Boundary element method for relative displacement of Eshelby inclusions in piezoelectric materials fused with DEM

With the advancement of technology, the inclusion problem of piezoelectric materials has gradually become a key research object. The aim of this study is to solve the relative rigid body displacement of Eshelby inclusion in piezoelectric materials. An improved Eshelby boundary element method is proposed, which combines the displacement extrapolation method to accurately calculate the mechanical properties of piezoelectric materials by introducing a strength factor. The improved method not only improves the calculation accuracy, but also effectively deals with the relative displacement of inclusions in piezoelectric materials. In the experiment, gallium arsenide is taken as an object, and the effectiveness of the improved method is verified by comparing J-integral method with stress method. The experimental results show that when the intensity factor is 1, 2, and 3, the error rates of generalized displacement calculation are 0.67%, 0.46%, and 0.39%, respectively. The errors of this method are 0.15%, 0.12%, 0.16%, 0.14%, and 0.16%, respectively, when measuring the relative displacement of inclusions and rigid bodies. These results show that the Eshelby boundary element method improved by displacement extrapolation has significant advantages in the treatment of boundary conditions and displacement analysis of piezoelectric materials. The improved method can effectively solve the problem of relative displacement of inclusions in piezoelectric materials, and has wide application prospect and high practical value.