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Generalized Coupled Thermoplasticity Taking into Account Large Strains: Part II. A Model of Non-compressible Elastic–Plastic Solid with Non-associated Plastic Flow Law

Faculty of Applications of Chemistry and Mechanics, Opole University of Technology, Luboszycka 5, 45-036 Opole, Poland

^* To whom correspondence should be addressed.

	Abstract

This paper is the second part of our work on generalized coupled thermoplasticity taking into consideration the large strains. In the first part of the work global uniqueness conditions for solution of fundamental incremental boundary-value problem were derived. In this part a model of non-compressible elasto-plastic body with non-associated plastic flow law is analyzed. The assumptions and constitutive equations for this model are presented and suitable comparison bodies dependent on kinematically admissible fields of velocity strain and statically admissible fields of velocity stress are derived. An attempt to derive local sufficiwent uniqueness condition for comparison bodies is also presented. This attempt was unsuccessful since it lead to contradictory results, which means that the derivation of local sufficient uniqueness condition for comparison bodies of non-compressible elasto-plastic body is still unsolved.

Key Words: Non-compressible elastic-plastic solids, non-associated plastic flow law, uniqueness conditions and bifurcation criteria, comparison body

First published on March 11, 2009
Mathematics and Mechanics of Solids 2009, doi:10.1177/1081286508100732


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