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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 |
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Vol. 17 (2022), No. 5, 403–420
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Abstract |
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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. |
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Keywords
antiplane V-notch, hardening material, multiple stress
singularity, plasticity, interpolating matrix method
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Milestones
Received: 15 October 2021
Revised: 27 March 2022
Accepted: 10 August 2022
Published: 22 February 2023
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Authors |
| Renyu Ge | |
| School of Architecture and Civil
Engineering Anhui Polytechnic University Wuhu China |
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| Zongjun Hu | |
| School of Civil Engineering Hefei University of Technology Hefei China |
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