Abstract
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.
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References
Lin Bai-song, Perfectly plastic stress fields at a stationary crack tip,Applied Mathematics and Mechanics,6, 5 (1985), 431 - 438.
Lin Bai-song, Elastic perfectly-plastic fields at a rapidly propagating crack-tip,Applied Mathematics and Mechanics,6, 10 (1985), 1017 - 1025.
Hill, R.,The Mathematical Theory of Plasticity, Oxford (1950).
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Communicated by Chien Wei-zang
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Bai-song, L. Anisotropic plastic stress field near a singular point. Appl Math Mech 8, 767–772 (1987). https://doi.org/10.1007/BF02017984
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DOI: https://doi.org/10.1007/BF02017984