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

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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.