Numerical modelling and homogenized constitutive law of large deforming fluid saturated heterogeneous solids

In this paper we treat interactions between large deforming solid and fluid media at the microscopic level. This phenomenon is responsible for viscoelastic behaviour observed as the hereditary creep at the macroscopic scale where the material model is described in terms of the homogenized (effective) parameters. The local microscopic and the upscaled global macroscopic problems are derived for the locally periodic porous microstructure with several inclusions. The parallel computational strategy is proposed to solve the local problems associated with specific microstructures evolving in time. On numerical examples using various geometries of the microstructures we demonstrate how the homogenized properties depend on deformation–diffusion processes undergoing in a particular micro-configuration.