURTHER INVESTIGATION OF A NEW HARDENING LAW IN CRYSTAL PLASTICITY}, volume={45}, ISSN={["0021-8936"]}, DOI={10.1115/1.3424352}, abstractNote={A simple theory of latent hardening in crystals, recently proposed by the authors [1], is applied to the determination of anisotropic hardening in slip systems of face-centered cubic crystals in the tensile test, based upon a parabolic resolved-shear-stress versus slip curve in the active system. The theory predicts the generally observed continuation of finite single slip beyond the crystallographic symmetry line. Moreover, the predicted diversity of finite distortional hardening among latent slip systems is in qualitative agreement with experiment.}, number={3}, journal={JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME}, author={HAVNER, KS and SHALABY, AH}, year={1978}, pages={500–506} }
 @article{shalaby_havner_1978, title={GENERAL KINEMATICAL ANALYSIS OF DOUBLE SLIP}, volume={26}, ISSN={["0022-5096"]}, DOI={10.1016/0022-5096(78)90015-7}, abstractNote={General kinematic solutions for double slip in fcc and bcc crystals are presented which are free from constitutive assumptions: that is, the analysis does not presuppose equal amounts of slipping on equallystressed slip systems, in contrast to the standard solutions (wherein Taylor hardening is implicitly assumed). The axis rotations and limiting positions on a stereographic projection are illustrated for several different slip-system combinations, initial axis positions (none on a symmetry line), and proportional slip ratios in both fcc and bcc crystals. It is suggested that the solutions have particular application to the experimental study of double slip in the tensile test of prestrained crystals.}, number={2}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={SHALABY, AH and HAVNER, KS}, year={1978}, pages={79–92} }
 @article{havner_1978, title={UNIFYING CONCEPTS IN PLASTICITY THEORY AND RELATED MATTERS IN NUMERICAL-ANALYSIS}, volume={46}, ISSN={["0029-5493"]}, DOI={10.1016/0029-5493(78)90183-8}, abstractNote={This paper summarizes a rate-independent theory for multiple-mode plastic straining which unifies constitutive equations of macroscopic solids and single crystals at both infinitesimal and finite strain. A basic symmetry postulate plays a key role in the general theory. This postulate enables stress and plastic mechanism rates to be derived from a saddle potential function and leads to connections between uniqueness of solution and minimum principles. One such principle permits the independent variation of displacement and plastic mechanism rates. This is significant to the investigation of convergence of the finite element method in incremental boundary value problems. The theory also has noteworthy consequences for the finite distortion of single crystals and the analysis of crystalline aggregates.}, number={1}, journal={NUCLEAR ENGINEERING AND DESIGN}, author={HAVNER, KS}, year={1978}, pages={187–201} }
 @article{havner_singh_1977, title={APPLICATION OF A DISCRETE POLYCRYSTAL MODEL TO ANALYSIS OF CYCLIC STRAINING IN COPPER}, volume={13}, ISSN={["0020-7683"]}, DOI={10.1016/0020-7683(77)90035-x}, abstractNote={A discrete polycrystal model, designed to simulate a metal aggregate macro-element, is applied to the study of cyclic straining in copper. The numerical method of solution (an adaptation of the “finite element method”) incorporates a convergent discrete Green's function within the constrained minimum principle which governs the (crystallographic) plastic shear increments at each load step. Isothermal elastic moduli of copper crystals and Taylor's hardening rule with constant hardening modulus are used in the calculations. Numerical results are obtained for macroscopic elastic properties, cyclic stress-strain curves (which indicate the contribution of aggregate heterogeneity to macroscopic hardening), macroscopic plastic work, and residual (latent) strain energy through four loading cycles between fixed macrostrain limits. Other estimates for elastic properties also are included, and all results are compared, both qualitatively and quantitatively, with published experiments. The predictions of the model are in general satisfactory.