@article{gordon_garaizar_1999, title={Wave speeds for an elastoplastic model for two-dimensional deformations with a nonassociative flow rule}, volume={57}, ISSN={["0033-569X"]}, DOI={10.1090/qam/1686188}, abstractNote={A system of partial differential equations describing elastoplastic deformations in two space dimensions is studied. The constitutive relations for plastic deformation include a nonassociative flow rule and shear strain hardening. After a change of variables, the characteristic speeds of plane wave solutions of the system are computed. For both plastic and elastic deformations, there are two nonzero wave speeds, referred to as fast and slow waves. It is shown that there are regions in stress space for which the speed of fast plastic waves exceeds the speed of fast elastic waves, which translates into a lack of uniqueness for certain initial value problems and introduces nontrivial difficulties for numerical methods. Finally, these regions are computed for an example using representative constitutive data.}, number={2}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Gordon, M and Garaizar, FX}, year={1999}, month={Jun}, pages={245–259} }
@article{garaizar_gordon_shearer_1998, title={An elastoplasticity model for antiplane shearing with a non-associative flow rule: Genuine nonlinearity of plastic waves}, volume={219}, ISSN={["0022-247X"]}, DOI={10.1006/jmaa.1997.5817}, abstractNote={In elastoplasticity models, there is a stress threshold or yield condition that plays a role in determining whether the material is deforming elastically or plastically. If the stress is below the threshold, then the deformation is elastic, and is typically modeled by linear elasticity. If the stress reaches the threshold, it is said to be at yield, and the deformation is considered to be plastic. In models of plastic deformation in which the material hardens with increasing stress, the stress-strain constitutive law is Ž typically nonlinear. Since the equations are hyperbolic at least up to some . maximum stress , nonlinearities can in principle lead to the formation of}, number={2}, journal={JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS}, author={Garaizar, FX and Gordon, M and Shearer, M}, year={1998}, month={Mar}, pages={344–363} }
@article{gordon_shearer_schaeffer_1997, title={Plane shear waves in a fully saturated granular medium with velocity and stress controlled boundary conditions}, volume={32}, ISSN={["0020-7462"]}, DOI={10.1016/S0020-7462(96)00080-7}, abstractNote={A one-dimensional system describing small shearing disturbances in a semi-infinite, fully saturated granular medium is studied. The system is fully non-linear as a result of the incrementally non-linear constitutive law for the material. In particular, there are two different wave speeds corresponding to loading or unloading of the material. Global solutions are constructed with boundary data consisting of a single pulse in either velocity or stress. In the case of velocity controlled boundary conditions, the solution is a traveling pulse of increasing kinetic energy which eventually unloads the material, regardless of whether the initial pulse loads or unloads. The solution with stress controlled boundary conditions has these features only if the initial stress pulse unloads the material. If the initial stress pulse is loading then the solution is a slowly traveling pulse of decreasing kinetic energy which is also loading.}, number={3}, journal={INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS}, author={Gordon, MS and Shearer, M and Schaeffer, D}, year={1997}, month={May}, pages={489–503} }