Abstract Single crystal plasticity plays a major role in the analysis of material anisotropy and texture evolution, treats each crystalline grain individually. The polycrystalline material response is obtained upon considering a structure consisting of various individual grains, often also considering interface effects at the grain boundaries. On the individual grain level, single crystal plasticity can be treated in the mathematical framework of multi-surface plasticity, leading to a constrained optimization problem wherein multiple constraints are defined as yield criteria on the different slip systems. In this work, we present a new algorithm for the solution of the constrained optimization problem based on the Infeasible Primal Dual Interior Point method (IPDIPM). The main motivation herein is the handling of the ill-posed problem without the use of simple perturbation technique, see e.g. Miehe and Schroder [2001]. The proposed algorithm, involving slack variables, is developed for the framework of small strain single crystal plasticity. The use of slack variables therein stabilizes the conventional method and allows for a temporary violation of the constraint condition during the optimization. Moreover, all slip systems are considered simultaneously, omitting an iterative active set search. Several numerical examples are simulated to show the performance of the developed algorithm.

中文翻译：

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基于不可行原对偶内点法的速率无关小应变晶体塑性新算法

摘要 单晶塑性在材料各向异性和织构演化的分析中起着重要作用，单独处理每个晶粒。多晶材料响应是在考虑由各种单个晶粒组成的结构时获得的，通常还考虑晶界处的界面效应。在单个晶粒水平上，可以在多表面塑性的数学框架中处理单晶塑性，从而导致约束优化问题，其中多个约束被定义为不同滑移系统的屈服准则。在这项工作中，我们提出了一种基于不可行原始对偶内点法 (IPDIPM) 的约束优化问题解决方案的新算法。这里的主要动机是在不使用简单扰动技术的情况下处理不适定问题，例如参见 Miehe 和 Schroder [2001]。所提出的算法涉及松弛变量，是为小应变单晶塑性框架开发的。其中松弛变量的使用稳定了传统方法，并允许在优化期间暂时违反约束条件。此外，所有滑动系统都被同时考虑，省略了迭代活动集搜索。模拟了几个数值例子来展示所开发算法的性能。其中松弛变量的使用稳定了传统方法，并允许在优化期间暂时违反约束条件。此外，所有滑动系统都被同时考虑，省略了迭代活动集搜索。模拟了几个数值例子来展示所开发算法的性能。其中松弛变量的使用稳定了传统方法，并允许在优化期间暂时违反约束条件。此外，所有滑动系统都被同时考虑，省略了迭代活动集搜索。模拟了几个数值例子来展示所开发算法的性能。