}, number={5}, journal={INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES}, author={HAVNER, KS and SINGH, C}, year={1977}, pages={395–407} }
 @article{havner_shalaby_1977, title={SIMPLE MATHEMATICAL-THEORY OF FINITE DISTORTIONAL LATENT HARDENING IN SINGLE-CRYSTALS}, volume={358}, ISSN={["1364-5021"]}, DOI={10.1098/rspa.1977.0186}, abstractNote={A simple (one-parameter) hardening law is proposed which accounts for the perpetuation of finite single slip, beyond the symmetry line, in the tensile test of f. c. c. crystals and reduces to Taylor’s rule at infinitesimal strain. This new law emerges as the simplest case of a general mathematical theory of finite deformation of elastic-plastic crystals. The fully anisotropic finite-distortional hardening of latent slip systems predicted by the simple theory is in qualitative agreement with experiment.}, number={1692}, journal={PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}, author={HAVNER, KS and SHALABY, AH}, year={1977}, pages={47–70} }
 @article{havner_1977, title={UNIFICATION, UNIQUENESS AND NUMERICAL-ANALYSIS IN PLASTICITY}, volume={13}, ISSN={["0020-7683"]}, DOI={10.1016/0020-7683(77)90045-2}, abstractNote={This paper addresses various aspects of a theory of multiple-mode plastic straining which unifies constitutive equations of macroscopic solids and single crystals (for both strain-hardening and strain-softening behavior). Emphasis is given to the determination of minimal criteria for uniqueness of solution to incremental boundary value problems based upon the general theory. It is established that these criteria are sufficient to assure convergence of the finite element method in such problems.}, number={7}, journal={INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES}, author={HAVNER, KS}, year={1977}, pages={625–635} }
 @article{havner_1977, title={UNIQUENESS CRITERIA AND MINIMUM PRINCIPLES FOR CRYSTALLINE SOLIDS AT FINITE STRAIN}, volume={28}, ISSN={["0001-5970"]}, DOI={10.1007/BF01208794}, number={1-4}, journal={ACTA MECHANICA}, author={HAVNER, KS}, year={1977}, pages={139–151} }
 @article{havner_patel_1976, title={CONVERGENCE OF FINITE-ELEMENT METHOD FOR A CLASS OF ELASTIC-PLASTIC SOLIDS}, volume={34}, ISSN={["1552-4485"]}, DOI={10.1090/qam/449142}, abstractNote={A proof of convergence of the finite-element method in rate-type, quasistatic boundary value problems is presented. The bodies considered may be discretely heterogeneous and elastically anisotropic, their plastic behavior governed by history-dependent, piecewise-linear yield functions and fully coupled hardening rules. Elastic moduli are required to be positive-definite and plastic moduli nonnegative-definite. Precise and complete arguments are given in the case of bodies whose surfaces are piecewise plane.}, number={1}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={HAVNER, KS and PATEL, HP}, year={1976}, pages={59–68} }
 @inproceedings{havner_1975, title={Some concepts and results from the mechanics of crystalline solids having possible application to theories of thermoviscoplasticity}, booktitle={Workshop on Applied Thermoviscoplasticity held October 13 and 14, 1975 at the Technological Institute, Northwestern University, Evanston, Illinois}, publisher={Evanston, IL: Technological Institute, Northwestern University}, author={Havner, K. S.}, year={1975}, pages={19–35} }
