Fast numerical computation of effective elastic moduli of porous materials

A fast numerical solver to compute effective properties of porous elastic composites is presented. Pores can be treated as a material phase with vanishing stiffness (vacuum) or as a compressible or incompressible material phase (e.g. air, water, oil). For the numerical homogenization (of porous materials), the equations of elasticity are reformulated as volume integral equations of Lippmann-Schwinger type for the local strain. This approach is particularly suited for 3D digital images (CT images) of complex microstructures and needs much less computational effort than finite element schemes to predict the effective properties [1]. As new application of this method we calculate amongst other the pore pressure coefficient for digital rocks. For validation the numerical results are compared with results of finite element schemes and measurements.