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

率无关晶体塑性的描述算法由于其高度的应用相关性，多年来一直是一个活跃的研究课题。速率无关算法需要确定主动滑移系统（主动集方法），这通常由于所得确定方程中的线性依赖性而导致不稳定的算法。另一方面，率相关晶体塑性公式的算法诱导的唯一性的主动滑移系统，但导致刚性微分方程，这往往需要非常小的时间步长的数值解。该项目的目的是在不可行的原始对偶内点法（IPDIPM）的框架内，在大变形率无关的晶体塑性的稳定和有效的算法的发展。这些约束优化问题的求解方法比非线性、非凸问题的有效集方法更稳定、更有效。IPDIPM中的有限晶体塑性的考虑尚未被研究。基于一个有前途的证明IPDIPM的概念在小变形的晶体塑性的背景下，一个一致的扩展大变形理论的追求。在我们的初步工作中，它可以表明，这种方法表现出内在的正则化的量的主动滑移系统。此外，不同的方法来提高该方法的稳定性和效率进行了追求。为此，各种方法来保持最优条件的追求和策略的障碍参数的有针对性的适应。替代线搜索方法和治疗的多目标的问题是进一步的主题。该项目旨在展示在现实领域的适用性，以及与以前使用的解决方案相比，该算法的竞争力。

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.