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REVIEW ARTICLES: General Lectures

Conservative Formulation of Large Deformation Plasticity

[+] Author and Article Information
James G. Glimm, Bradley J. Plohr

Department of Applied Mathematics and Statistics, State University of New York, Stony Brook NY 11794-3600

David H. Sharp

Complex Systems Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos NM 87545

Appl. Mech. Rev 46(12), 519-526 (Dec 01, 1993) (8 pages) doi:10.1115/1.3120313 History: Online April 29, 2009

Abstract

We explain several ideas which may, either singly or in combination, help achieve high resolution in simulations of large-deformation plasticity. Because of the large deformations, we work in the Eulerian picture. The governing equations are written in a fully conservative form, which are correct for discontinuous as well as continuous solutions. Models of shear bands are discussed. These models describe the internal dynamics of a developed shear band in terms of time-asymptotic states; in other words, the smooth internal structure is replaced by a jump discontinuity, and the shear band evolution is determined by jump relations. This analysis is useful for high resolution numerical methods, including both shock capturing and shock tracking schemes, as well as for the understanding and validation of computations, independently of the underlying method. Preliminary computations, which illustrate the feasibility of these ideas, are presented.

Copyright © 1993 by American Society of Mechanical Engineers
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