An Invariant-Based Flow Rule for Anisotropic Plasticity Applied to Composite Materials

[+] Author and Article Information
Andrew C. Hansen, David E. Walrath

Department of Mechanical Engineering, University of Wyoming, Laramie, WY 82071

Donald M. Blackketter

Department of Mechanical Engineering, University of Idaho, Moscow, ID 83843

J. Appl. Mech 58(4), 881-888 (Dec 01, 1991) (8 pages) doi:10.1115/1.2897701 History: Received March 03, 1989; Revised June 30, 1990; Online March 31, 2008


In this paper we discuss some fundamental problems associated with incremental anisotropic plasticity theories when applied to unidirectional composite materials. In particular, we question the validity of an effective stress-strain relation for highly anisotropic materials of this nature. An effective stress-strain relation is conventionally used to determine a flow rule for plastic strain increments. It is our view that such a relation generally does not exist for many high-performance unidirectional composites. To alleviate the problem associated with defining an effective stress-strain curve we develop an anisotropic plasticity theory in which the flow rule does not requires such a relation. The proposed theory relies on developing an accurate expression for a scalar hardening parameter g (σ). The general form of g (σ) is substantially reduced by invoking invariance requirements based on material symmetry. The general invariant-based theory developed herein is specialized to case of transverse isotropy and applied to the analysis of a nonlinear elastic-plastic unidirectional composite material. The invariant-based theory is shown to produce superior results over the traditional approach for a series of uniaxial and biaxial load cases predicted using finite element micromechanics.

Copyright © 1991 by The American Society of Mechanical Engineers
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