About the damage to building materials and structures

We consider the damage to building materials and structures as the initial stage of dynamic process of its destruction. For the mathematical description of the initial stage of material destruction we apply recently proposed mathematical model of a non-equilibrium phase transitions formulated in terms of the Cahn-Hillard theory of spinodal decomposition. The representation of the damage process as a non-equilibrium phase transitions is carried out on the principles of thermodynamics and taking into account the specific geometric forms of the investigated construction. This allows to describe the damage process in details. So, the changes in building material under load due to the mechanisms of creep, plasticity, ductile or brittle fracture are considered as a non-equilibrium phase transitions. A mathematical model is a one-dimensional spatial variables initial-boundary problem for a system of four differential equations of second and fourth orders. Because of the nonlinearity of the system its analytical solution is difficult. So for it solution, we apply numerical methods. For the numerical solution of the problem a finite-difference scheme of second order accuracy is used. The numerical results confirm the conclusion that the mathematical model describes the main features of the process. Numerical study of one-dimensional models allows to go to the two-dimensional case and compared obtained results with experimental data