Mathematical model of destruction of a thermoporoelastic medium

The work is devoted to the development of a mathematical model for describing the evolution of a thermoelastic medium with account for its destruction. The model is a modifi cation of the Biot three-dimensional model with two continua: a porous deformable skeleton and a mobile single-phase fl uid. The system of equations consists of fundamental mass, momentum, and energy conservation laws and is closed by thermodynamically coordinated determining relations. To derive the determining relations, use is made of the second law of thermodynamics that accounts for irreversible energy expenditures on the formation of a new surface of cracks. The form of the determining relations was obtained with the use of the Coleman–Noll procedure, which guarantees their thermodynamic coordination. The destruction of a medium is considered within the framework of the theory of continual destruction. To quantitatively estimate the degree of destruction, the damageability parameter is introduced, which is involved in all of the basic determining relations and, in particular, exerts its infl uence on the magnitude of elastic moduli. To determine the evolution of the damageability parameter, use is made of a kinetic equation. The applicability of the proposed model is shown with the example of calculation modeling heat carrier pumping into a thermoelastic medium
The work is devoted to the development of a mathematical model for describing the evolution of a thermoelastic medium with account for its destruction. The model is a modifi cation of the Biot three-dimensional model with two continua: a porous deformable skeleton and a mobile single-phase fl uid. The system of equations consists of fundamental mass, momentum, and energy conservation laws and is closed by thermodynamically coordinated determining relations. To derive the determining relations, use is made of the second law of thermodynamics that accounts for irreversible energy expenditures on the formation of a new surface of cracks. The form of the determining relations was obtained with the use of the Coleman–Noll procedure, which guarantees their thermodynamic coordination. The destruction of a medium is considered within the framework of the theory of continual destruction. To quantitatively estimate the degree of destruction, the damageability parameter is introduced, which is involved in all of the basic determining relations and, in particular, exerts its infl uence on the magnitude of elastic moduli. To determine the evolution of the damageability parameter, use is made of a kinetic equation. The applicability of the proposed model is shown with the example of calculation modeling heat carrier pumping into a thermoelastic medium
Author:  A. S. Meretina E. B. Savenkov
Keywords:  thermoporoelasticity, destruction, thermodynamic coordination, Coleman–Noll procedure
Page:  365-376