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In this paper, an unconditionally stable algorithm for the numerical integration and finite-element implementation of a class of pressure dependent plasticity models with nonlinear isotropic and kinematic hardening is presented. Existing algorithms are improved in the sense that the number of equations to be solved iteratively is significantly reduced. This is achieved by exploitation of the structure of Armstrong-Frederik-type kinematic hardening laws. The consistent material tangent is derived analytically and compared to the numerically computed tangent in order to validate the implementation. The performance of the new algorithm is compared to an existing one that does not consider the possibility of reducing the number of unknowns to be iterated. The algorithm is used to implement a time and temperature dependent cast iron plasticity model, which is based on the pressure dependent Gurson model, in the finite-element program ABAQUS. The implementation is applied to compute stresses and strains in a large-scale finite-element model of a three cylinder engine block. This computation proofs the applicability of the algorithm in industrial practice that is of interest in applied sciences.
In this paper the yield surface of a recently presented microstructure-based volume element of the gray cast iron material GJL-250 is assessed after different plastic loading histories. The evolution of the yield surface is investigated for different volumetric, deviatoric and uniaxial loadings. The micromechanical material properties of the metallic matrix and the graphite inclusions are validated by means experimental stress-strain hysteresis loops. The metallic matrix is modeled as elastic-plastic with a non-linear kinematic hardening law. The graphite inclusions are described by means of a volumetric strain state dependent Young’s modulus. The results show that the shape of the yield surface does not change significantly in comparison to the initial yield surface after pure deviatoric loadings. After volumetric loadings, the dependence of the material on the Lode angle is significantly reduced. Uniaxial tensile preloadings result in a deformed yield surface, whereby the magnitude of the deformation depends on the applied load. Uniaxial preloadings to compression do not change the shape of the initial yield surface.