Computational semi-analytic code for stress singularity analysis

Abstract

Problems of stress singularities in single or multi-material corners have been addressed by many authors over the years. Most of the authors presented closed-form corner-eigenequations for special cases, and often there is no easy way to check if the solution is correct. In this work, we present a general computational tool that can solve many different cases of stress singularity problems for multi-material corners under generalized plane strain. The semi-analytic code is based on the matrix formalism presented in Mantič et al. (1997, 2014); Barroso et al. (2003); Herrera-Garrido et al. (2022) and is developed in MATLAB. The following boundary conditions are implemented: stress-free, fixed, 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), or frictional sliding. The following interface condition between two consecutive materials are implemented: perfectly bonded, and frictionless or frictional sliding. The code can analyze both open and closed (periodic) corners, composed of one or multiple materials with isotropic, transversely isotropic or orthotropic (with any orientation) constitutive laws. The code has proven to be a reliable, very accurate, robust and easy-to-use tool, which has been verified by comparing the results computed with those obtained by other authors. A summary of the corner singularity problems solved is presented. The results of the corner singularity analysis obtained by the code can be further used for prediction of crack onset at the corner tip by the Coupled Criterion of Finite Fracture Mechanics and FEM, see García and Leguillon (2012) and references therein.