A new multiscale computational method for electromechanically coupled analysis of heterogeneous piezoelectric composites

Abstract

This article is concerned with the electromechanically coupled multiscale behaviors of the heterogeneous piezoelectric materials, which consist of periodic or non-periodic distributed microstructures. A multiscale framework based on the extended multiscale finite element method is developed to capture the large-scale solutions on the coarse-scale mesh without resolving the entire small-scale features. In this method, the microscale fluctuations in the mechanical displacement and electrical potential are related to the macroscopic deformation and electrical fields through the multiscale base functions. To improve the accuracy of the multiscale method, the periodic boundary conditions are developed to calculate the multiscale base functions for those piezoelectric structures composed of periodic microstructures. Moreover, the oversampling techniques are introduced to derive the oscillatory boundary conditions to construct the base functions for those piezoelectric structures with non-periodic heterogeneous microscopic features. The efficiency and accuracy of the multiscale method proposed for the piezoelectric materials are validated through the examples where the structures consist of periodic or non-periodic heterogeneous microstructures. The results indicate that the multiscale method developed can effectively obtain the macroscale response of piezoelectric materials (displacement or electrical potential) as well as the response in the microscale (stress or electrical displacement).