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

该研究项目的目的是对具有界面的微观非均匀材料的本构行为进行基于机制的均匀化。这种界面的例子是现代复合材料中的相界或粘合接头、陶瓷中的裂纹或多晶金属中的晶界。本研究的重点是考虑颗粒和纤维增强复合材料。预期的方法可以直接用于其他提到的材料。为了均匀化这类材料的本构响应，基于多尺度问题的细观力学发展了一种降阶方法。因此，寻求使用低维函数空间的界面分离矢量和内部变量的空间分布的近似。这个低维空间的参数化是基于数值实验，它允许考虑的影响，几何和物理的不均匀性，对宏观本构响应。被检查的材料的微观本构行为建模为一个广义标准材料（GSM）。然后均匀化材料在宏观尺度上也是一个广义的标准材料的变分公式是要开发。该方法的实施应归因于高数值效率，以允许在大规模结构计算中的宏观模拟的积分点处使用所得的材料模型。

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.