A porothermoelasticity theory for anisotropic medium

Abstract

The concept of porothermoelasticity has been developed to investigate the thermal and mechanical behavior of elastic materials with porosity. This approach combines the theory of heat conduction with poroelastic constitutive equations and by incorporating the coupling of temperature field with the stresses and pore pressure. The mathematical modeling of the porothermoelastic material to various practical problems has attracted researchers in recent years due to its wide applications to geomechanics, where the coupled thermal and poro-mechanical processes play an essential role. The porothermoelasticity theory with relaxation parameter and predicting the finite speed for the isotropic medium has been established by Youssef (Int J Rock Mech Min 44(2):222–227, 2007) and by Sherief and Hussein (Transp Porous Med 91(1):199–223, 2012). However, the governing equations of the porothermoelasticity theory including the effects of temperature as well as temperature-rate terms for an anisotropic medium are yet to be derived. Hence, in view of the useful applications of the subject, the present work is motivated to derive the set of governing equations for the theory of temperature-rate-dependent fluid-saturated anisotropic poroelastic medium from the fundamental laws of thermodynamics. Further, we establish a uniqueness theorem for the general porothermoelastic problem of an anisotropic medium based on the present theory. Lastly, we solve a half-space problem of porothermoelasticity for isotropic medium to show the implementation of the present theory and investigate the effects of the relaxation times and porosity parameter over the distributions of various field variables by considering kerosene-saturated sandstone medium. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.