Volume 42 Issue 12
Dec.  2021
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LI Cong, HU Bin, NIU Zhongrong. Asymptotic Solutions of Plastic Stress and Displacement at V-Notch Tips Under Anti-Plane Shear[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1258-1275. doi: 10.21656/1000-0887.420045
Citation: LI Cong, HU Bin, NIU Zhongrong. Asymptotic Solutions of Plastic Stress and Displacement at V-Notch Tips Under Anti-Plane Shear[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1258-1275. doi: 10.21656/1000-0887.420045

Asymptotic Solutions of Plastic Stress and Displacement at V-Notch Tips Under Anti-Plane Shear

doi: 10.21656/1000-0887.420045
  • Received Date: 2021-02-20
  • Accepted Date: 2021-02-20
  • Rev Recd Date: 2021-05-27
  • Available Online: 2021-11-23
  • Publish Date: 2021-12-01
  • An efficient method was developed to determine the first- and high-order terms of asymptotic solutions of plastic stress and displacement near V-notch tips under anti-plane shear in power-law hardening materials. Through introduction of the asymptotic series expansions of stress and displacement fields around the V-notch tip into the fundamental equations of the elastoplastic theory, the governing ordinary differential equations (ODEs) with the stress and displacement eigen-functions were established. Then the interpolating matrix method was employed to solve the resulting nonlinear and linear ODEs. Consequently, the high-order stress exponents and the associated eigen-solutions were obtained. The presented method, being capable of dealing with the V-notches with arbitrary opening angles and strain hardening indexes under anti-plane shear, has the advantages of great versatility and high accuracy. Typical examples were given to demonstrate the accuracy and effectiveness of this method.

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