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Analysis of multiple plastic stress singularities for antiplane V-notches in hardening materials by using the interpolating matrix method

Renyu Ge and Zongjun Hu

Vol. 17 (2022), No. 5, 403–420

Here, an efficient method is given to determine higher-order plastic stress singularities of general antiplane V-notches in a power-law hardening material. Owing to strong stress singularity, the notch tip regions arise in plastic deformation. First, the asymptotic displacement field in terms of radial coordinate at the notch tip is adopted. By introducing the displacement expressions into the fundamental differential equations of the plastic theory, it results in a set of nonlinear ordinary differential equations (ODEs) with the stress singularity orders and the associated eigenfunctions. Then, the interpolating matrix method is used to solve the eigenvalue problems of the ODEs by means of an iteration process. Several leading plastic stress singularity orders of the antiplane V-notches and cracks are obtained. The associated eigenvectors of the displacement and stress fields in the notch tip region are simultaneously determined with the same degree of accuracy. The validity and accuracy of the present method are demonstrated by comparing with the existed results for the typical examples.

antiplane V-notch, hardening material, multiple stress singularity, plasticity, interpolating matrix method
Received: 15 October 2021
Revised: 27 March 2022
Accepted: 10 August 2022
Published: 22 February 2023
Renyu Ge
School of Architecture and Civil Engineering
Anhui Polytechnic University
Zongjun Hu
School of Civil Engineering
Hefei University of Technology