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

Abstract

The thermal shock response of a gradient elastic half-space is examined using a higher-order finite element procedure. The half-space is assumed to experience convective heat transfer at its free surface with a fluid that undergoes a sudden change of its temperature. Simulations have been performed for different values of the microstructural parameters. The thermoelastic pulses within the gradient material 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.Theodosios K. Papathanasiou and Francesco Dal Corso gratefully acknowledge support from the European Union FP7 project “Mechanics of refractory materials at high–temperature for advanced industrial technologies” under contract number PIAPP–GA–2013–609758. Panos A. Gourgiotis gratefully acknowledges support from the ERC Advanced Grant “Instabilities and nonlocal multiscale modelling of materials” FP7-PEOPLE-IDEAS-ERC-2013-AdG (2014-2019)