Stress Concentration near an Elastic Ellipsoidal Inclusion in an Infinite Body

The elastic problem is considered for a body containing an ellipsoidal inclusion under the conditions of uniaxial tension. The problem is reduced to the solution of a system of three integro-differential equations for the jumps of stresses and displacements on the surfaces of the inclusion. The exact solution of these equations is obtained and relations for the approximate evaluation of stresses in the matrix and inclusion are presented. Various special cases of the problem are analyzed and fairly simple formulas convenient for the engineering strength analysis of inhomogeneous bodies are deduced.