@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_trangenstein_1998, title={Adaptive mesh refinement and front-tracking for shear bands in an antiplane shear model}, volume={20}, ISSN={["1095-7197"]}, DOI={10.1137/S1064827597319271}, abstractNote={In this paper we describe a numerical algorithm for the study of shear-band formation and growth in a two-dimensional antiplane shear of granular materials. The algorithm combines front-tracking techniques and adaptive mesh refinement. Tracking provides a more careful evolution of the band when coupled with special techniques to advance the ends of the shear band in the presence of a loss of hyperbolicity. The adaptive mesh refinement allows the computational effort to be concentrated in important areas of the deformation, such as the shear band and the elastic relief wave. The main challenges are the problems related to shear bands that extend across several grid patches and the effects that a nonhyperbolic growth rate of the shear bands has in the refinement process. We give examples of the success of the algorithm for various levels of refinement.}, number={2}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Garaizar, FX and Trangenstein, J}, year={1998}, month={Sep}, pages={750–779} }
 @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} }