Differential constitutive equations of incompressible media with finite deformations |
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Authors: | A L Svistkov B Lauke |
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Institution: | (1) Institute of Continuous Media Mechanics, Ural Division, Russian Academy of Sciences, Perm’, 614013, Russia;(2) Leibniz-Institut für Polymerforschung Dresden e.V., Dresden, 01069, Germany |
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Abstract: | A method is proposed for constructing a system of constitutive equations of an incompressible medium with nonlinear dissipative
properties with finite deformations. A scheme of the mechanical behavior of a material is used, in which the points are connected
by horizontally aligned elastic, viscous, plastic, and transmission elements. The properties of each element of the scheme
are described with the use of known equations of the nonlinear elasticity theory, the theory of nonlinear viscous fluids,
and the theory of plastic flow of the material under conditions of finite deformations of the medium. The system of constitutive
equations is closed by equations that express the relation between the deformation rate tensor of the material and the deformation
rate tensor of the plastic element. Transmission elements are used to take into account a significant difference between macroscopic
deformations of the material and deformations of elements of the medium at the structural level.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 158–170, May–June, 2009. |
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Keywords: | constitutive equations finite deformations elasticity plasticity viscosity incompressible medium mechanical properties |
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