Ashby chart-assisted physics-informed machine learning-based prediction of elastic constants of isotropic cylinders and cuboids of arbitrary sizes

Estimation of elastic constants by conventional methods using a universal testing machine or ultrasonic time-of-flight-diffraction method is not feasible for all specimen sizes even for isotropic materials. In this work, we report on the development of artificial neural network (ANN)-based (deep learning) and XGBoost-based (machine learning) models that determine the elastic constants of isotropic materials, in cuboidal or cylindrical shapes, suitable for measurements in resonant ultrasound spectroscopy. First, the exact ranges of Young's modulus E and density rho were determined from Ashby charts, and Poisson's ratio nu from material databases for metals, polymers, and ceramics. A combination of COMSOL, a software for finite-element method, with MATLAB was used to simulate the eigenfrequencies of cylinders of radius r is an element of[1,7] and length & ell;is an element of[4,10] mm and cuboids of size [a, b, c]is an element of[1,10] mm for all three classes of materials. About 5000 and 8000 sets of simulated data of eigenfrequencies for each class of material and shape were used to train the machine and deep learning models for cylinders and cuboids respectively. The hyperparameters for machine learning (ML) and deep learning (DL) models were optimized to predict the properties. For cylinders, the median of percentage errors (MPEs) in estimating E were 0.8% for metals, 1.3% for ceramics, and 8.9% for polymers; The MPEs for nu were 3.9%, 1.9%, and 5.2%, respectively. For cuboids, the MPEs in estimating E were 0.3% for metals, 0.8% for ceramics, and 5.8% for polymers, while the MPEs for nu were 3.3%, 2.4%, and 4.8%, respectively. These results establish the genuineness and applicability of the artificial intelligence models that have been developed.