Acceleration waves in thermoelastic complex media with temperature-dependent phase fields

We analyze homothermal acceleration waves in complex materials (those with active microstructure) in the presence of an internal constraint that links the temperature to a manifold-valued phase-field describing a generic material microstructure at a certain spatial scale. Such a constraint leads to hyperbolic heat conduction even in the absence of macroscopic strain; we show how it influences the way acceleration waves propagate. The scheme describes a thermoelastic behavior that is compatible with dependence of the free energy on temperature gradient (a dependence otherwise forbidden by the second law of thermodynamics in the traditional non-isothermal description of simple bodies). We eventually provide examples in which the general treatment that we develop applies.