 @article{havner_1974, title={ASPECTS OF THEORETICAL PLASTICITY AT FINITE DEFORMATION AND LARGE PRESSURE}, volume={25}, ISSN={["0044-2275"]}, DOI={10.1007/bf01590262}, number={6}, journal={ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}, author={HAVNER, KS}, year={1974}, pages={765–781} }
 @article{havner_1974, title={On bending of a crystal to a cylindrical surface}, volume={41}, journal={Journal of Applied Mechanics: Transactions of the ASME}, author={Havner, K. S.}, year={1974}, pages={1984–1988} }
 @article{havner_singh_varadarajan_1974, title={Plastic deformation and latent strain energy in a polycrystalline aluminum model}, volume={10}, DOI={10.1016/0020-7683(74)90028-6}, abstractNote={A crystalline aggregate model of aluminum is evaluated for nearly uniaxial stressing. Progression of crystallographic slip, a hysteresis effect in a strain cycle, and heat generated and latent strain energy stored during plastic deformation are investigated. Close correspondence is found between calculated and experimental results for percentages of heat and latent energy. A proof is included that total mechanical energy dissipated is absolutely less than macroscopic plastic work for all paths. Paccчитывaют знaчeниe вeличины нaгpyжeния пpи дeфopмaции пoчти oднoocнoй мoдeли aлюминиeвoгo кpиcтaлличecкoгo aгpeгaтa. Иccлeдyют paзвитиe кpиcтaллoгpaфичecкoгo cкoльжeния; гиcтepeзиcный эффeкт в циклe нaпpяжeния; paзвитчie гeнepиpyющeгocя тeплa и cкpытoй энepгии нaпpяжeния, oбpaзyющичcя вo вpeмя плacтичecкoй дeфopмaции. Meждy paccчитaнными и экcпepимeнтaльными peзyльтaтaми в oтнoшeнии пpoцeнтoв тeплa и cкpытoй энepгии нaшли yдoвлeтвopитeльнoe cooтвeтcтвиe. Bключaют дoкaзaтeльcтвo, чтo oбщaя pacceяннaя мeчaничecкaя энepгия нa мнoгo мeнee, чeм мaкpocкoпичecкaя paбoтa плacтичecкoй дeфopмaции вceгo пpoбeгa чacтиц.}, journal={International Journal of Solids and Structures}, author={Havner, Kerry and Singh, C. and Varadarajan, R.}, year={1974}, pages={853–862} }
 @article{havner_varadarajan_1973, title={A quantitative study of a crystalline aggregate model}, volume={9}, DOI={10.1016/0020-7683(73)90087-5}, abstractNote={A discrete aggregate model is applied to the study of theoretical macroscopic response of f.c.c. Metal polycrystals. General, dual inequalities of macroscopic plasticity theory are reviewed and exhibited on subsequent yield surfaces in both stress and strain space as calculated for aluminum under biaxial straining. Predicted stressstrain curves are shown corresponding to a partial cycle of loading and reverse loading. The aggregate model contains several thousand crystallographic slip systems, and all quantitative results are obtained through sequential solution of constrained quadratic programming problems governing the incremental crystal shears. C цeлью нccлeдoвaния тeopeтичecкoгo мaкpocкoпичecкoгo пoвeдeння гpaнeцeнтpaнpo-. вaнныx кyбичecкиx мeтaллнчecкнx пoлнкpиcтaллoв пpнмeпяeтcя диcкpeтнa. coвoкyпнaя мoдeль, вBoбщe, пpoвepяyтcя дyaльныe нepaвнcтвa мaкpocкoличecкoй тeopнн плacтичнocтн н пoкaзывaютcя, нa пocлeдyyщнx пoбepxнocтяx тeчeния, кaк для пpocтpaнcтвa нaпpяжeнии тaк и дeфopмaций, в кaчecтвe paccчитaнныx для aлyминня глoд влняннeм двyxocнoй дeфopмaцни. yкaзaнo, чтo пpeдcкaзaнныe кpивыe нaпpяжeния-дeфopмaция cooтвeтcтвyют чacтнoмy никлy нaгpyзкн н paзгpyзки. coвoкyниaя мoдeль coдepжнт в ceбe нecкoлькo тыcяч кpиcтaллoгpaфнчecкиx cиcтeм cкoльжeния. Пoлyчaютcя вce кoлнчecтвeиныe peзyльтaты вcлeдcтвиe peщeння зaдaч cтecнeннoгo квaдpaтнчecкoгo пpoгpaммиpoвaния, oпpeдeляющнx нocтeпeннo нapacтayщнe cдвнги кpиcтaллoв.}, journal={International Journal of Solids and Structures}, author={Havner, Kerry and Varadarajan, R.}, year={1973}, pages={379–394} }
