Analysis of shock waves in a mixture theory of a thermoelastic solid and fluid with distinct temperatures

The continuum theory of mixtures is used to describe a medium consisting of a solid phase and fluid phase, both compressible and attributed distinct deformation, temperature, entropy, and internal energy fields. Continuum balance laws are presented, and constitutive equations consistent with thermodynamic restrictions are postulated. Jump conditions for shock waves are established. Evolution equations for transient, i.e., unsteady, shock wave propagation are newly derived for an ideal mixture consisting of an arbitrary number of nonlinear thermoelastic solids, whereby inviscid thermoelastic fluid behavior is attained for a given constituent under more restrictive constitutive assumptions. Detailed calculations of Hugoniot response and shock decay are specialized to the case of a two-phase mixture of a single solid and a single fluid, where physical properties pertinent to lung parenchymal tissue containing air are assigned. Local constitutive behaviors for this lung mixture model correspond to a compressible neo-Hookean solid phase and an ideal gas fluid phase. Predictions of the model offer new information on origins of soft tissue trauma, in the context of prior experimental observations, for dynamic impact or shock loading of the lung.