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インパクトファクター: 1.016 5年インパクトファクター: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN 印刷: 1543-1649
ISSN オンライン: 1940-4352

# International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v9.i4.50
pages 409-423

## INVERSE STOCHASTIC HOMOGENIZATION ANALYSIS FOR A PARTICLE-REINFORCED COMPOSITE MATERIAL WITH THE MONTE CARLO SIMULATION

Sei-ichiro Sakata
Department of Electronic and Control Systems Engineering, Interdisciplinary Faculty of Science and Engineering, Shimane University, Japan
F. Ashida
Department of Electronic and Control Systems Engineering, Interdisciplinary Faculty of Science and Engineering, Shimane University, Japan
Y. Shimizu
Graduate School of Shimane University, Japan

### 要約

This paper proposes a numerical method for identifying microscopic randomness in an elastic property of a component material of a particle-reinforced composite material. Some reports on the stochastic homogenization analysis considering a microscopic random variation can be found in the literature. A microscopic stress field is influenced by the microscopic variation, and stochastic microscopic stress analysis is also important. In the previous reports it is assumed that the microscopic random variation is known. However, it is sometimes difficult to identify a microscopic random variation in a composite material, especially after the manufacturing process. Therefore, an identification process for microscopic randomness by solving an inverse problem is needed for the stochastic microscopic stress analysis. This kind of problem is called "inverse stochastic homogenization." In this paper solving an inverse stochastic homogenization problem is attempted with inverse homogenization analysis and Monte Carlo simulation is used for the stochastic homogenization analysis. The inverse homogenization analysis is performed with the homogenization method and an optimization technique. Some techniques for the inverse stochastic homogenization analysis with the Monte Carlo simulation are developed. With numerical results, validity and accuracy of the methods are discussed.

### 参考

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2. Guedes, M. and Kikuchi, N., Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. DOI: 10.1016/0045-7825(90)90148-F

3. Kaminski, M. and Kleiber, M., Perturbation based stochastic finite element method for homogenization of two-phase elastic composites. DOI: 10.1016/S0045-7949(00)00116-4

4. Kaminski, M., Stochastic finite element method homogenization of heat conduction problem in fiber composites.

5. Kaminski, M., Generalized perturbation-based stochastic finite element method in elastostatics. DOI: 10.1016/j.compstruc.2006.08.077

6. Kaminski, M., Sensitivity and randomness in homogenization of periodic fiber-reinforced composites via the response function method. DOI: 10.1016/j.ijsolstr.2008.10.003

7. Kennedy, J. and Eberhart, R. C., Particle swarm optimization.

8. Mori, T. and Tanaka, K., Average stress in matrix and average elastic energy of materials with misfitting inclusions. DOI: 10.1016/0001-6160(73)90064-3

9. Press, W. H., Teukolski, S. A., Vetterling, W. T., and Flannery, B. P., Numerical Recipes in C (Japanese Ed.).

10. Sakata, S., Ashida, F., Kojima, T., and Zako, M., Three-dimensional stochastic analysis using a perturbation-based homogenization method for homogenized elastic property of inhomogeneous material considering microscopic uncertainty.

11. Sakata, S., Ashida, F., and Kojima, T., Stochastic homogenization analysis on elastic properties of fiber reinforced composites using the equivalent inclusion method and perturbation method.

12. Sakata, S., Ashida, F., and Zako, M., Kriging-based approximate stochastic homogenization analysis for composite material. DOI: 10.1016/j.cma.2007.12.011

13. Sakata, S. and Ashida, F., Ns-Kriging based microstructural optimization applied to minimizing stochastic variation of homogenized elasticity of fiber reinforced composites. DOI: 10.1007/s00158-008-0296-6

14. Sakata, S., Ashida, F., and Kojima, T., Stochastic homogenization analysis for thermal expansion coefficients of fiber reinforced composites using the equivalent inclusion method with perturbation-based approach. DOI: 10.1016/j.compstruc.2009.12.007

15. Sakata, S., Ashida, F., and Enya, K., Stochastic analysis of microscopic stress in fiber reinforced composites considering uncertainty in a microscopic elastic property. DOI: 10.1299/jmmp.4.568

16. Stefanou, G., The stochastic finite element method: Past, present and future. DOI: 10.1016/j.cma.2008.11.007

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