NDLI: Exact solutions of the equations of motion for an incompressible viscoelastic Maxwell medium

Content Provider	Springer Nature Link
Author	Pukhnachev, V. V.
Copyright Year	2009
Abstract	The unsteady plane-parallel motion of a incompressible viscoelastic Maxwell medium with constant relaxation time is considered. The equations of motion of the medium and the rheological relation admit an extended Galilean group. The class of solutions of this system which are partially invariant with respect to the subgroup of the indicated group generated by translation and Galilean translation along one of the coordinate axes is studied. The system does not have invariant solutions, and the set of partially invariant solutions is very narrow. A method for extending the set of exact solutions is proposed which allows finding solutions with a nontrivial dependence of the stress tensor elements on spatial coordinates. Among the solutions obtained by this method, the solutions describing the deformation of a viscoelastic strip with free boundaries is of special interest from a point of view of physics.
Starting Page	181
Ending Page	187
Page Count	7
File Format	PDF
ISSN	00218944
Journal	Journal of Applied Mechanics and Technical Physics
Volume Number	50
Issue Number	2
e-ISSN	15738620
Language	English
Publisher	Springer US
Publisher Date	2009-03-18
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	viscoelastic medium incompressibility Maxwell relation Galilean group partially invariant solution free boundary motion Mechanical Engineering Mathematical Modeling and Industrial Mathematics Applications of Mathematics Mechanics, Fluids, Thermodynamics Fluids Mechanics
Content Type	Text
Resource Type	Article
Subject	Mechanics of Materials Condensed Matter Physics Mechanical Engineering

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