Finite element simulation of a gradient elastic half-space subjected to thermal shock on the boundary

The influence of the microstructure on the macroscopical behavior of complex materials is disclosed under thermal shock conditions. The thermal shock response of an elastic half-space subjected to convective heat transfer at its free surface from a fluid undergoing a sudden change of its temperature is investigated within the context of the generalized continuum theory of gradient thermoelasticity. This theory is employed to model effectively the material microstructure. This is a demanding initial boundary value problem which is solved numerically using a higher-order finite element procedure. Simulations have been performed for different values of the microstructural parameters showing that within the gradient material the thermoelastic pulses are found to be dispersive and smoother than those within a classical elastic solid, for which the solution is retrieved as a special case. Energy type stability estimates for the weak solution have been obtained for both the fully and weakly coupled thermoelastic systems. The convergence characteristics of the proposed finite element schemes have been verified by several numerical experiments. In addition to the direct applicative significance of the obtained results, our solution serves as a useful benchmark for modeling more complicated problems within the framework of gradient thermoelasticity.