Numerical simulations of piezoelectricity and triboelectricity: From materials, structures to devices

Piezoelectric and triboelectric materials have been extensively reported with the capabilities of generating polarized charges or voltages under various types of mechanical strains or deformations. Research on piezoelectricity and triboelectricity has been developed from single crystals to ceramics, polymers, composite materials, etc. These materials have been widely used in various fields mainly due to the advantages of high softness, low loss rate and strong stability. To understand the material properties while predicting the mechanoelectrical response, numerical methods have been recognized as an important tool to unveil and optimize the performance. By constructing complex material models, the numerical simulation method can deeply understand the operating principles of piezoelectric materials and triboelectric materials, simulate and verify the experimental process and results, evaluate the experimental parameters, and analyze the influence of different structures on the performance of the equipment, which helps to reduce the design cost and shorten the development cycle. Furthermore, it is beneficial to improve the design efficiency and optimize the performance of future equipment assembled with piezoelectric or triboelectric materials. However, lack of review article has been conducted to overview the existing numerical studies of piezoelectricity and triboelectricity, nor has study been carried out to outlook the future development trends. To address such research gap while discussing this interesting topic, this review article reviews the main numerical simulation techniques from materials, structures to devices at the different levels. Polarized polyvinylidene fluoride (PVDF), lead zirconate titanate (PZT), piezoelectric single crystals and composite materials are particularly discussed in the piezoelectric family, and triboelectric series consists of polymers, cellulose materials, and metallic materials are presented. Two main directions of numerical simulations of piezoelectric and triboelectric materials are described as the MD modeling from the atomic to the microscale, and the finite element modeling (FEM) from the mesoscopic to the macroscale. Furthermore, we discuss the three numerical simulations of multiscale simulation method, density function theory (DFT) and generalized finite difference method (FDM). Eventually, we discuss the development trends of numerically investigating piezoelectricity and triboelectricity in terms of the advantages and disadvantages of the discussed five numerical methods.