Abstract
This study is devoted to an examination of wave motion in nonlinear thermoelastic solids. For this purpose, a new materially nonlinear constitutive relation for thermoelastic solids has been developed. The development makes use of the principles of continuum thermomechanics and takes into account Gibb’s free energy. On the basis of the nonlinear constitutive relations so developed the fundamental equations of wave propagation for a nonlinear thermoelastic uniaxial solid have been constructed. These are further simplified for a nonconducting nonlinear uniaxial material. The initial conditions and boundary conditions are stated. The jump conditions for simple waves and shock waves in such a material are derived. Shock amplitude relation has been obtained on the basis of kinematic compatibility relations. Solution of the system of basic equations, with boundary conditions, initial conditions and jump and shock conditions at the wave front has been obtained by the method of characteristics and a combination of finite difference and finite element methods. Numerical results are presented in graphical form for uniaxial waves.
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