Acta Mechanica

, Volume 182, Issue 1, pp 31–111

Elastoplasticity beyond small deformations


DOI: 10.1007/s00707-005-0282-7

Cite this article as:
Xiao, H., Bruhns, O.T. & Meyers, A. Acta Mechanica (2006) 182: 31. doi:10.1007/s00707-005-0282-7


This article is concerned with some essential aspects of representative ideas and viewpoints as well as developments in formulations of rate-independent elastoplasticity beyond the small deformation range. Kinematical and physical foundations underlying the basic variables, and the essential constitutive structures implied by the work postulate are examined and discussed, pro and con, from an integrated viewpoint based on certain coherent threads running through various formulations. Their constitutive and computational implications are elucidated and contrasted by analysing the main structural features based on their basic variables. Emphasis is placed on new issues and new understanding, and on physically pertinent variables and formulations.

In particular, attention is focused on the essential complexity of elastoplastic fields. It is suggested that residual stress fields attendant upon the removal of external loadings or actions should be indispensable prerequisites for ensuring the geometrical compatibility property of an elastoplastic body as material continuum. A further artificial process of destressing an elastoplastic body would inevitably lead to the loss of its geometrical compatibility and thus to the loss of the kinematical grounds for the usual compatible continuous bodies, such as the loss of the notion of line elements, etc. This might suggest that the elastoplastic deformation should be an inherently inseparable physical entity in the usual sense of compatibility.

It is explained that a physically pertinent formulation for the incremental essence of flow-like characteristics of elastoplastic behaviour should be an objective Eulerian formulation based upon the Kirchhoff stress (weighted Cauchy stress) and the natural deformation rate (stretching). According to the latest development, it is possible to establish a straightforward Eulerian rate theory without involving additional ``elastic'' or ``plastic'' deformation-like variables. With so many possibilities in formulating objective Eulerian rate constitutive relations, in particular, for the choices of objective rates among an unlimited number of plausible candidates, it is demonstrated how a unique, self-consistent, general constitutive structure may be derived from two physical consistency criteria by synthesizing and developing a number of essential ideas contributed in previous efforts. With this general self-consistent structure based on Kirchhoff stress and the stretching, it is rigorously found from the work postulate that the normality rule for plastic flow and the convexity property of the yield surface in classical elastoplasticity for the small deformation range may be extended to be general facts even for the case covering the whole deformation range, thus leading to a self-consistent Eulerian rate theory of finite elastoplasticity with the appealingly simple essential structure as in the classical case.

Copyright information

© Springer-Verlag Wien 2006

Authors and Affiliations

  1. 1.Ruhr-Universität BochumBochumGermany