Accurate Finite Element Simulations of Dynamic Behaviour: Constitutive Models and Analysis with Deep Learning

Owing to the challenge of capturing the dynamic behaviour of metal experimentally, high-precision numerical simulations have become essential for analysing dynamic characteristics. In this study, calculation accuracy was improved by analysing the impact of constitutive models using the finite element (FE) model, and the deep learning (DL) model was employed for result analysis. The results showed that FE simulations with these models effectively capture the elastic-plastic response, and the ZA model exhibits the highest accuracy, with a 26.0% accuracy improvement compared with other models at 502 m/s for Hugoniot elastic limit (HEL) stress. The different constitutive models offer diverse descriptions of stress during the elastic-plastic response because of temperature effects. Concurrently, the parameters related to the yield strength at quasi-static influence the propagation speed of elastic waves. Calculation show that the yield strength at quasi-static of 6061 Al adheres to y = ax + b for HEL stress. The R-squared (R2) and mean absolute error (MAE) values of the DL model for HEL stress predictions are 0.998 and 0.0062, respectively. This research provides a reference for selecting constitutive models for simulation under the same conditions.

Microwave Absolute Distance Measurement Method with Ten-Micron-Level Accuracy and Meter-Level Range Based on Frequency Domain Interferometry

A microwave absolute distance measurement method with ten-micron-level accuracy and meter-level range based on frequency domain interferometry is proposed and experimentally demonstrated for the first time. Theoretical analysis indicates that an interference phenomenon occurs instantaneously in the frequency domain when combining two homologous broad-spectrum microwave beams with different paths, and the absolute value of the distance difference between the two paths is only inversely proportional to the period of frequency domain interference fringes. The proof-of-principle experiments were performed to prove that the proposed method can achieve absolute distance measurement in the X-band with standard deviations of 15 μm, 17 μm, and 26 μm and within ranges of 1.69 m, 2.69 m, and 3.75 m. Additionally, a displacement resolution of 100 microns was realized. The multi-target recognition performance was also verified in principle. Furthermore, at the expense of a slight decrease in ranging accuracy, a fast distance measurement with the single measurement time of 20 μs was achieved by using a digitizer combined with a Fourier transform analyzer. Compared with the current microwave precision ranging technologies, the proposed method not only has the advantages of high precision, large range, and rapid measurement capability, but the required components are also easily obtainable commercial devices. The proposed method also has better complex engineering applicability, because the ten-micron-level ranging accuracy is achievable only by using a simple Fourier transform without any phase estimation algorithm, which greatly reduces the requirement for signal-to-noise ratio.