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An objective time-integration procedure for isotropic rate-independent and rate-dependent elastic-plastic constitutive equations. (English) Zbl 0714.73023
Summary: In a large class of rate-independent and rate-dependent elastic-plastic constitutive equations the elasticity is modeled in hypoelastic form, with the stress rate being taken as the Jaumann derivative, so as to make the constitutive model properly frame-indifferent or objective. Here, we present a fully-implicit, stable time-integration procedure for implementing such constitutive models in displacement-based finite element procedures. The numerical procedure preserves the very desirable feature of incremental objectivity. The overall procedure is a generalization of the well known “radial-return” algorithm of classical rate-independent plasticity, and it is therefore well suited for implementation in large-scale finite element codes. As an example, we have implemented the time-integration procedure in the finite element code ABAQUS. To check the incremental objectivity, accuracy, and stability of the algorithm some representative problems are solved.

74S30 Other numerical methods in solid mechanics (MSC2010)
74C99 Plastic materials, materials of stress-rate and internal-variable type
74S05 Finite element methods applied to problems in solid mechanics
74B20 Nonlinear elasticity
74A20 Theory of constitutive functions in solid mechanics
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74C20 Large-strain, rate-dependent theories of plasticity
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