provide the macroscopic linkage between the ‘‘softening’’ or ‘‘damaging’’ material and the ultimate loss ofstress carrying capability that arises in the context of the technologically important class of problems thatinvolve strong discontinuities and/or much weaker velocity gradients.The current review of our model proceeds with a summary for the criterion of stress collapse due toadiabatic shear. The problem of simple shearing is reviewed and the details of ultimate stress collapse aredescribed as a function of both the driving imperfections and the homogeneous response of a work-hardening, strain-rate hardening and thermally softening material. We will describe a simple generalizationof this scheme to formulate a macroscopic failure model for damage due to shear localization and theincorporation of this more general model within the context of finite element analysis techniques. We will
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