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A critical review of the state of finite plasticity. (English) Zbl 0712.73032
Summary: The object of this paper is to provide a critical review of the current state of plasticity in the presence of finite deformation. In view of the controversy regarding a number of fundamental issues between several existing schools of plasticity, the areas of agreement are described separately from those of disagreement. Attention is mainly focussed on the purely mechanical, rate-independent, theory of elastic-plastic materials, although closely related topics such as rate-dependent behaviour, thermal effects, experimental and computational aspects, microstructural effects and crystal plasticity are also discussed and potentially fruitful directions are identified.
A substantial portion of this review is devoted to the area of disagreement that covers a detailed presentation of argument(s), both pro and con, for all of the basic constitutive ingredients of the rate- independent theory such as the primitive notion or definition of plastic strain, the structure of the constitutive equation for the stress response, the yield function, the loading criteria and the flow and the hardening rules. The majority of current research in finite plasticity theory, as with its infinitesimal counterpart, still utilizes a (classical) stress-based approach which inherently possesses some shortcomings for the characterization of elastic-plastic materials. These and other anomalous behavior of a stress-based formulation are contrasted with the more recent strain-based formulation of finite plasticity. A number of important features and theoretical advantages of the latter formulation, along with its computational potential and experimental interpretation, are discussed separately.

MSC:
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74C20 Large-strain, rate-dependent theories of plasticity
74C99 Plastic materials, materials of stress-rate and internal-variable type
74A20 Theory of constitutive functions in solid mechanics
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