Two-scale asymptotic homogenization analysis of piezoelectric composite materials in generalized curvilinear coordinates

Abstract

This paper presents a comprehensive study on applying the two-scale asymptotic homogenization method to derive the effective properties of piezoelectric composite materials characterized by generalized periodicity in curvilinear coordinates. The methodology involves formulating the homogenization problem in a general curvilinear framework suitable for materials with complex geometric configurations. By systematically deriving the homogenized equations and effective coefficients, the paper provides a robust theoretical foundation for understanding the macroscopic behavior of piezoelectric composites under various loading conditions. The model’s versatility is demonstrated through its application to specific curvilinear coordinate systems, including the helix coordinate system and cylindrical coordinates with wavy geometry. These examples highlight the potential of the proposed approach in analyzing and designing piezoelectric materials with intricate geometries. The state-of-the-art numerical homogenization methods have also validated the proposed homogenization method, ensuring its accuracy and robustness.