Homogenization and modeling of fiber structured materials

Abstract

For the mechanical modeling and simulation of the heterogeneous composition of a fiber structured material, the material properties at the micro level and the contact between the fibers have to be taken into account. The material behavior is strongly influenced by the material properties of the fibers, but also by their geometrical arrangement. In consideration of the different length scales the problem involves, it is necessary to introduce a multi scale approach based on the concept of a representative volume element (RVE). For planar structures like technical textiles the macromodel is discretized by shell elements. In contrast the microscopic RVE is modeled with three dimensional elements to account for the contact between the fibers. The macro-micro scale transition requires a method to impose the deformation at a macroscopic point onto 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. For the micromacro transition the averaged forces and the resulting moments have to be extracted by a homogenization scheme. From these results an effective constitutive law can be derived.