 @inbook{havner_1973, title={An analytical model of large deformation effects in crystalline aggregates}, ISBN={9001775705}, booktitle={Foundations of plasticity}, publisher={Leyden: Noordhof International}, author={Havner, K. S.}, year={1973}, pages={93–106} }
 @article{havner_1973, title={MECHANICS OF CRYSTALLINE SOLIDS}, volume={21}, ISSN={["0022-5096"]}, DOI={10.1016/0022-5096(73)90007-0}, abstractNote={Elastic-plastic constitutive behavior of cubic crystals (and aggregates) at large pressure is investigated taking account of a thermodynamic basis for lattice straining. Particular attention is directed to quasi-static processes in which an explicit Schmid law governing active slip systems is adopted. Connections between a precise normality rule and the pressure-dependence of moduli and critical shear strengths are analyzed and their implications assessed.}, number={6}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={HAVNER, KS}, year={1973}, pages={383–394} }
 @article{havner_1972, title={HILLS STRESS RATE IN CONTINUUM MECHANICS OF POLYCRYSTALS}, volume={14}, ISSN={["0001-5970"]}, DOI={10.1007/bf01184857}, number={2-3}, journal={ACTA MECHANICA}, author={HAVNER, KS}, year={1972}, pages={183-&} }
 @article{havner_1971, title={A discrete model for the prediction of subsequent yield surfaces in polycrystalline plasticity}, volume={7}, DOI={10.1016/0020-7683(71)90089-8}, abstractNote={A discrete model suitable for the analysis of polycrystalline aggregate response under macroscopically uniform, quasi-static loading is developed, with particular emphasis on the characteristics of subsequent yield surfaces in stress or strain space. Internal stress and deformation states are determined from approximating, piecewise linear infinitesimal displacement fields within crystal grains, based upon broadly defined constitutive behavior which permits inclusion of cubic or hexagonal crystal anisotropy and relatively general hardening laws over crystallographic slip systems. Appropriate aggregate matrices are established as symmetric, positivedefinite, and internal fields corresponding to the solution of the discrete model are proved to be unique. It is further shown that the final calculation of incremental crystal shears can be posed as a quadratic programming problem. Oпpeдeляeтcя диcкpeтнaя мoдeль, пpигoднaя для aнaдизa пoBeдeния пoликpиcтaлличecкoгo зaпoлнитeля пoд Bлияниeм мaкpocкoпичecки oднopoднoй, кBaзиcтaмичecкoй нaгpyзки, co cпeциaльным yчeтoм чapaктepиcтик пoBepчнocтeй тeчeния B пpocтpaнcтBe нaпpяжeний и дeфopмaции. Bнyтpeнниe нaпpяжeния и дeфopмaции oпpeдeляютcя пyтeм пpиближeния кycoчныч, линeйныч, инфинитeзимaльныч пoлeй дeфopмaций c кpиcтaлличecкими зepнaми, нa ocнoBe шиpoкo oпpeдeлeннoгo кoнcтцтyтиBнoгo пoBeдeния, кoтopoe дaeт Boзмoжнocть Bключить кyбичecкyю или гeкcaгoнaльнyю кpиcтaлличecкyю aнизoтpoпию и cooтBecтBeннo oбшиe зaкoны yпpoчнeния для кpиcтaлличecкич cиcтeм cкoльeнмя. BыBoдятcя cooтBecтByющиe мaтpицц зaпoлнитeля B кaчecтBe cиммeтpичecкцч и пoлoжитeльнo oпpeдeлeнныч. Bнyтpeнниe пoля, cooтBecтByющиe peшeнию диcкpeтнoй мoдeли, oкaзыBaютcя eдинcтBeнными. Дaлee yкaзaнo, чтo ocтaтoчнoe peшeниe для пpиpaщeния cдBигoB кpиcтaллoB мoжнo paccмaтpиBaть B кaчecтBe зaдaчи кBaдpaтaчeoкoиo пpoгpaммиpoBaния.}, journal={International Journal of Solids and Structures}, author={Havner, Kerry}, year={1971}, pages={719–730} }
