STATISTICAL HOMOGENIZATION OF RANDOM POROUS MEDIA

Abstract

. In recent times, the scientific community paid great attention to the influence of inher-ent uncertainties on system behavior and recognize the importance of stochastic and statistical approaches to engineering problems [21]. In particular, statistical computational methods may be useful to the constitutive characterization of complex materials, such as composite materials characterized by non-periodic internal micro-structure. Random porous media exhibit a microstructure made of randomly distributed pores embedded into a continuous matrix. They can be modelled as a bi-material system in which circular soft inclusions (pores) with random distribution and variable diameters are dispersed in a stiffer matrix. A key aspect, recently investigated by many researchers, is the evaluation of appropriate mechanical properties to be adopted for the study of their behaviour. Differently from classical homogenization approaches, in the case of materials with random microstructure it is not possible to ‘a-priori’ define a Representative Volume Element (RVE), this being an unknown of the problem. Statistical homogenization procedures may be adopted for the