A semi-analytical matrix formalism for stress singularities in anisotropic multi-material corners with frictional boundary and interface conditions

Abstract

A new general semi-analytic procedure for the characterisation of singular asymptotic elastic states in the vicinity of the apex of linearly elastic anisotropic multi-material corners, including frictional contact, is developed and tested. The corners can consist of any finite number of homogeneous wedges defined by polar sectors. The variability of configurations covered is enormous as frictional contact can be considered on one or more outer boundary surfaces or interfaces, in addition to a large variety of homogeneous boundary conditions and perfect bonding or frictionless sliding interface conditions between wedges in the corner. The Coulomb rate-independent and dry frictional contact law is assumed. One of the novelties is that, in addition to the singularity exponent λ, the angle ω of the friction tangential stress vector on each frictional contact surface is an a priory unknown to be determined by solving a nonlinear corner eigensystem. The procedure, which considers power-law stress singularities, is based on the Stroh formalism of anisotropic elasticity, assuming generalised plane strain (2.5D) conditions, and on the semi-analytic matrix formalism for wedge transfer-matrices and boundary and interface condition matrices. This makes it, firstly, very suitable for computational implementations, secondly, very efficient especially in cases with several perfectly bonded homogeneous wedges, and, thirdly, very accurate due to its fully semi-analytic nature. The code developed is tested by solving a large variety of examples, comparing the present results with those obtained by solving closed-form corner-eigenequations deduced by previous authors for specific useful practical configurations, confirming the extremely high accuracy of the present code in the computation of λ and ω. The differences observed in some cases with anisotropic materials are explained by the fact that some of the previous authors did not take the true 3D Coulomb friction law into account.