 @article{havner_1971, title={On convergence of a discrete aggregate model in polycrystalline plasticity}, volume={7}, DOI={10.1016/0020-7683(71)90067-9}, abstractNote={A discrete aggregate model, recently proposed by the author [1] as a basis for quantitative studies in polycrystalline plasticity, is extended and further analyzed herein. The discretized internal stress and strain increment fields, uniquely determined from the solution of a constrained quadratic programming problem, are proved to be strictly convergent to the solution of the corresponding continuum boundary value problem. Thus, the model is rigorously confirmed as a rational approximation well-suited for computational investigations of aggregate behavior. Racшиpaeтcя и aнaлиpизyeтcя дaлee диcкpeтнaя aггpeгaтиaя мoдeль, нeдaвнo пpeдлoжeннaя aвтopoм [1], в cмыcлe ocнoвы для кaчecтвeнныч иccлeдoвaний в пoликpиcтaлличecкoй плacтичocти, Пoля диcкpeтизoвaнныч внyтpeнныч нaпpяжeний и пpиpaщeний дeфopмaции, oднoзнaчнo oпpeдeлeнныe иe peщeния зaдaчи oгpaничeннoгo квaдpaтичнoгo пpoгpaммиpoвaния, oкaзывaютcя тoчнo cчoдимыми к peшeнию cooтвeтcтвyющeй кpaeвoй зaдaчи cплoшнoй cpeды. зaтeм, этa мoдeль тoчнo пoдтвepждeнa кaк paциoиaльиoe пpиближeниe пpитoднoe для pacчeтныч иccлeдoвaний пoвeдeния aггpeгaтнoй мoдeли.}, journal={International Journal of Solids and Structures}, author={Havner, Kerry}, year={1971}, pages={1269–1275} }
 @article{havner_1969, title={A discretized variational formulation of anisotropic small strain plasticity problems}, volume={11}, DOI={10.1016/0029-5493(70)90154-8}, abstractNote={A general deformation theory of small elastic-plastic strains in an orthotropic material is presented together with a variational formulation and solution technique for the associated discretized plane strain problem. Quasi-linear difference equations are obtained through minimization of the discretized potential energy function, resulting in positive definite stiffness matrices (given appropriate constraints on the elastic and plastic parameters of the material). Alternate ways of organizing the iterative calculation steps for digital computer are discussed. In addition, an analytic stress path criterion for the orthotropic deformation theory is given, based upon the concept of a corner forming on the yield surface.}, journal={Nuclear Engineering and Design}, author={Havner, Kerry}, year={1969}, pages={308–322} }
 @article{havner_1969, title={A path criterion for deformation plasticity theory}, volume={95}, journal={Journal of the Engineering Mechanics Division}, author={Havner, K. S.}, year={1969}, pages={747–761} }
 @inbook{havner_1969, title={Mathematical theories of material behavior}, ISBN={0471563153}, booktitle={Metal fatigue: Theory and design}, publisher={New York: Wiley}, author={Havner, K. S.}, year={1969}, pages={14–65} }
 @article{havner_1969, title={The theoretical behavior of a polycrystalline solid as related to certain general concepts of continuum plasticity}, volume={5}, DOI={10.1016/0020-7683(69)90059-6}, abstractNote={This paper is directed toward establishing general characteristics of continuum stress-plastic strain relations from Schmid's Law of plastic slip in individual crystal grains. To this end certain theoretical results obtained by Lin are reaffirmed through a rigorous derivation, and the principle of maximum plastic work is extended to small elastic-plastic strains in an isotropic polycrystalline aggregate. It is shown that the macroscopic incremental plastic strain vector over a unit volume of a fine-grained solid is strictly normal to a yield surface in macrostress space only if the individual crystals are elastically isotropic. The resulting equations for polycrystalline solids are contrasted with those obtained from certain stability postulates and thermodynamic foundations in continuum plasticity, and general features of similarity are discussed. Paбoтa имeeт цeлью oпpeдeлить oбщиe чapaктepиcтики зaвиcимocтeй cплoшнoй cpeды типa нaпpяжeниe—плacтиkhcyecкaя дeфopмaция, иcчoдя из зaкoнa плacтиkhcyeeкoгo cкoльжeния Шмидтa в индивидyaльныч, кpиcтaллиkhcyecкич зepнaч. Для этoгo внoвь пoдтвepждaютeя, пyтeм тokhcyнoгo