Three-dimensional constitutive relations of ideal plasticity and the flow on the coulomb-tresca prism edge |
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Authors: | V A Kovalev Yu N Radaev |
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Institution: | (1) Department of Mechanical Engineering, Florida State University, 32303 Tallahassee, FL, USA |
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Abstract: | In the present paper, we consider basic relations of the mathematical theory of plasticity for the spatial state corresponding
to the edge of the Coulomb-Tresca prism, which follow from the generalized associated flow law restricting the plastic flow
freedom for the above states to the minimal possible extent. We found that the spatial relations of the theory of plasticity,
formulated by A. Yu. Ishlinsky in 1946, can be derived from the above version of the theory of flow. We show that the A. Yu.
Ishlinsky constitutive relations for states on the Coulomb-Tresca prism edge express the commutativity of the stress tensor
and the tensor of plastic strain increments. We obtained one explicit form of the constitutive relation relating the stress
tensor to the plastic strain increments for the stressed states corresponding to the Coulomb-Tresca prism edge. |
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