On the Main Hypotheses of the General Mathematical Theory of Plasticity and the Limits of Their Applicability


The article discusses and analyzes the issues of applicability and the limits of applicability of some of the main hypotheses of the general mathematical theory of plasticity. In the theory of elastoplastic deformation processes, this is the postulate of the isotropy of initially isotropic bodies, in which the invariance of orthogonal transformations of the process images is established when a relationship between stresses and deformations is established. In the theory of flow, this is a hypothesis about the decomposition of total deformations into elastic and plastic deformations and the influence on its relationship between stresses and deformations under complex loading.

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Correspondence to V. G. Zubchaninov.

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Translated by I. K. Katuev

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Zubchaninov, V.G. On the Main Hypotheses of the General Mathematical Theory of Plasticity and the Limits of Their Applicability. Mech. Solids 55, 820–826 (2020). https://doi.org/10.3103/S0025654420060163

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  • elasticity
  • plasticity
  • stress and strain tensors
  • invariants
  • complex loading
  • stress and strain vectors
  • isotropy postulate
  • deformation decomposition hypothesis