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Efficient non-linear homogenization of materials with interfaces using order-reduction methodes

使用降阶方法对具有界面的材料进行高效非线性均质化

基本信息

批准号：
222281942
负责人：
Professor Dr.-Ing. Felix Fritzen
金额：
--
依托单位：
Professur für Data Analytics in Engineering
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2017-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/222281942?language=en
关键词：
Efficient non linear homogenization materials

项目摘要

The aim of the research project is the mechanism-based homogenization of the constitutive behaviour of micro-heterogeneous materials with interfaces. Examples for such interfaces are phase boundaries or adhesive joints in modern composites, cracks in ceramics or grain boundaries in poly-crystalline metals. The focus in the present study is on the consideration of particle- and fibre-reinforced composites. The anticipated methods can directly be transferred for the other mentioned materials. In order to homogenize the constitutive response of such materials an order-reduction approach is developed based on the micro-mechanics of the multi-scale problem. Therefore, an approximation of the spatial distribution of the interfacial separation vector and the internal variables using a low-dimensional function space is sought for. The parametrisation of this low-dimensional space is based on numerical experiments, which allow for the consideration of the influence of both, geometrical and physical heterogeneities, on the macroscopic constitutive response. The microscopic constitutive behaviour of the examined materials is modelled as a generalized standard material (GSM). Then the homogenized material on the macroscopic scale is also a generalized standard material for which a variational formulation is to be developed. The implementation of the method shall attribute for a high numerical efficiency in order to allow the usage of the resulting material model at the integration points of macroscopic simulations in large-scale structural computations.

该研究项目的目标是基于机理的具有界面的微观非均质材料本构行为的均匀化。这类界面的例子有现代复合材料中的相界或粘接接头、陶瓷中的裂纹或多晶金属中的晶界。目前研究的重点是颗粒和纤维增强复合材料的考虑。对于其他提到的材料，可以直接调用预期的方法。为了使这类材料的本构响应趋于均匀，基于多尺度问题的细观力学原理，提出了一种降阶方法。因此，使用低维函数空间来寻求界面分离矢量和内部变量的空间分布的近似。这种低维空间的参数化是基于数值实验的，它允许考虑几何和物理异质性对宏观本构响应的影响。所考察材料的微观本构行为被建模为广义标准材料(GSM)。那么，宏观尺度上的均匀材料也是广义标准材料，需要建立变分公式。该方法的实施应具有高的数值效率，以便允许在大型结构计算中的宏观模拟的集成点使用所得到的材料模型。