The influence of external action on the dynamics of elastic, thermal and concentration waves propagation

Abstract

This paper presents the nonlinear coupled mathematical model allowing investigating the interrelation between the mechanical, thermal and diffusion processes in solid body. The model takes into account the finiteness of relaxation times of mass and heat fluxes. This is of interest for dynamical processes with characteristic times comparable to relaxation times, when the changes in the temperature and impurity concentration are described by hyperbolic thermal conductivity and diffusion equations. Additionally, the model takes into account the temperature and concentration dependencies of the diffusion coefficients; it gives rise to additional nonlinearity. The model is thermodynamically consistent and follows from the nonlinear equations of the thermoelastic diffusion theory. The implicit difference scheme of second approximation order in time and spatial steps, linearization relatively to known time moment and double-sweep method are used for the numerical implementation of the equation system. Examples of interrelating wave propagating under external actions are considered. The results show that distortions in the strain/stress and temperature distributions appear due to the interaction between the phenomena of different physical nature. The specific rates of different physical processes are different. Although diffusion is the slowest of them all, the influence of the diffusion wave is reflected in stress and strain waves far beyond the diffusion wave front. It is shown that regardless of the external action character and impulse form, the influence of the considered processes on each other does not change, but the wave picture becomes much more complicated with increasing number of actions.