NDLI: Mathematical model of an incompressible viscoelastic Maxwell medium

Content Provider	Springer Nature Link
Author	Pukhnachev, V. V.
Copyright Year	2010
Abstract	Nonstationary motions of incompressible viscoelastic Maxwell continuum with a constant relaxation time are considered. Because in an incompressible continuous medium, pressure is not a thermodynamic variable but coincides with the stress-tensor trace to within a factor, it follows that, separating the spherical part from this tensor, one can assume that the remaining part of the stress tensor has zero trace. In the case of an incompressible medium, the equations for the velocity, pressure, and stress tensor form a closed system of first-order equations which has both real and complex characteristics, which complicates the formulation of the initial-boundary-value problem. Nevertheless, the resolvability of the Cauchy problem can be proved in the class of analytic functions. Unique resolvability of the linearized problem was established in the classes of functions of finite smoothness. The class of effectively one-dimensional motions for which the subsystem of three equations is a hyperbolic one was studied. The results of an asymptotic analysis of the latter imply the possible formation of discontinuities during the evolution of the solution. The general system of equations of motion admits an infinite-dimensional Lie pseudo-group which contains an extended Galilean group. The theorem of the invariance of the conditions on the a priori unknown free boundary was proved to obtain exact solutions of free-boundary problems. The problem of deformation of a viscoelastic strip subjected to tangential stresses applied to the free boundary is considered as an example of application of this theorem. In this problem, a scale effect of short-wave instability caused by the absence of diagonal dominance of the stress tensor deviator was found.
Starting Page	546
Ending Page	554
Page Count	9
File Format	PDF
ISSN	00218944
Journal	Journal of Applied Mechanics and Technical Physics
Volume Number	51
Issue Number	4
e-ISSN	15738620
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2010-08-10
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	viscoelastic medium incompressibility Maxwell relation Galilean group free-boundary problems Mechanical Engineering Mathematical Modeling and Industrial Mathematics Applications of Mathematics Classical Continuum Physics Fluid- and Aerodynamics Mechanics
Content Type	Text
Resource Type	Article
Subject	Mechanics of Materials Condensed Matter Physics Mechanical Engineering

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