MD- and ML-based size-parameter calibration for the non-classical continuum theories

The accurate determination of the size-parameters is crucial for the application of the non-classical continuum theory to characterize the size-effects. This study takes into account of the size-effects and multiple influencing factors and utilizes the molecular dynamics (MD) simulations in conjunction with the machine learning (ML) technique for the precise calibration of the size-parameters required in the non-classical continuum theories. Firstly, theoretical solutions for the elastic wave dispersion relations within the frameworks of the nonlocal elasticity and nonlocal strain-gradient models are derived using the analytical integral Legendre polynomial method. Subsequently, MD simulations are performed to determine the group velocity dispersion relations of the Lamb and SH waves in aluminum plates of varying thickness. Finally, the nonlinear relationships between the guided wave group velocities and the size-parameters are established by the ML technique based on the neural network model. The present study reveals that the size-effects of the elastic wave propagation are closely related to the wavelength, the guided wave mode, and the thickness of the plates. The calibrated nonlocal elasticity theory can predict the guided wave group velocity only within a limited range of the nanoplate thickness. In contrast, the calibrated nonlocal strain-gradient theory demonstrates an excellent performance across all ranges of the nanoplate thickness.