The Investigation of Problems of Healing of Cracks by Injection of Fluids with Inclusions in Various Thermoelastic Media

The purpose of this paper is to investigate the problem of healing of cracks in infinite thermo elastic surroundings by currents of fluids with inclusions. The process of healing is result of growing of layer of sediments on crack’s surfaces due to transverse diffusion currents of crystalline inclusions which leads to closing of crack. The obtained analytical formulae for vertical displacements of boundary of crack and graphs of it allow determine coordinates and time moments of zero width of crack, i.e. process of healing of crack. The applications to biological and technological problems when as mixture is used fluid with camphor crystalline as well as to geothermal cracks with fluid currents containing silicon crystalline with application to geophysics, and results of calculations also can be used in meso mechanics. The investigation of obtained curves of dependence of times and coordinates of healing of cracks processes is done as by deterministic treatment, as well as on account of possible randomness, taking places for micro sizes of cracks by methods of nonlinear wave dynamics. The main methods of investigation of healing problem for cracks are taking into account of thermo diffusion and thermo elasticity stresses and displacements effects and trybological supplements in boundary condition on the cracks., and solution of posed problem of thermo elasticity by method of integral transformations of Laplace and Fourier, method of Winner-Hopf. The analytical solution for displacements of mentioned unsteady plane problem is brought to effective Smirnov-Sobolev form. The calculations of integrals for displacements on crack surface are carried out for number of typical constants of media and parameters of biomechanical, technological, geophysical, nanophysics problems. Furthermore there are carried out applications of methods of nonlinear wave dynamics to finding of probabilities of processes of healing of cracks.These analytic and numerical methods based on dynamic thermo-elasticity approximation on account of diffusion currents of inclusions in fluid mixture in cracks allow determine time and coordinate of closing of cracks. Besides are examined obtained curves of healing processes by methods of nonlinear waves dynamics. These methods can be applied also to extremely processes of transition from meso level defects to synchronized processes of generation of macro cracks and fracture.