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.

拟议研究项目的目标是基于一阶系统的有限弹塑性领域的混合有限元公式的开发、构建和分析。由于目前还没有可用的仿真工具能够为此类问题提供可靠的解决方案，因此该项目的目标是为该领域提供现代离散化技术的新途径。最小二乘有限元法 (LSFEM) 尤其可以生成应力的精确近似值，这在固体机械问题中通常是主要关注点。这种方法避免了应力和位移有限元空间的兼容性 (inf-sup) 条件要求，从而产生更通用的组合。此外，还获得了特别针对准不可压缩材料的鲁棒数值行为。 在大量研究中，申请人在LSFEM及其在数学和力学合作支持的固体力学应用方面取得了长期的联合经验基础。基于此次合作取得的进展，现在可以共同解决有限塑性问题。该项目的主要任务可分为三个步骤。首先，将针对弹性子问题开发该方法的组件，以便将其扩展到有限乘法弹塑性模型。之后，所得到的公式将通过优先计划提供的基准问题以及通过计算实际复杂的微异质结构（例如双相钢）进行数值验证。为了提高效率和鲁棒性，这些计算以多项研究为指导，例如：适应性、近似空间的选择和适当的权重。该研究项目旨在为有限弹塑性框架内的结构力学问题的非常规离散方法领域制定新的质量标准。