A conservative formulation for plasticity

Authors:
Bradley J Plohr;David H Sharp
Affiliations:
State University of New York, Stony Brook, New York 11794 USA;Theoretical Division-Complex Systems Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 USA
Venue:
Advances in Applied Mathematics
Year:
1992

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Abstract

In this paper we propose a fully conservative form for the continuum equations governing rate-dependent and rate-independent plastic flow in metals. The conservation laws are valid for discontinuous as well as smooth solutions. In the rate-dependent case, the evolution equations are in divergence form, with the plastic strain being passively convected and augmented by source terms. In the rate-independent case, the conservation laws involve a Lagrange multiplier that is determined by a set of constraints; we show that Riemann problems for this system admit scale-invariant solutions.