Mechanics of Small-Scale Spherical Inclusions Using Nonlocal Poroelasticity Integrated with Light Gradient Boosting Machine

Detecting inclusions in materials at small scales is of high importance to ensure the quality, structural integrity and performance efficiency of microelectromechanical machines and products. Ultrasound waves are commonly used as a non-destructive method to find inclusions or structural flaws in a material. Mathematical continuum models can be used to enable ultrasound techniques to provide quantitative information about the change in the mechanical properties due to the presence of inclusions. In this paper, a nonlocal size-dependent poroelasticity model integrated with machine learning is developed for the description of the mechanical behaviour of spherical inclusions under uniform radial compression. The scale effects on fluid pressure and radial displacement are captured using Eringen's theory of nonlocality. The conservation of mass law is utilised for both the solid matrix and fluid content of the poroelastic material to derive the storage equation. The governing differential equations are derived by decoupling the equilibrium equation and effective stress-strain relations in the spherical coordinate system. An accurate numerical solution is obtained using the Galerkin discretisation technique and a precise integration method. A Dormand-Prince solution is also developed for comparison purposes. A light gradient boosting machine learning model in conjunction with the nonlocal model is used to extract the pattern of changes in the mechanical response of the poroelastic inclusion. The optimised hyperparameters are calculated by a grid search cross validation. The modelling estimation power is enhanced by considering nonlocal effects and applying machine learning processes, facilitating the detection of ultrasmall inclusions within a poroelastic medium at micro/nanoscales.