One-dimensional nonlinear model of generalized thermo-electro elasticity.

Abstract 

We investigate a one-dimensional nonlinear model of thermo-electroelasticity in extended thermodynamics and quasi-electrostatic regime, with thermal conductivity and relaxation time dependent on temperature and heat flux. The aim is to assess the effect of quadratic nonlinear couplings between mechanical, thermal, and electric fields, known to impact solution stability. Two wave propagation speeds are confirmed: the coupled thermoelastic wave and the heat wave. Formulae are provided for these speeds, showing their dependence on temperature, heat flux, and electric field. The purely thermal case is also considered. The results may be useful for describing interactions in polarizable materials and their design. Numerical analysis using finite-difference techniques demonstrates the wave nature of heat propagation and the effect of coupling constants on material behavior under thermal load, relevant for designing materials with specific thermal responses.