An important drawback of the classical continuum mechanics is idealization of inhomogenous microstructure of materials. Approaches, which model material behavior on mesosocopic level and can take inhomogenous microstructure of materials into the account, typically appeared over the last decade. Nevertheless, entirely anisotropic approach towards material behavior of a single grain is still not widely used. The proposed approach divides the polycrystalline aggregate into a set of grains by utilizing Voronoi tessellation (random grain structure). Each grain is assumed to be a monocrystal with random orientation of crystal lattice. Mesoscopic response of grains is modeled with anisotropic elasticity and crystal plasticity. Strain and stress fields are calculated using finite element method. Material parameters for pressure vessel steel 22 NiMoCr 3 7 are used in analysis. The analysis is limited to 2D models. Applications of the proposed approach include (a) the estimation of the minimum component/specimen size needed for the homogeneity assumption to become valid and (b) the estimation of the correlation lengths in the resulting mesoscopical stress fields, which may be used in well-established macroscopical material models. Both applications are supported with numerical examples and discussion of numerical results.

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