вывoдa, нeкoтopыe тeopeтиkhcyecкиe peзyльтaты, пoлykhcyeнныe Линoм. Oбoбщaeтcя пpинцип мaкcимaльнoй плacтиkhcyecкoй paбoты нa cлykhcyaй мaлыч, yпpyгo-плaeтиkhcyecкич дeфopмaций в изoтpoпнoй пoликpиcтaллиkhcyecкoй coвoкyпнocти. Пoкaзaнo, khcyтo мaкpocкoпиkhcyecкий пocтeпeннo нapacтaющий вeктop плacтиkhcyecкoй дeфopмaции пo eдинцe oбъeмa идeaльнo зepниcтoгo тeлa, являeтcя coвepшeннo яopмaльным к пoвepчнocти тekhcyeния, в пpoeтpaнeтвe мaкpoнaпpяжeний, тoлькo тoгдa, кoгдa индивидyaльныe кpиcтaллы yпpyгo изoтpoпны. Cpaвнивaютeя peзyльтиpyющиe ypaвнeния для пoликpиcтaллиkhcyecкич тeл c ypaвнeниями, вытeкaющими из нeкoтopыч пoeтyлятoв yeтoйkhcyивocти и тepмoдинaмиkhcyecкич ocнoв тeopии плacтиkhcyнocти cплoшнoй cpeды. Oбcyждaютcя oбшиe cвoйeтвa пoдoбия.}, journal={International Journal of Solids and Structures}, author={Havner, Kerry}, year={1969}, pages={215–226} }
 @article{havner_1968, title={On convergence of iterative methods in plastic strain analysis}, volume={4}, DOI={10.1016/0020-7683(68)90061-9}, abstractNote={Two general formulations and solution techniques for plane strain plasticity problems are investigated: the effective force and material-stiffness matrix iteration methods. Compatible finite-difference models are derived by minimizing a discretization ef the potential energy function over a general boundary configuration, using the Hencky-Nadai hardening law to mathematically model the material behavior. The resultant material stiffness matrices are symmetric, positive definite, and block tri-diagonal. Analytical and numerical studies of the accuracy and convergence characteristics of the methods are given for matrices of order 1000. Иccлeдyeтcя двe oбщиe фopмyлиpoвки и мeтoды peшeния зaдaч лпocкoгo дeфopмaциoннoгo cocтoяния плacтичнocти: Meтoд зффeктивнoй cилы и мeтoд итepaции мaтpицы кoзффициeнтoв жecткocти мaтepиaлa. Bывoдитcя coглacныe, кoнeчнo-paзнocтныe мoлeлн пyтeм минимaлизaции нaдиcкpeтизaции фyнкции пoтeнциaльнoй зиepгии пo oбщeй кoнфигypaции кoнтypa, иcпoльзyя зaкoн yпpoчнeния Xeнки-Haдaя, c цaлью пpeлcтaвлeиия мaтeмaтичecки пoвeдeния мaтepиaлa. Cyммapныe мaтpицы кoзффициeнтoв жecткocти мaтepиaлa являютcя cиммeтpичными, пoлoжитeльиo oпpeдeлeнными и блoчными, тpeчдиaгoнaльными. Пpивoдятcя aнaлитичecкиe и чиcлeнныe иccлeдoвaния чapaктepиcтик тoчнocти и cчoдимocти мeтoдoв для мaтpицы paнгa 1000.}, journal={International Journal of Solids and Structures}, author={Havner, Kerry}, year={1968}, pages={491–508} }
 @article{havner_stanton_1967, title={ON ENERGY-DERIVED DIFFERENCE EQUATIONS IN THERMAL STRESS PROBLEMS}, volume={284}, ISSN={["0016-0032"]}, DOI={10.1016/0016-0032(67)90585-6}, abstractNote={This paper is concerned with the analysis and solution of variationally-derived finite difference equations in mixed boundary value problems of plane thermoelastic stress and thermoelastic strain. The relationship between these equations at the boundary and the natural boundary conditions is derived, and convergence to the explicit boundary equations with decreasing grid size is shown. Efficient decomposition and solution techniques for the positive definite, quasi-tridiagonal coefficients matrix are presented. Numerical studies are included for a finite, thin plate subjected to a parabolic temperature field.}, number={2}, journal={JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS}, author={HAVNER, KS and STANTON, EL}, year={1967}, pages={127-&} }
