关键词: 混合扩展多尺度有限元, 功能梯度材料, 压电材料, 力电耦合

Abstract:

Functionally graded piezoelectric material (FGPM) is an electromechanical coupling material of conti- nuous property variation.Due to the heterogeneity of the FGPM property,investigating the mechanics of this mate- rial has posed a great challenge.In this paper,an analytical model describing the electromechanical coupling of the FGPM is constructed based on the mixed extended multi-scale finite element method (MEMsFEM). In the model,the multi-scale base functions of electrical fields are set up by using the traditional multi-scale finite element method,and the multi-scale base functions of displacement fields in different directions are set up by using the ex- tended multi-scale finite element method.Moreover,the coupling terms are introduced to model the coupling a- mong the displacement fields in different directions.Since constructing multi-scale base functions helps capture the material heterogeneity effectively,it is feasible to solve the problem in a coarse grid scale,which can significantly reduce the computation amount.Finally,the proposed method is proved to be effective and efficient by numerical examples.It is thus concluded that the proposed method provides an effective approach to simulating the mechani- cal behaviors of functionally graded materials.

Key words: mixed extended multi-scale finite element method, functionally graded materials, piezoelectric materi- al, electromechanical coupling