Applied Mathematics and Mechanics

, Volume 8, Issue 8, pp 767–772 | Cite as

Anisotropic plastic stress field near a singular point

  • Lin Bai-song


On condition that any perfectly plastic stress component near a singular point is nothing but the function of θ only, making use of equilibrium equations and Hill anisotropic yield condition, we derive the general analytical expressions of the anisotropic plastic stress field near a singular point in both the cases of anti-plane and in-plane strains. Applying these general analytical expressions to the concrete cracks and the plane-strain bodies with a singular point, the anisotropic plastic stress fields at the tips of Mode I, Mode II, Mode III and mixed mode I–II cracks, and the limit loads of anisotropic plastic plane-strain bodies with a singular point are obtained.


Mathematical Modeling Singular Point Industrial Mathematic General Analytical Expression Equilibrium Equation 
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    Lin Bai-song, Perfectly plastic stress fields at a stationary crack tip,Applied Mathematics and Mechanics,6, 5 (1985), 431 - 438.CrossRefGoogle Scholar
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    Lin Bai-song, Elastic perfectly-plastic fields at a rapidly propagating crack-tip,Applied Mathematics and Mechanics,6, 10 (1985), 1017 - 1025.CrossRefGoogle Scholar
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    Hill, R.,The Mathematical Theory of Plasticity, Oxford (1950).Google Scholar
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    Kachanov, L.M.,Foundation of the Theory of Plasticity, London (1971).Google Scholar

Copyright information

© Shanghai University of Technology 1987

Authors and Affiliations

  • Lin Bai-song
    • 1
  1. 1.Central-South University of TechnologyChangsha

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