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A common application of piezoelectric transducers is to obtain operational data from working structures and dynamic components. Collected data can then be used to evaluate dynamic characterization of the system, perform structural health monitoring, or implement various other assessments. In some applications, piezoelectric transducers are bonded inside the host structure to satisfy system requirements; for example, piezoelectric transducers can be embedded inside the biopolymers of total joint replacements to evaluate the functionality of the artificial joint. The interactions between the piezoelectric device (inhomogeneity) and the surrounding polymer matrix determine the mechanical behavior of the matrix and the electromechanical behavior of the sensor. In this work, an analytical approach is employed to evaluate the electromechanical performance of 2-D plane strain piezoelectric elements of both circular and rectangular-shape inhomogeneities. These piezoelectric elements are embedded inside medical grade ultra-high molecular weight (UHMW) polyethylene, a material commonly used for bearing surfaces of joint replacements, such as total knee replacements (TKRs). Using the famous Eshelby inhomogeneity solution, the stress and electric field inside the circular (elliptical) inhomogeneity is obtained by decoupling the solution into purely elastic and dielectric systems of equations. For rectangular (non-elliptical) inhomogeneities, an approximation method based on the boundary integral function is utilized and the same decoupling method is employed. In order to validate the analytical result, a finite element analysis is performed for both the circular and rectangular inhomogeneities and the error for each case is calculated. For elliptical geometry, the error is less than 1% for stress and electric fields inside and outside the piezoelectric inhomogeneity, whereas, the error for non-elliptical geometry is obtained as 11% and 7% for stress and electric field inside the inhomogeneity, respectively.
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