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.
An Invariant-Based Flow Rule for Anisotropic Plasticity Applied to Composite Materials
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Hansen, A. C., Blackketter, D. M., and Walrath, D. E. (December 1, 1991). "An Invariant-Based Flow Rule for Anisotropic Plasticity Applied to Composite Materials." ASME. J. Appl. Mech. December 1991; 58(4): 881–888. https://doi.org/10.1115/1.2897701
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