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Microscale modelling and homogenization of fiber structured materials

Various phenomena occurring on the macrosscale result from physical and mechanical behaviour on the microscale [1]. For the mechanical modeling and simulation of the heterogeneous composition of fiber structured material, in addition to the material properties the contact between the fibers has to be taken into account. The material behaviour is strongly influenced by the material properties of the fiber, but also by the geometrical structure. Periodically arranged fibers like woven, knitted or plaited fabrics and randomly oriented ones like fleece can be distinguished in their arrangement. In consideration of different lengthscales the problem involves, it is necessary to introduce a multiscale approach based on the concept of a representative volume element (RVE). The macro‐micro scale transition requires a method to impose the deformation gradient on the RVE by suited boundary conditions. The reversing scale transition, based on the HILL‐MANDEL condition, requires the equality of the macroscopic average of the variation of work on the RVE and the local variation of the work on the macroscale [2]. For the micro‐macro transition the averaged stresses have to be extracted by a homogenization scheme. From these results an effective material law can be derived. Beside the theoretical aspects, we present the stress‐strain relation for RVE‐models and different boundary conditions. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)