The concept of Voronoi tessellation has recently been extensively used in materials science, especially to model the geometrical features of random microstructures like aggregates of grains in polycrystals, patterns of intergranular cracks and composites. Solution of the underlying field equations usually requires use of numerical methods such as finite elements.The framework for automatic generation of quadrilateral finite element meshing of planar Voronoi tessellation is proposed in the paper, resulting in a powerful set of tools to be used in the rather wide field of micromechanics. As far as feasible, the implementation of features built in commercially available mesh generators was pursued. Additionally, the minimum geometric requirements for a "meshable" tessellation are outlined.Special attention is given to the meshes, which enable explicit modelling of grain boundary processes, such as for example contact (closure of cracks) or friction between grains. This is inline with numerical examples, which are oriented towards the fracture mechanics, in particular to the development of intergranular microcracks and/or their impact on the effective behaviour of the polycrystal.The examples were evaluated using the commercially available general-purpose finite element code ABAQUS. The usual continuum mechanics based numerical methods and boundary conditions were safely applied to aggregates of randomly oriented polycrystals with anisotropic elastic material behavior as computational domains.

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To save costs, an early validation of functionality is necessary for the crash application of short fibre reinforced polymers by numerical simulation. For this an experimental determination of mechanical values and a numerical material model is essential. In this work the mechanical values of a short fibre reinforced polymer were determined at varied strain rates and in different directions under compression, shear and tension loading. With data of this experiments a new orthotropic-linear elastic and both orthotropic and strain rate dependent plastic material model is developed. It considers the hydrostatic pressure dependency of the hardening material and a failure which is influenced by directions, strain rates und multiaxial states of stresses. The validation of material model and characteristic mechanical values is conducted by simulations of determining experiments of the material behaviour as well as at dynamic impact tests