THE CRITICAL ANGLE OF THE ANISOTROPIC ELASTIC WEDGE SUBJECT TO UNIFORM TRACTIONS

The classical solution for an isotropic elastic wedge loaded by a uniform pressure on one side of the wedge becomes infinite when the wedge angle 2θ0 satisfies the equation tan 2θ0 = 2θ0. This is the critical wedge angle which also renders infinite solutions for other types of loadings. In this paper, we study, the associated problem for the anisotropic elastic wedge. We first present uniform stress solutions which are possible for symmetric loadings. For antisymmetric loadings, a uniform stress solution is in general not possible and we present a non-uniform stress solution in which the stress depends on θ but not on r. The non-uniform stress solution breaks down at a critical angle. We present an equation for the critical angle which depends on the elastic constants. The Stroh formalism is employed in the analysis. An integral representation of the solution is obtained by using new identities which are derived in the paper.