High-order Asymptotic Analysis for the V-notch in a Power-law Hardening Material

The aim of this study is to determine the complete elastic–plastic stress asymptotic solutions at the plane V-notch tip with the two edges being clamped–clamped, free-clamped and free-friction. Firstly, the displacement and stress fields around the notch tip are expressed as asymptotic expansions, and then, these asymptotic expansions are substituted into the displacement–strain relation and the equilibrium equations to establish the ordinary differential equations (ODEs). Finally, the interpolating matrix method is employed to solve the eigenvalue problem of the ODEs, and consequently, the leading-order and higher-order stress and displacement eigen-solutions at the notch tip are obtained. Numerical examples demonstrate that the presented method has the advantages of great versatility and high accuracy.