On the modelling of non‐linear kinematic hardening at finite strains with application to springback—Comparison of time integration algorithms

Abstract

SUMMARYThe paper discusses the derivation and the numerical implementation of a finite strain material model for non-linear kinematic and isotropic hardening. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong-Frederick kinematic hardening. In addition, a comparison between several numerical algorithms for the integration of the evolution equations is conducted. In particular, a new form of the exponential map that preserves the plastic volume and the symmetry of the internal variables, as well as two modifications of the backward Euler scheme are discussed. Finally, the applicability of the model for springback prediction is demonstrated by performing simulations of the draw-bending process and a comparison with experiments. The results show an excellent agreement between simulation and experiment.

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Material Modelling of Evolving Elastic and Plastic Anisotropywith Application to Deep Drawing Processes

“…Exploiting the dissipation inequality leads to the important result that all tensor-valued internal variables are symmetric. Thus, the integration of the evolution equations can be efficiently performed by means of a newly-developed form of the exponential map algorithm [9] based on an implicit time integration scheme. It automatically satisfies plastic incompressibility in every time step, and in addition, has the advantage of retaining the symmetry of the internal variables.…”