Mathematical simulation and solution of the problem of cracking under coatings in elastic bodies

We propose a mathematical model for the description of the stress-strain state of a body with coating in the presence of a crack located on their interface. In this model, we take into account the correlations between all types of strains in the coating and in the body. We deduce integro-differential equations with integration over the region covered by the crack for the determination of the jump of displacements on its opposite faces. This approach enables one to evaluate both the concentration of stresses in the vicinity of the crack and the degree of buckling of the coating caused by the opening displacement of the crack faces.