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Mathematics and Mechanics of Solids
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On the Evolution of Plasticity and Incompatibility

Anurag Gupta

Department of Mechanical Engineering University of California, Berkeley, CA 94720, USA

David J. Steigmann

Department of Mechanical Engineering University of California, Berkeley, CA 94720, USA

James S. Stölken

Department of Mechanical Engineering Lawrence Livermore National Laboratory Livermore, CA 94550, USA

The phenomenological theory of elastic—plastic response is reconsidered in the light of recent opinion regarding the constitutive character of the constituent elastic and plastic deformations. The primary role of dissipation in the physics of plastic evolution is emphasized and shown to lead to the clarification of a number of open questions. Particular attention is given to the invariance properties of the elastic and plastic deformations, to the kinematics of discontinuities, and to the role of material symmetry in restricting constitutive equations for elastic response, yield and plastic evolution.

Key Words: Plasticity • compatibility • interfaces • symmetry

This version was published on December 1, 2007

Mathematics and Mechanics of Solids, Vol. 12, No. 6, 583-610 (2007)
DOI: 10.1177/1081286506064721
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[Abstract] [PDF]