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Ellipticity conditions of the static equations of nonlinear elasticity

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

The relations of the nonlinear model of the theory of elasticity are considered. The Cauchy and the strain gradient tensors are taken to be the characteristics of the stress-strain state of a body. Sufficient conditions under which the static equations of elasticity are of elliptic type are established. These conditions are expressed in the form of constraints imposed on the derivatives of the elastic potential with respect to the strain-measure characteristics. The cases of anisotropic and isotropic bodies are treated, including the case where the Almansi tensor is taken to be the strain measure. The plane strain of a body is investigated using actual-state variables.

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Authors
  1. V. D. Bondar’
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Additional information

Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 196–203, March–April, 1999.

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Bondar’, V.D. Ellipticity conditions of the static equations of nonlinear elasticity. J Appl Mech Tech Phys 40, 360–366 (1999). https://doi.org/10.1007/BF02468535

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  • DOI: https://doi.org/10.1007/BF02468535

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