A robust algorithm for single crystal plasticity based on the infeasible primal-dual interior point method

• Applicant: Professorin Dr.-Ing. Lisa Scheunemann
• Subject Area: Mechanics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 507890620

Algorithms for the description of rate-independent crystal plasticity have been an active research topic for many years due to their high application relevance. Rate-independent algorithms require a determination of the active slip systems (active-set method), which generally leads to unstable algorithms due to linear dependencies in the resulting determination equations. On the other hand, algorithms for rate-dependent crystal plasticity formulations induce uniqueness of the active slip systems, but lead to stiff differential equations, which often require extremely small time steps for the numerical solutions. This project aims at the development of a stable and efficient algorithm for rate-independent crystal plasticity at large deformations within the framework of the infeasible primal-dual interior point method (IPDIPM). These solution methods for constrained optimization problems are more stable and efficient than active-set methods for nonlinear, non-convex problems. The consideration of finite crystal plasticity within the IPDIPM has not yet been investigated. Based on a promising proof of concept of IPDIPM in the context of crystal plasticity at small deformations, a consistent extension to the theory of large deformations is pursued. In our preliminary work it could be shown that this method exhibits an intrinsic regularization of the amount of active slip systems. In addition, different approaches to improve the stability and efficiency of the method are pursued. To this end, various approaches to maintaining optimality conditions are pursued and strategies for the targeted adaptation of the barrier parameter are investigated. Alternatives to the line search method and the treatment of the multiobjectivity of the problem are further topics. The project aims at demonstrating the applicability in realistic areas as well as the competitiveness of the algorithm in comparison to previously used solution methods.

• DFG Programme: Research Grants