Thermoelastic Analysis of Porous Media Using a Multiscale Asymptotic Expansion Homogenization Method

Abstract

In this study, a multiscale finite element analysis coupled with the asymptotic expansion homogenization (AEH) method is employed to investigate the linear thermoelastic behavior of a porous medium. A stochastic method using a mixture of Gaussian functions distribution is used to generate microstructures. The simulated microstructures are produced based on the porosity of a Marcellus shale sample. The AEH method is used to determine the homogenized material properties of simulated random microstructures. A porous medium with material and transport properties that vary between the bedding layers and the matrix is generated. The influence of gas pressure, as well as thermal and mechanical loading on the porous medium is studied and the influence of the pore size and porosity of microstructures on the evolution of stress is investigated.