A powerful matrix formalism for stress singularities in anisotropic multi-material corners. Homogeneous (orthogonal) boundary and interface conditions

Abstract

A computational code based on a semianalytic procedure for the determination of the characteristic exponents and the singular stress and displacement fields in multi-material corners is developed. Linear elastic anisotropic materials under generalized plane strain state are considered. This code is a universal computational tool able to analyze both open and closed (periodic) corners, composed of one or multiple materials with isotropic, transversely isotropic or orthotropic constitutive laws, covering both mathematically non-degenerate and degenerate materials in the framework of Stroh formalism. In multi-material corners, material junctions with perfectly bonded or frictionless sliding interfaces can be studied. The considered homogeneous boundary conditions cover stress free and fixed faces, or faces with some restricted or allowed direction of displacements, defined either in the reference frame aligned with the cylindrical coordinate system or in an inclined reference frame. The code is developed in MATLAB and it is based on the Stroh matrix formalism for anisotropic elasticity, the concept of transfer matrix for single material wedges, and on the matrix formalism for homogeneous (orthogonal) boundary conditions. The comparison of the characteristic exponents obtained by the present code and by the solution of closed-form eigenequations available in the literature, has a two-fold objective, first to exhaustively check the general computational implementation of the matrix formalism presented, and second to check the closed-form expressions of eigenequations for relevant specific cases published in the literature.