Computer experiments were performed to investigate behavior of mesoscopic stress responses in a simulated polycrystalline material sample containing a fairly large number of constituent grains for a number of polycrystalline materials. Kro¨ner-Kneer structure-based model was adopted and refined to provide an efficacious numerical approach to local mesoscopic stresses. The approach is developed on a concept of average fields of grains for arbitrarily polygon-shaped grains. Three criteria were proposed for classifying speculated material structure weaknesses in all simulated material samples. It is found that material structure weaknesses can be well correlated by defined “Orientation-Geometry Factor” and “Relevance Parameter.” Not only grain-orientation but also grain geometry exerts strong influences on mesoscopic stress distribution, hence the distribution of material structure weaknesses in simulated polycrystalline material samples. Computer experiments lead to correlated relationships that links material structure weaknesses with local microstructure, and a database for discrimination of material structure weaknesses in the material samples. The homogenization of materials with locally anisotropic microstructure is also discussed.
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