ON THE PROPAGATION OF SINGULAR SURFACES IN THERMOELASTICITY

摘要

In the present contribution, having set forth in a proper framework the theory of finite-strain themtoelasticity and the accompanying jump equations at moving singular surfaces, we introduce the canonical equations of energy and momentum that govern the thermomechanics across these surfaces; the latter typically include phase-transition fronts and shock waves with differing thermal conditions. The approach emphasizes the role played by the so-called Eshelby material stress issued from the theory of material inhomogeneitks in defining a driving force acting on the surface. A compatible thermo-mechanical framework is obtained when the power expanded by this driving force in a motion of the surface is none other than the dissipation at this surface, whence the possibility to use a kinetic relation at the latter, that will respect the second law of thermodynamics. This is shown to be generalized to more complex cases such as those of deformable media endowed with a microstructure, and electromagnetic continua with prevailing electroelastic or magnetoelastic interactions. This is completed by a series of numerical simulations that illustrate the motion of discontinuities in thermodynamical terms. These examples deal with the (1D) propagation of adiabatic fronts in a bar of shape-memory alloy, the (2D) interaction of a wave front in an austenitic phase containing a martensitic inclusion, and the (2D) progress of a wave due to a step-wise loading in a plate of thermoelastic shape-memory alloy.