Homogenisation of Microheterogeneous Materials Considering Interfacial Delamination at Finite Strains

In modern engineering, composite materials gained importa nce because of their specific properties requested by the individual application. They consist of inclusions suc h as particles or fibres which are introduced into a binding matrix material in order to “design” special material behav iour. In case of particle inclusions, typical materials are concrete, aluminum-boron or rubber filled with carbon. F ibre reinforced composites are typically stiffened by glass-, carbon- or aramid fibres. Recently, fibre reinforced metals are also subject to detailed investigation and application. In all cases the mechanical behaviour on the mi cro level defines the resulting material behaviour on the macro scale, which is needed from an engineering point of view in an arbitrary design process. The effective properties of the overall material depend on the geometry ofthe microstructure and the material properties of the constituents. In case of finite strains one can observe in terfacial degradation in a cohesive zone between the matrix material and the inclusions. In this paper we focus onthe homogenisation process of such materials with interfacial delamination. Here the difficulties arise fromthe geometrical and material nonlinearities. Even for linear elasticity this homogenisation can hardly be done an alytically. Therefore we apply the finite element method to get a numerical approximation for the mechanical behavio ur of a representative volume element (RVE). The homogenisation then is done with a statistically represent ative set of RVEs. In order to increase the efficiency and accuracy of the computations the finite element meshes are re fined adaptively using non-conforming elements.