The propagation and growth of acceleration waves in heat-conducting elastic materials

摘要: In the thermo-mechanical theory of continua an acceleration wave may be defined as a propagating singular surface on which strain, velocity, temperature and entropy are continuous discontinuities in acceleration, strain rate gradient occur. We study here basic properties such waves homogeneous heat-conducting elastic bodies, placing no restriction symmetry material. paper has strongly influenced course recent research non-linear TRUESDELL [1961] discussed propagation through finitely strained material according to purely mechanical elasticity. The central result this analysis is FRESNEL-HADAMARD theorem, requiring amplitude travelling given direction right proper vector certain tensor, called acoustical depends upon state deformation at location wave. speed determined by number tensor associated with amplitude, thus there up three speeds can propagate, different corresponding distinct amplitudes. FRES~,mL-HADAMARO theorem determines but places its magnitude. For plane homogeneously deformed isotropic GREEN [1964, 1965] shown that magnitude either increases without bound over finite interval time t, decays towards zero t ~ , or remains constant. These results have been extended arbitrary form CHEN [1968, 1, 2] JtrNEJA & NARiBOLI [1970], general materials CrrEN [1970, (in respect longitudinal transverse waves*) CHADWICK OGDEN [1971, 1]. An growth hyperelastic embracing both these generalizations SUI-IVBI BOWEN WANG [1970] studied.