0
research-article

How to realize volume conservation during finite plastic deformation

[+] Author and Article Information
He-Ling WANG

AML, CNMM, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China; Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL, 60208, USA
heling.wang@northwestern.edu

Dong-jie Jiang

AML, CNMM, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China
jdj05@mails.tsinghua.edu.cn

Li-Yuan Zhang

AML, CNMM, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China
zhangly@ustb.edu.cn

Bin Liu

AML, CNMM, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China
liubin@tsinghua.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4037882 History: Received August 03, 2017; Revised September 06, 2017

Abstract

Volume conservation during plastic deformation is the most important feature, and should be realized in elastoplastic theories. However, it is found in this paper that an elastoplastic theory is not volume conserved if it improperly sets an arbitrary plastic strain rate tensor to be deviatoric. We discuss how to rigorously realize volume conservation in finite strain regime. An accurate condition of volume conservation is first clarified and used in this paper that the density of a volume element after the applied loads are completely removed should be identical to that of the initial stress free states. For elastoplastic theories that adopt the unloading stress free configuration, the accurate condition of volume conservation is satisfied only if specific definitions of the plastic strain rate are used among many other different definitions. For the elastoplastic theories that do not adopt the unloading stress free configuration, it is even more difficult to realize volume conservation as the information of the stress free configuration lacks. To find a universal approach of realizing volume conservation for elastoplastic theories whether or not adopt the unloading stress free configuration, we propose a single assumption that the density of material only depends on the trace of the Cauchy stress by using their objectivities. Two strategies are further discussed to satisfy the accurate condition of volume conservation: directly and slightly revising the tangential stiffness tensor or using a properly chosen stress/strain measure and elastic compliance tensor. Their volume conservation is demonstrated by both theoretical proof and numerical examples.

Copyright (c) 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In