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

描述速率无关晶体塑性的算法由于具有很高的应用价值，多年来一直是一个活跃的研究课题。与速率无关的算法需要确定活动滑移系(活动集方法)，这通常会导致算法不稳定，因为在所得到的确定方程中存在线性相关性。另一方面，速率相关晶体塑性方程的算法导致了活动滑移系统的唯一性，但导致了刚性的微分方程组，其数值解通常需要极小的时间步长。本项目的目的是在不可行的原始-对偶内点法(IPDIPM)的框架内，发展一种稳定而有效的算法来计算大变形条件下与速率无关的晶体塑性。这些求解约束优化问题的方法比求解非线性、非凸问题的有效集方法更稳定、更有效。在IPDIPM中考虑有限晶体塑性还没有被研究过。基于在小变形时晶体塑性的背景下IPDIPM概念的一个有希望的证明，寻求对大变形理论的一致扩展。在我们的初步工作中，该方法可以显示出活动滑移系数量的内在规律性。此外，还寻求了不同的方法来提高方法的稳定性和效率。为此，寻求各种保持最优条件的方法，并研究针对障碍参数的定向适应的策略。线搜索法的替代方法和问题的多客观性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.