A return mapping algorithm for a class of cyclic plasticity models. (English) Zbl 0823.73021

Hopperstad, O. S.; Remseth, S.

Int. J. Numer. Methods Eng. 38, No. 4, 549-564 (1995).

Summary: A return mapping algorithm for a class of cyclic plasticity models is presented. The constitutive model includes a quadratic yield criterion and multi-component formulations of nonlinear isotropic and kinematic hardening. Thus, both initially isotropic and anisotropic materials can be described, and a proper description of the hysteresis loops and the cyclic hardening response of materials under cyclic loading is obtained. The return mapping algorithm employs the closest point projection scheme in combination with a decomposition method, to obtain an efficient and robust integration of the constitutive model. The consistent tangent operator is derived in closed form, and is found to be unsymmetric due to the nonlinear evolution of the kinematic hardening terms. The accuracy and robustness of the algorithm are assessed through numerical examples.

MSC:

74S30	Other numerical methods in solid mechanics (MSC2010)
74C99	Plastic materials, materials of stress-rate and internal-variable type

Keywords:

stress point integration; quadratic yield criterion; nonlinear isotropic and kinematic hardening; hysteresis loops; closest point projection scheme; decomposition method; consistent tangent operator

Software:

ABAQUS/Standard

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