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

速率无关晶体塑性描述算法由于具有较高的应用相关性，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动系统（活动集方法），这通常会导致算法不稳定，因为结果确定方程中存在线性依赖关系。另一方面，速率相关晶体塑性公式的算法诱导了主动滑移系统的唯一性，但导致了僵硬的微分方程，这通常需要极小的时间步长来求解数值解。本项目旨在在不可行的原对偶内点法（IPDIPM）框架内，开发一种稳定有效的大变形下速率无关晶体塑性的算法。这些求解约束优化问题的方法比求解非线性非凸问题的活动集方法更稳定和有效。在IPDIPM中考虑有限晶体塑性的研究尚未进行。基于在小变形晶体塑性背景下IPDIPM概念的有希望的证明，对大变形理论进行了一致的扩展。在我们的初步工作中可以表明，这种方法表现出活动滑动系统数量的内在正则化。此外，本文还探讨了提高该方法稳定性和效率的不同途径。为此，研究了各种维持最优条件的方法，并研究了有针对性地适应障参数的策略。替代线搜索方法和多客观性问题的处理是进一步的主题。该项目旨在展示该算法在现实领域的适用性以及与以前使用的求解方法相比的竞争力。

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.