Abstract
It is shown that the complete system of equations of elasticity theory for an isotropic medium admits a unique representation in the hypoelastic form (the tensor of the rate of change of stresses is a linear function of the tensor of strain rates with coefficients depending on the invariants of the stress tensor). It is necessary to this end that the hypothesis be satisfied on the determination of strains by stresses which are unknown. Any arbitrariness in the choice of the coefficients of the hypoelastic relation may result in the thermodynamic identity being infringed.
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Literature cited
V. Prager, Introduction to Plasticity, Addison-Wesley (1959).
S. K. Godunov and E. I. Romenskii, “Nonstationary equations of nonlinear elasticity theory in Eulerian coordinates,” Prikl. Mekhan. Tekh. Fiz., No. 6, 124–144 (1972).
A. Green and J. Adkins, Large Elastic Deformation and Nonlinear Continuum Mechanics, 2nd ed., Oxford Univ. Press (1970).
M. L. Wilkins, “Computations of elasto-plastic flows,” in: Symp. Computing Methods in Hydrodynamics [Russian translations], Mir, Moscow (1967).
Additional information
Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 133–138, March–April, 1974.
The author would like to express his thanks to V. F. Kurapatenko, V. A. Svidinskii, and S. K. Godunov for the interest they have taken in this work and their critical remarks.
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Romenskii, E.I. Hypoelastic form of equations in nonlinear elasticity theory. J Appl Mech Tech Phys 15, 255–259 (1974). https://doi.org/10.1007/BF00850669
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DOI: https://doi.org/10.1007/BF00850669