Effective Thermoviscoelasticity of a Saturated Porous Ground

The linearized model of reciprocal motion of an elastic porous body and a viscous compressible liquid in pores is considered, with the heat transfer effect being taken into account. It is assumed that the porous body has a periodic geometry and that the ratio of the pattern periodic cell and the diameter of the entire thermo-mechanical system is a small parameter in the model. The homogenization procedure, i.e. a limiting passage as the small parameter tends to zero, is fulfilled. As the result, we conclude that the limiting distributions of temperature and displacements of the media solve a well-posed initial-boundary value problem for the model of linear thermoviscoelasticity with memory of shape and heat. Moreover, coefficients of this newly constructed model arise from microstructure, more precisely; they are uniquely defined by data in the original model. Homogenization procedure is based on the method of two-scale convergence and is mathematically rigorously justified.