Wave speeds for an elastoplastic model for two-dimensional deformations with a nonassociative flow rule

Gordon, Michael; Garaizar, F. Xabier

doi:10.1090/qam/1686188

Authors: Michael Gordon and F. Xabier Garaizar
Journal: Quart. Appl. Math. 57 (1999), 245-259
MSC: Primary 74C05; Secondary 35Q72, 74E20, 74J99
DOI: https://doi.org/10.1090/qam/1686188
MathSciNet review: MR1686188
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Abstract: 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.

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