Efficient Finite Element Modeling of Piezoelectric Transducers for Wave-Propagation-Based Analysis

Modeling piezoelectric elements (piezos) using the finite element method with electro-mechanical coupling requires significant computational resources. The electro-mechanical interaction between piezo and structure in the interface will consume the most computational resources because it needs to be updated for each time step. If many piezos are involved, the wave-propagation-based analysis, including simulations of the wave motion, will be handicapped and might lead to the cancellation of the computation. Therefore, a simplified approach for modeling the piezoelectric response is presented, accounting for a ‘purely’ mechanical interaction between piezo and structure, where the electric potential is calculated analytically by multiplying the first two mechanical principal-strain components with the piezoelectric constants a posteriori. This way, the calculation of the equilibrium of the piezoelectric material is omitted which reduces the computational cost significantly without loss of accuracy in the piezoelectric response. An application case is demonstrated, where steel-ball impacts on an aluminum plate were successfully localized using a wave-propagation-based localization method (time reverse modeling), and the piezos were modeled with a simplified mechanical material behavior.