Anisotropic Elasticity and Multi-material Singularities

Abstract

Multi-material wedges associated with convergence of geometrical and material discontinuity generally show singular stress fields. Under a temperature load, the different sectors of the wedge experience incompatible thermal expansions. Jumps of the tangential thermal strains across the various radial interfaces of the wedge may be compensated by a suitable particular solution. The remote boundary condition are then taken care of by combining the particular solution with various eigensolutions of the wedge. In this work, a general scheme is developed for constructing particular solutions of arbitrary multi-material wedges under uniform temperature loads. These closed-form particular solutions generally contain terms with logarithmic dependence on the radial coordinate r. The solution scheme also yields particular solutions when the loading on the multi-material wedge is a uniform strain ∞ z in the out-of plane direction.