 @article{havner_1966, title={ON FORMULATION AND ITERATIVE SOLUTION OF SMALL STRAIN PLASTICITY PROBLEMS}, volume={23}, ISSN={["0033-569X"]}, DOI={10.1090/qam/99938}, abstractNote={This paper is concerned with a general method of formulation and iterative solution of small displacement plasticity problems, using the Hencky-Nadai hardening law as mathematical model for the material behavior. Beginning with a minimum energy principle for small thermal-mechanical strains under simple external loading, quasi-linear partial differential equations are formulated and a method of iteration by successive solutions is proposed. A finite-difference discretization of the equations (in two dimensions) is obtained through minimization of the total potential energy function, leading to positive definite symmetric matrices for general boundary configurations.}, number={4}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={HAVNER, KS}, year={1966}, pages={323-&} }
 @article{havner_glassco_1966, title={On energy balance criteria in ductile fracture}, volume={2}, journal={International Journal of Fracture Mechanics}, author={Havner, K. S. and Glassco, J. B.}, year={1966}, pages={506–525} }
 @article{havner_1965, title={FINITE-DIFFERENCE SOLUTION OF 2 VARIABLE THERMAL AND MECHANICAL DEFORMATION PROBLEMS}, volume={2}, ISSN={["0022-4650"]}, DOI={10.2514/3.28226}, abstractNote={A numerical solution of thermoelastic stress and deformation problems governed by two linear, second-order, elliptic partial differential equations in two unknowns is presented. The analysis is applicable to both axially symmetric solids and variable thickness plates with temperature-dependent material properties. Body forces caused by rotation and/or temperature gradients and boundary conditions corresponding to any combination of prescribed tractions and displacements are considered. A general digital computer program based upon a finite-difference discretization and utilizing the method of successive overrelaxation is briefly described. Selected results from turbomachinery problems and a numerical comparison with the classical rotating ellipsoid are included.}, number={4}, journal={JOURNAL OF SPACECRAFT AND ROCKETS}, author={HAVNER, KS}, year={1965}, pages={542-&} }
 @book{havner_1963, title={Influence coefficients for circular plates}, volume={15}, journal={Research Publication (Oklahoma State University. School of Civil Engineering)}, publisher={Stillwater, OK: Oklahoma State University, School of Civil Engineering}, author={Havner, K. S.}, year={1963} }
 @book{analysis of flat plates by the algebraic carry-over method, vol. ii - tables_1961, volume={119}, journal={Publication (Oklahoma State University. Engineering Experiment Station)}, institution={Stillwater, OK: Oklahoma State University, Engineering Experiment Station}, year={1961} }
 @book{analysis of flat plates by the algebraic carry-over method, vol. i - theory_1960, volume={118}, journal={Publication (Oklahoma State University. Engineering Experiment Station)}, institution={Stillwater, OK: Oklahoma State University, Engineering Experiment Station}, year={1960} }
 @book{tuma_havner_1959, title={Analysis of continuous beams on elastic supports by carry-over moments}, volume={7}, journal={Research Publication (Oklahoma State University. School of Civil Engineering)}, institution={Stillwater, OK: Oklahoma State University, School of Civil Engineering}, author={Tuma, J. J. and Havner, K. S.}, year={1959} }
 @book{havner_tuma_1959, title={Influence lines for continuous beams}, volume={106}, journal={Publication (Oklahoma State University. Engineering Experiment Station)}, institution={Stillwater, OK: Oklahoma State University, Engineering Experiment Station}, author={Havner, K. S. and Tuma, J. J.}, year={1959} }
 @article{tuma_havner_hedges_1958, title={Analysis of frames with curved and bent members}, volume={84}, number={ST 5}, journal={Proceedings of the American Society of Civil Engineers, Structural Division}, publisher={New York: American Society of Civil Engineers}, author={Tuma, J. J. and Havner, K. S. and Hedges, F.}, year={1958} }