The dilatation line in an elastic wedge

Abstract

A solution for a dilatation line which occupies an arbitrary position in an elastic wedge with free surfaces and an arbitrary apex angle is found for the first time. The analytical expressions are given in the Mellin space for the stress fields of the dilatation line. It is shown that the free surfaces of the wedge strongly affect upon the stress fields. The axial and hydrostatic stress components are not equal to zero outside the dilatation line. They are strongly inhomogeneous and can change their signs, while their magnitude is comparable with that of the other non-vanishing stress components. They also demonstrate strong non-monotonic and alternating dependence on the wedge apex angle. For the wedge apex angles of 180° and 360°, the non-vanishing stress components of the dilatation line are represented in an explicit form. The results obtained can be used for solving similar problems for long elastic dilatation inclusions of arbitrary cross section embedded to wedge-shaped elastic bodies. The paper is devoted to the memory of our friend and colleague Igor Sevostianov who gave a great contribution to micromechanics of composite and porous materials.