Propagation of coupled thermomechanical waves in uniaxial inelastic solids

A strain-rate dependent formulation of the problem of the propagation of longitudinal waves in inelastic rods is presented for the general case in which the deformation process is assumed to be nonisothermal, nonadiabatic and second-sound effects are accounted for. The formulation incorporates a thermodynamically motivated set of constitutive equations previously developed by the authors. The set of field equations is analyzed to obtain conditions under which two waves, one leading and the other lagging, propagate in a uniaxial solid. Two wavefronts propagate with different velocities. Jump conditions at the wave fronts are developed. Initial and boundary conditions are given to complete the statement of the problem of the propagation of coupled thermomechanical waves in inelastic uniaxial solids.