Wave patterns in a nonclassic nonlinearly-elastic bar under Riemann data

Recently there has been interest in studying a new class of elastic materials, which is described by implicit constitutive relations. Under some basic assumption for elasticity constants, the system of governing equations of motion for this elastic material is strictly hyperbolic but without the con...

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Bibliographic Details
Published in:International journal of non-linear mechanics 2017-05, Vol.91, p.76-85
Main Authors: Huang, Shou-Jun, Rajagopal, K.R., Dai, Hui-Hui
Format: Article
Language:English
Subjects:
Constitutive relationships
Convexity
Dissipation
Elastic bodies
Elastic properties
Elasticity
Equations of motion
Implicit constitutive relation
Kinetic relations
Materials elasticity
Rarefaction
Riemann problem
Shock waves
Studies
Wave patterns
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Summary:Recently there has been interest in studying a new class of elastic materials, which is described by implicit constitutive relations. Under some basic assumption for elasticity constants, the system of governing equations of motion for this elastic material is strictly hyperbolic but without the convexity property. In this paper, all wave patterns for the nonclassic nonlinearly elastic materials under Riemann data are established completely by separating the phase plane into twelve disjoint regions and by using a nonnegative dissipation rate assumption and the maximally dissipative kinetics at any stress discontinuity. Depending on the initial data, a variety of wave patterns can arise, and in particular there exist composite waves composed of a rarefaction wave and a shock wave. The solutions for a physically realizable case are presented in detail, which may be used to test whether the material belongs to the class of classical elastic bodies or the one wherein the stretch is expressed as a function of the stress.
ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2017.02.008