Abstract
The equilibrium and compatibility equations for viscoplastic medium with an arbitrary material function relating the stress intensity to the strain rate intensity is considered. A general form of the function ensuring complete integrability of two-dimensional equations has been found. The obtained function has an N-shaped (spinodal) graph and in particular cases corresponds to a linearly viscous liquid and perfectly plastic solid. A change of the strain rate sensitivity sign corresponds to a change in the type of the system and passing over the discontinuity line in a solid. The obtained function provides decoupling of the operator in a pair of two-dimensional subspaces where the equations are exactly linearized. The results of this study allows us to extend the class of integrable problems to so-called “active materials” (or “materials with internal dynamics”), which have aroused considerable interest.
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Original Russian Text © I.E. Keller, 2013, published in Doklady Akademii Nauk, 2013, Vol. 451, No. 6, pp. 643–646.
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Keller, I.E. Integrability of the equilibrium and compatibility equations for a viscoplastic medium with negative strain rate sensitivity. Dokl. Phys. 58, 362–365 (2013). https://doi.org/10.1134/S1028335813080132
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DOI: https://doi.org/10.1134/S1028335813080132