Guidelines for element size and type selection for the finite element simulation of laser-induced elastic waves in thermoelastic laser ultrasonic testing

This paper explores spatial discretization within finite element simulations of laser-induced elastic waves within the context of Laser Ultrasonic Testing (LUT). Motivated by discrepancies and oscillations detected in temperature and displacement results in the literature, we traced these issues back to spatial discretization challenges. These challenges originate from rapid localized heating and the generation and propagation of high-frequency waves across a relatively large domain. This study effectively addresses and rectifies these inaccuracies, offering guidance for selecting the appropriate element size and type. We examined two element types: four-node quadrilaterals (Q4) employing first-order Lagrange and nine-node quadrilaterals (Q9) using second-order Lagrange shape functions. Our analysis encompasses mesh refinement strategies, exploration of time and frequency domain plots for temperature and displacement, as well as an evaluation of different pulse durations. Our findings demonstrate that Q9 elements attain accuracy with grids four times larger than Q4 elements for temperature and wave propagation analyses. Furthermore, we observe that lower frequency waves exhibit reduced sensitivity to element size, emphasizing the relationship between element size and elastic wave frequency. Pulse durations in the 6 to 30 ns range affect the required element size in the heat-affected zone but exert minimal influence on wave frequency and spatial discretization in the remainder of the domain. Finally, we present a new formula for element size selection based on the dominant frequency. This study provides a comprehensive guideline for selecting element size and type, enabling the attainment of accurate results while effectively managing computational costs.