Assessment on the performance of distinct stress integration algorithms for complex non-quadratic anisotropic yield criteria

In this work, three distinct return mapping algorithms are presented and analyzed in detail: (i) a semi-explicit algorithm that accounts for the sub-incrementation technique, which reduces to (ii) a fully-explicit algorithm and, finally, (iii) a semi-implicit algorithm,. In order to describe the complex anisotropic behaviour of some metals, such as aluminium alloys, two non-quadratic anisotropic yield criteria were implemented: the Yld91 and Yld2004-18p. The performance of the developed algorithms is inferred in a series of sheet metal forming benchmarks and the quality of the results is assessed when compared to experimental results presented in the literature. The numerical simulations show that the semi-implicit algorithm is quite efficient with the von Mises yield criterion. However, when anisotropy is taken into account, the algorithm requires several iterations to return the stresses to the yield surface, particularly when the stresses are located at corner regions of that surface. The semi-explicit algorithm proved to be the most robust and efficient algorithm with anisotropic yield criteria. The good agreement between the experimental data and the obtained numerical results demonstrate the high efficiency of the presented algorithms and the ability of the anisotropic criteria to predict the material’s complex anisotropic behaviour.