ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract In this paper we examine the influence of a general initial state of stress upon the propagation of infinitesimal (or weak) discontinuities in nonlinear relativistic elasticity. This influence, which materializes in alterations in the wave speeds, the general nonseparability in longitudinal and transverse waves, and the growth of the amplitude of infinitesimal discontinuities so as to form shock fronts, is first studied on the basis of a model of relativistic elasticity called hypoelasticity of zeroth order. The analytical treatment, however, is manageable only for the case of principal wave fronts for which the spatial direction of propagation coincides with a principal direction of the initial state of stress and, consequently, the wave fronts separate into longitudinal and transverse ones. Such notions as those of apparent elasticity moduli appear naturally in the analysis. Then a model of thermodynamical relativistic elasticity, referred to as neo-Hookean elasticity, is shown to be representable, insofar as wave-front propagation is concerned, by a special model of hypoelasticity of first order. The qualitative results obtained before concerning the influence of initial stresses are shown to apply equally to this description.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01609849
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