Concurrent Multiscale Modelling of Piezoelectric Metamaterials -- A New Approach for Design of Energy Harvesters

Piezoelectric metamaterials have been a promising solution for energy harvesters, sensors, and actuators, especially after the success in development of 3D printing technology of piezoelectric metamaterials. However, modelling and design of piezoelectric metamaterials still rely on the traditional FE modelling and trial-and-error procedures, which is usually time and labor consuming due to the complexity of the multiscale structures of piezoelectric metamaterials.
In recent years, concurrent multiscale modelling methods have shown their potential in modelling complicated multiscale materials and structures, while most of them are difficult to implement which is mainly due to the required specific control scripts and lack of transferability from one specific problem to another. The direct finite element square (DFE2) method proposed by Prof. Vincent Tan has addressed most of these problems by combing macro- and meso-scale FE models in concurrent multiscale modelling to be one FE model at meso-scale, and thus enables a monolithic FE solution strategy for concurrent multiscale analysis via available features in commercial software.
In this work, the DFE2 method was further improved to facilitate concurrent multiscale modelling of piezoelectric responses, whereby the energy equilibrium between different scales is satisfied by introducing an extended Hill-Mandel homogenization condition accounting for the coupled electromechanical responses. Comparison between the simulations results obtained from DFE2 and DNS models shows a favorable accuracy and efficiency of the proposed piezoelectric DFE2 method, which will be greatly valuable in the future for design of energy harvesters.