This study is focused on the multi-scale modelling strategy for complex and heterogeneous microstructures of real materials by automatic image-based modelling and finite element mesh superposition method. The synergetic application of the conventional asymptotic homogenization method and the authors' mesh superposition method has been proposed to obtain the microscopic responses under high gradient of macroscopic fields at the macroscopic crack tip and/or interface, for instance. For complex and random microstructures, automatic image-based voxel meshing by means of x-ray CT is commonly required; however, it cannot always adapt to the mathematical theory of microscopic modelling in the mesh superposition method. Therefore, a modelling technique for mesh refinement is proposed in this paper using additional elements for insulation in consideration of the theoretical background of the mesh superposition method.In this paper, we provide the modelling procedure and its theoretical consideration of mesh refinement for flexible modelling of real materials. To demonstrate the technique, a numerical example of a porous ceramic component with random microstructure and macroscopic crack is illustrated.
This paper presents the multi-scale stress analysis of trabecular bone by the homogenization method bridging nano-micro-macro scales. Three-dimensional microstructure of trabeculae is obtained by the X-ray CT and the imagebased modeling technique. Biological apatite (BAp) crystallite orientation is considered in the microstructure model by means of the anisotropic mechanical properties. The c-axis of BAp is set up as the maximum principal stress direction under the long term macroscopic stress condition. These properties are automatically assigned to each voxel element. To determine appropriately the microstructure model, the trabeculae morphology is analyzed and quantified as the trabecular density distribution. The proposed method is applied to pig's femur. It was revealed by the morphology analysis and homogenized macroscopic properties that the trabecular bone has plate-like characteristics. The predicted anisotropic level of the macroscopic properties was quantitatively coincident with the measured value by the X-ray diffraction analysis.
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