Homogenization of heterogeneous, fibre structured materials

This contribution presents a multi-scale homogenization method to model fibre structured materials. On the macroscopic level textiles are characterized by a large area-to-thickness ratio, such that a discretization with shell elements is numerically efficient. The material behavior is strongly influenced by the heterogeneous micro structure. To capture the contact on the micro level, the RVE is explicitly modelled by means of a volumetric micro sample and a shell specific homogenization scheme is applied to transfer the microscopic response to the macro level. Theoretical aspects are discussed and a numerical example for contact behavior of a periodic knitted structure is give