Theoretical and simulation analysis of a rectangular crack in the piezoelectric material

Piezoelectric materials are significantly affected in their mechanical and electrical properties due to the presence of internal cracks (especially rectangular cracks), which in turn impacts the reliability and functionality of the devices.This paper investigates the problem of rectangular cracks in piezoelectric materials through theoretical analysis and numerical simulation. First, the electromechanical coupling governing equations and constitutive relationships of piezoelectric materials are established to analyze the stress field and electric displacement field at the crack tip, providing a theoretical basis for crack propagation behavior. Subsequently, the finite element method is employed to simulate the electromechanical coupling characteristics of rectangular cracks, revealing the variation patterns of stress, displacement, and potential contour plots under mechanical and electromechanical loading for different piezoelectric materials. Finally, The random forest machine learning and response surface method are used for the first time to study rectangular cracks in piezoelectric materials.A random forest regression model is applied to predict the data, and from the residual scatter plot provided, the accuracy of the prediction model is found to be high. Moreover, response surface methodology is used to analyze the influence of crack length, mechanical load, and electric field on crack propagation, offering an optimal model design scheme.