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

Area of Science:

• Solid Mechanics
• Materials Science
• Electromagnetism

Background:

• Internal cracks, particularly rectangular ones, critically impair the mechanical and electrical properties of piezoelectric materials.
• This degradation compromises the reliability and functionality of devices utilizing these materials.

Purpose of the Study:

• To investigate the electromechanical coupling effects of rectangular cracks in piezoelectric materials.
• To establish a theoretical framework for analyzing crack tip fields and propagation behavior.
• To introduce novel machine learning and response surface methodologies for crack analysis.

Main Methods:

• Theoretical analysis using electromechanical coupling equations and constitutive relationships.
• Numerical simulation via the finite element method to model crack behavior under various loads.
• Application of random forest machine learning for predictive modeling and response surface methodology for influence analysis.

Main Results:

• Theoretical analysis provides insights into stress and electric displacement fields at crack tips.
• Finite element simulations reveal stress, displacement, and potential variations under mechanical and electromechanical loading.
• The random forest model demonstrates high prediction accuracy for crack behavior.
• Response surface methodology identifies key factors influencing crack propagation.

Conclusions:

• Rectangular cracks pose a significant threat to piezoelectric material performance.
• The developed theoretical and numerical models accurately capture crack-induced effects.
• Machine learning and response surface methods offer powerful tools for analyzing and optimizing piezoelectric materials with internal cracks.