Variational Formulation, Discrete Conservation Laws, and Path-Domain Independent Integrals for Elasto-Viscoplasticity

[+] Author and Article Information
J. C. Simo, T. Honein

Applied Mechanics Division, Stanford University, Stanford, CA 94305

J. Appl. Mech 57(3), 488-497 (Sep 01, 1990) (10 pages) doi:10.1115/1.2897050 History: Received October 29, 1987; Revised October 13, 1988; Online March 31, 2008


A discrete variational formulation of plasticity and viscoplasticity is developed based on the principle of maximum plastic dissipation. It is shown that the Euler-Lagrange equations (spatial conservation laws) emanating from the proposed discrete Lagrangian yield the equilibrium equation, the strain-displacement relations, the stress-strain relations, the discrete flow rule and hardening law in the form of closest-point-projection algorithm, and the loading/unloading conditions in Kuhn-Tucker form. Lack of invariance of the discrete Lagrangian relative to the group of material translations precludes the classical Eshelby law from being a conservation law. However, a discrete inhomogeneous form of Eshelby’s conservation law is derived which leads to a path-domain independent integral that generalizes the classical J -integral to elasto-viscoplasticity. It is shown that this path-domain independent integral admits a physical interpretation analogous to Budiansky and Rice interpretation of the classical J -integral.

Copyright © 1990 by The American Society of Mechanical Engineers
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