Effective Thermoviscoelasticity of a Saturated Porous Ground
Abstract: The linearized model of joint motion of an elastic heat-conducting porous skeleton and a viscous compressible thermofluid filling the pore space is considered. It is assumed that the pore space has a periodic geometry and the model incorporates a small parameter, which is the ratio of micro- and macroscopic length scales. A homogenization procedure, i.e., a limiting transition as the small parameter tends to zero, is fulfilled. It is established as the result, that the limiting distributions of displacements and temperature solve a well-posed homogenized linear model of thermoviscoelasticity with shape and heat memory. Moreover, the coefficients of the homogenized model are uniquely defined by data given for microstructure. The homogenization procedure is fulfilled fully rigorously by means of the two-scale convergence method.