Geometrical numerical algorithms for a plasticity model with Armstrong–Frederick kinematic hardening rule under strain and stress controls

In this paper, we approach the numerical integration problem of a plasticity model with the Armstrong-Frederick kinematic hardening rule on back stress through a combination of the techniques of integral representation and geometrical integrator. First, the internal symmetry group of the constitutive model is investigated. Then, we develop two geometrical integrators for strain control and stress control, respectively. These integrators are obtained by a discretization of the integral representation of the constitutive equations and an exponential approximation of the quasi-linear differential equations system for the relative stress, which guarantee to retain the consistency condition exactly without the need for any iterations. Some numerical examples are used to assess the performance of the new algorithms. The measures in terms of stress relative errors and also isoerror maps confirm that our schemes are superior to the classical radial return methods.

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