Accuracy and stability of integration algorithms for elastoplastic constitutive relations. (English) Zbl 0585.73057

Summary: An analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper. Reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well- known trapezoidal and midpoint rules to fit the present context. Other integration schemes such as the radial return, mean normal and closest point procedures are particular cases of this general formulation. The meaning of first and second-order accuracy in the presence of the plastic consistency condition is examined in detail, and the criteria derived are used to identify two second-order accurate members of the proposed algorithms. A general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed. With the aid of this methodology, the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule. Finally, numerical examples are presented that illustrate the performance of the algorithms.


74S30 Other numerical methods in solid mechanics (MSC2010)
65D30 Numerical integration
74C99 Plastic materials, materials of stress-rate and internal-variable type
74S99 Numerical and other methods in solid mechanics
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