Goal-oriented adaptive finite elements for parameter identification of conventional and additive micromorphic continuum models

用于传统和加性微形态连续体模型参数识别的目标导向自适应有限元

• 批准号: 226812732
• 负责人: Dr.-Ing. Ismail Caylak, since 3/2024
• 金额: --
• 依托单位: Lehrstuhl für Technische Mechanik (LTM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/226812732?language=en
• 关键词: Goal; oriented; adaptive; finite; elements

Due to deficiencies of local continua, in particular pathological mesh dependency of FE solutions on the numerical side and failure to simulate length scale dependent problems on the theoretical side, generalized continuum theories have wide areas of applications. In this project, we address the class of micromorphic continua, containing micropolar (Cosserat) continua and microstrain continua as important special cases. In the previous project, we dealt with goal-oriented adaptive FEM for micromorphic elasticity and plasticity towards an error-controlled simulation of the direct problem. In addition, a novel continuum type labeled as additive micromorphic continuum has been proposed for finite strain elasticity, enabling a flexible transition of different continua and weightingthem differently if required. On this basis, this project primarily addresses the following issues:• With conventional micromorphic theories in the sense of Eringen, we consider size effects in linear elasticity. New experiments will be designed for identifying parameters of related micromorphic models, where notches of varying sizes are used to activate size effects in sand specimens for cold-box casting.• The novel additive micromorphic model will be extended to elastoplasticity including damage. Since it contains micropolar and microstrain continua as special cases, a selection of a proper continuum is expected to be done automatically via an inverse problem based on experimental data. It will be illustrated by simulating the whole damaging process of a cold-box sand. The advantage of the new additive model is to account for the rotation of sand particles and the deformation of the binder with proper weights.• Inverse problems for parameter identification will be handled for both conventional and additive micromorphic models based on experimental data. As a heterogeneous deformation state is required, a sensitivity analysis will be carried out on the basis of discretized variational formulations for the FEM. Special care will be paid to the additive model with a time-dependent character.• To enhance the numerical efficiency of the parameter identification, adaptive FEM will be developed for an effective meshing (spatial and temporal discretization for time-dependent problems). The challenging part is to develop appropriate goal-oriented error estimators to drive the corresponding adaptive algorithms.

由于局部连续体的不足，特别是数值方面有限元解的病态网格依赖性和理论方面无法模拟长度尺度依赖性问题，广义连续体理论具有广泛的应用领域。在这个项目中，我们讨论了一类微形态连续体，包括微极（Cosserat）连续体和微应变连续体作为重要的特例。在之前的项目中，我们处理了面向目标的微形态弹性和塑性自适应有限元法，以解决直接问题的误差控制仿真。此外，一种新的连续体类型被标记为有限应变弹性的加性微形态连续体，可以实现不同连续体的灵活过渡，并根据需要对它们进行不同的加权。在此基础上，本项目主要解决以下问题：•使用Eringen意义上的传统微形态理论，我们考虑线性弹性中的尺寸效应。将设计新的实验来确定相关微形态模型的参数，其中不同尺寸的缺口用于激活冷箱铸造砂样的尺寸效应。•新的加性微形态模型将扩展到包括损伤在内的弹塑性。由于它包含微极和微应变连续体作为特殊情况，因此期望通过基于实验数据的反问题自动选择合适的连续体。通过模拟冷箱砂的整个破坏过程来说明这一点。新加性模型的优点是考虑了砂粒的旋转和适当重量的粘结剂的变形。•参数识别的逆问题将处理基于实验数据的传统和加性微形态模型。由于需要非均质变形状态，将在有限元离散变分公式的基础上进行灵敏度分析。将特别注意具有时间依赖性的加性模型。•为了提高参数识别的数值效率，将开发自适应有限元法进行有效的网格划分（时间相关问题的空间和时间离散化）。具有挑战性的部分是开发适当的面向目标的误差估计器来驱动相应的自适应算法。