A Finite Element Model for Calculating the Stresses in Bars with Microstructure Loaded by Ultra-Short Laser Pulses

A finite element solution for the thermal stress field, generated in elastic bars with micro-structure is presented in this paper. The heat transfer phenomenon is governed by the non-Fourier law of Maxwell-Vernotte-Cattanneo. Heat losses due to free convection are supposed to occur along the bar. The micro-structure is taken into account in the elastic model by adopting the first strain gradient model. As a first approximation, the effects of micro-inertia are ignored. Furthermore, the thermal and mechanical fields are assumed uncoupled, so that the energy equation is independent of any strain rates. As a model problem, we consider a micro-bar, mechanically fixed and thermally insulated at both ends, stimulated by an ultra-short laser pulse. For the spatial discretization of the heat equation, we use quadratic C0-continuous Lagrange elements, while for the corresponding gradient elasticity equations, Hermite C1-continuous elements are employed. The semi-discrete system of equations is integrated in time using the implicit Newmark method. However, for this class of wave propagation problems, the explicit Newmark or equivalently, the central difference method is the most suitable. Nonetheless, some sort of numerical smoothing procedures are needed to avoid the numerical oscillations which are not physical.