FINITE STRAIN WORK-HARDENING THEORY FOR RATE INDEPENDENT ELASTO-PLASTICITY

A finite strain constitutive theory for a special class of isotropic, rate independent, elastic-plastic materials is proposed. The development proceeds from the assumed existence of a free energy function and the requirement that the postulate of Il'iushin be satisfied for all processes. A precise formulation of the hypothesis of invariance of elastic properties under continued plastic flow, however, leads to an important identity which restricts the class of admissible energy functions and allows for a useful restatement of the known stability requirements. In particular, it is established that a yield function that depends only on the invariants of Kirchhoff stress must necessarily conform to an explicit convexity requirement and act as a potential, in the classical sense, for the plastic strain increments. With this, a complete analogy with the classical small strain development of rate independent elasto-plasticity is established. © 1979.