A parallelised algorithm to identify arbitrary yield surfaces in multiscale analyses

Plasticity is a common phenomenon in many materials. Furthermore, it is also commonly applied in multiscale analyses. Plasticity is mainly characterised by the yield function. This function distinguishes between the elastic and the plastic material domain. The transition surface is denoted as the yield surface, and characterises the material behaviour significantly. In the contribution at hand, an algorithm is proposed, which can identify arbitrary yield surfaces. No assumptions regarding the geometry, kinematics, or material model need to be incorporated. The algorithm can identify yield surfaces as long as a function can be formulated, which measures the distance of any point in the principal stress space to the yield surface, and an indicator exists, which characterises the behaviour of the material to be elastic or plastic. Hence, a very general algorithm is achieved, which can also be applied to crystal plasticity. The property of star-convexity of yield surfaces is exploited. This algorithm is also well suited for the application in high performance computing environments. Furthermore, the proposed algorithm can be applied to the identification of initial damage surfaces as well. The proposed algorithm is validated on one macroscopically formulated yield function. Subsequently, it is applied to multiscale frameworks to highlight the benefits of the proposed approach. Furthermore, the capabilities of the algorithm to also identify yield surfaces after hardening are presented. Important properties of such yield surfaces are highlighted. The good scalability within distributed memory systems is shown, and the applicability for anisotropic yield surfaces is demonstrated. • Numerical approach on identifying arbitrary yield surfaces. • Application onto multiscale analyses. • Application onto distributed memory systems.