Stochastic homogenization analysis of a porous material with the perturbation method considering a microscopic geometrical random variation

• We analyze a stochastic homogenization problem of a periodic porous material.
• Microscopic geometrical random variations are considered.
• The perturbation method and the finite difference method are employed for analysis.
• Accuracy of the several orders of the perturbation approach is investigated.
• The method is validated compared with an experimental result for a practical problem.

This paper discusses stochastic homogenization analysis of a periodic porous material fabricated using a rapid prototyping technique. A rapid prototyping system will be helpful to fabricate an order-made structure stably consisting of a porous material having a desired void distribution than a general porous material, but the influence of a geometrical random variation of pores should be still investigated, because some geometrical parameters are difficult to be perfectly controlled. In this paper, the stochastic homogenization analysis is performed for evaluation of the probabilistic characteristics of the homogenized elastic properties for a geometrical random variation in microstructure. The perturbation-based approach with the finite difference scheme is proposed for stochastic homogenization analysis of the porous material considering a parametric geometrical random variation. Influence of the random variations of microscopic geometry parameters on the homogenized elastic property is investigated, and accuracy of the finite difference based perturbation approach is discussed. In addition, a numerical result is compared to the experimental result, and applicability of the stochastic homogenization analysis to a practical problem is investigated.