A novel formulation for elastoplasticity has been recently proposed by Liu and Hong. These authors have explored the internal symmetry of the constitutive model for perfect plasticity to ensure that the consistency condition is satisfied at each time step. Moreover, for perfect plasticity, they have converted the usual nonlinear elastoplastic constitutive model into a linear system of ordinary differential equations in redefined variables. The present paper is concerned with general isotropic workhardening. With the present formulation, it is still possible to satisfy the elastoplastic consistency condition at every time step, without the need for iterations even for nonlinear workhardening. The resulting system of ordinary differential equations, however, is, in general, nonlinear. Different strategies for obtaining numerical solutions of these equations are proposed in this paper, one of them based on group theory. Numerical solutions from the different schemes, for a simple illustrative example, are presented in the paper.
Computational Isotropic-Workhardening Rate-Independent Elastoplasticity
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Mar. 17, 2002; final revision, Apr. 24, 2003. Associate Editor: B. M. Moran. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Mukherjee, S., and Liu, C. (October 10, 2003). "Computational Isotropic-Workhardening Rate-Independent Elastoplasticity ." ASME. J. Appl. Mech. September 2003; 70(5): 644–648. https://doi.org/10.1115/1.1607356
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