On a novel approach to the problem of the concentration of elastic stresses near a crack

Abstract

The three-dimensional problem of the theory of elasticity dealing with the concentration of stresses near plane cracks is used to describe a novel approach to solving the problem. The proposed approach is based, unlike the traditional approach, on obtaining an expression for the stress field as simple as that for the displacements, but using new harmonic functions connected, in a prescribed manner, with the normally used harmonic functions of the displacement field. In the case of a plane plane crack the new representation for the stress field leads to three-dimensional integral equations of a single type and solvable separately, replacing the system of three integrodifferential equations of the traditional approach. Moreover, the simple integral equations obtained must be solved in a wider than usual class of functions, namely on the class of functions containing non-integrable singularities. All this leads to a significant simplification of the formula for the stress intensity coefficient.