First-order system least squares finite elements for finite elasto-plasticity

有限弹塑性的一阶系统最小二乘有限元

• 批准号: 255798245
• 负责人: Professor Dr.-Ing. Jörg Schröder
• 金额: --
• 依托单位: Institut für Mechanik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/255798245?language=en
• 关键词: First; order; system; least; squares

The goal of the proposed research project is the development, construction and analysis of mixed finite element formulations in the field of finite elasto-plasticity on the basis of first-order systems. Since there are no simulation tools available at the moment that are capable to provide reliable solutions for such problems, the ambition of this project is to provide a new access with modern discretization techniques in this field. The least squares finite element method (LSFEM), in particular produces accurate approximations of stresses which are often of primary interest in the context of solid mechanical problems. This approach avoids the requirement of a compatibility (inf-sup) condition for the finite element spaces for stresses and displacements leading to more general combinations. Furthermore, a robust numerical behavior particularly for quasi-incompressible materials is obtained.In numerous investigations the applicants achieved a long-term joint experience basis with respect to the LSFEM and its application to solid mechanics supported by a cooperation between mathematics and mechanics. On the basis of the advances obtained within this cooperation it is now possible to jointly address problems of finite plasticity.The main tasks of the project can be divided into three steps. Firstly, the components of the method will be developed for the elastic subproblem in order to extend them to the model of finite multiplicative elasto-plasticity. After that, the resulting formulations will be validated numerically by means of the benchmark problems provided by the Priority Programme as well as by computations of real complex microheterogeneous structures as for instance of dual-phase steels. In order to improve the efficiency and robustness, these computations are guided by several investigations concerning e.g. adaptivity, choice of the approximation spaces and suitable weighting.This research project aims at setting new standards of quality in the field of non-conventional discretization methods for structural mechanical problems in the framework of finite elasto-plasticity.

拟议的研究项目的目的是根据一阶系统的有限弹性塑性性领域中混合有限元配方的开发，构建和分析。由于目前尚无仿真工具能够为此类问题提供可靠的解决方案，因此该项目的野心是在该领域使用现代离散技术提供新的访问。最小二乘有限元法（LSFEM），特别是在固体机械问题的背景下通常产生的应力准确近似。这种方法避免了对有限元元素空间的兼容性（INF-SUP）条件的要求，以使应力和位移导致更一般的组合。此外，在众多研究中，申请人在LSFEM及其在数学和机械学之间的合作支持的固体机械方面获得了长期的联合经验基础，尤其是对准压缩材料的鲁棒行为。根据在此合作中获得的进步，现在可以共同解决有限可塑性的问题。该项目的主要任务可以分为三个步骤。首先，该方法的组件将为弹性子问题开发，以将其扩展到有限乘弹性塑性性的模型。之后，将通过优先级程序提供的基准问题以及通过实际复杂的微观体系结构（例如双相钢）的计算来验证所得的公式。为了提高效率和鲁棒性，这些计算由有关例如适应性，近似空间的选择和合适的加权。该研究项目旨在在有限弹性塑性性框架内针对非惯例离散方法领域的结构机械问题设定新的质量标准。