Non-local Stress Analysis of Heterogeneous Media by Image-based. Mesh Superposition Method and Its Verification

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By combining the orginal Finite Element Mesh Superposition Method and the Image-based Modeling technology with high-resolution X-ray CT system, a novel "Image-based Mesh Superposition Meth" has been proposed. The proposed method can solve such non-local stress problems as interface problems, locally apppearing yielding zone or damaged zone and problems with high strain gradient. Hence, this method can overcome the problems to which the current multi-scale computational methods can not be applied.The high-resolution X-ray CT used in this study can provide the CT images with 2.6μm resolution. The numerical model for finite element analysis is automatically generated using the voxel finite elements. To solve the very large-scale algebraic equations generated by this image-based modeling technique, an element-by-element iterative solver and the out-of-core skyline method with renumbering by RCM method are used. To determine the microstructure model, a morphology analysis methodology has al … More so been proposed. The macroscopic model is generated using the homogenized (averaged) mechanical properties calculated by the asymptotic homogenization theory. The microscopic stress is calculated by the original finite element mesh superposition method. On a standard personal computer, a three-dimensional non-local problem with approximately 100,000 voxel elements is solvable.The developed computational method has been applied to real porous ceramics. The predicted homogenized properties of porous alumina with needle-like pores have been verified through comparison with experimentally measured values. The error was only 1%. To verify the accuracy of the microscopic stress calculated by the mesh superposition method, two-dimensional analysis has been carried out and compared with conventional finite element analysis with fine mesh. For a two-dimensional interface crack problem of dissimilar porous materials, very good coincidence was obtained between the proposed and reference analyses.To visualize the calculated three-dimensional distribution of the microscopic stresses, original software named V-SEM (Visualization and Stress Evaluation of material Microstructures) has been developed especially designed for the image-based multi-scale analysis. It is helpful to evaluate the microscopic stress quantitatively by plotting the histogram. Less