Wave propagation and shear band formation in finite deformable constrained thermoelastic solids

Linear weak shock wave propagation and the existence of shear bands are examined in finitely deformed constrained thermoelastic solids. We consider a compressible solid with certain type of internal constraints. The specific internal constraint cases of temperature dependent extensibility and the purely mechanical inextensibility are considered separately. The equation of motion of weak shock waves is recovered by using the theory of singular surfaces. The constitutive equations of constrained materials are written as the summation of constrained and unconstrained counterparts of the relevant quantities. The jumps of certain field variables across the shock wave front are obtained by using Taylor series expansions of them. The propagation condition of shock waves in a thermoelastic solid is obtained by using the strain-energy function corresponding to Duhamel-Neumann expression. The solution of resulting eigenvalue problem yield the propagation speeds of weak shock waves. The propagation speeds of weak shock waves are determined for particular state of deformations. Formation of shear bands and the magnitudes of critical stretches are obtained for the deformation states of uniaxial, biaxial extension and for uniform dilation.