The general theory of simple waves in Green-elastic and Cauchy-elastic materials is given. Such waves generate three-dimensional unsteady deformations. Boundary conditions producing such waves are derived together with conditions under which shocks occur. The theory is used to illustrate conditions behind acceleration fronts moving into homogeneously deformed regions and also the modes of propagation of fronts moving into a simple wave. The steady flow of an elastic material past a rigid developable surface is discussed. Simple waves which are principal waves are also discussed.
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Communicated by M. M. Schiffer
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Varley, E. Simple waves in general elastic materials. Arch. Rational Mech. Anal. 20, 309–328 (1965). https://doi.org/10.1007/BF00253139
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