Influence of material microstructures on heat transfer: universal effects

Abstract We develop a nonlinear framework in which finite-speed heat propagation emerges naturally from microstructural effects, even without invoking ad hoc modifications of Fourier’s law. A structural invariance requirement of the Clausius–Duhem inequality under general diffeomorphism-based observer changes is adopted to derive thermodynamically consistent evolution equations that incorporate manifold-valued phase fields to represent internal microstructure. Internal constraints between temperature and microstructural variables give rise to non-linear hyperbolic structures, reflecting wave-like thermal dynamics. We discuss the theoretical foundations of this viewpoint not considering strain and propose appropriate simulations to corroborate the theoretical findings. The key point of our work is that, within the framework we establish, the derived microstructural effects on heat transfer are universal in the sense that they do not depend on specific microstructural shapes.