Modeling the inverse effect of piezoelectricity on the mechanical behavior of smart (piezoelectric) materials utilizing the finite element method (FEM) involves a comprehensive framework that encompasses various components and intricacies. By employing the FEM, researchers aim to analyze and understand the intricate interplay between the mechanical behavior and piezoelectric properties of smart materials. This modeling process involves the utilization of numerical techniques which help to examine the inverse effects of piezoelectricity on mechanical behavior in a precise and accurate manner. The FEM provides a robust and efficient approach to simulate the intricate behavior and response of smart materials under different loading conditions, considering the complex interactions between the mechanical and electrical fields. Through this modeling approach, researchers are able to gain valuable insights into the underlying mechanisms and phenomena governing the inverse effect of piezoelectricity, thereby paving the way for the development of advanced smart materials with enhanced performance and functionality. Therefore, modeling the inverse effects of piezoelectricity on the mechanical behavior of smart materials using the finite element method is a fundamental and crucial aspect of material science research, contributing to advancements in various fields such as robotics, energy harvesting, and structural health monitoring.

The main objective of this work is to model the effect of inverse piezoelectricity on the mechanical behavior of piezoelectric materials; we applied the principles of continuum mechanics to mechanical and electrical considerations to calculate the mechanical field when an electric field is applied to the piezoelectric structure.