Propagation of Shock Waves in Thermoelastic Solids in View of Singular Surfaces

Overview

Shock waves are mathematically modeled as first-ordered propagating singular surfaces [1, 2], since physical variables like the particle velocity, the stress, the deformation gradient, and the temperature suffer jump discontinuities across the shock-wave front. Kinematics of elastic continua, the physical laws of the conservation of linear momentum and energy, the entropy production inequality, and the basic constitutive relations of thermoelastic solids are briefly presented. Shock-wave propagation velocities in linear elastic solids are derived to constitute a basis for the determination of corresponding speeds in thermoelastic solids. Finally, the propagation of weak shock waves in thermoelastic solids is investigated, and the effect of thermal properties of solids on the speeds of propagation of shock waves is concluded.

Continuum Kinematics

The region occupied by a body during its deformation is called configuration (Fig. 1). The initial state at time zero and the...