Determination of full piezoelectric complex parameters using gradient-based optimization algorithm

Abstract

At present, numerical techniques allow the precise simulation of mechanical structures, but the results are limited by the knowledge of the material properties. In the case of piezoelectric ceramics, the full model determination in the linear range involves five elastic, three piezoelectric, and two dielectric complex parameters. A successful solution to obtaining piezoceramic properties consists of comparing the experimental measurement of the impedance curve and the results of a numerical model by using the finite element method (FEM). In the present work, a new systematic optimization method is proposed to adjust the full piezoelectric complex parameters in the FEM model. Once implemented, the method only requires the experimental data (impedance modulus and phase data acquired by an impedometer), material density, geometry, and initial values for the properties. This method combines a FEM routine implemented using an 8-noded axisymmetric element with a gradient-based optimization routine based on the method of moving asymptotes (MMA). The main objective of the optimization procedure is minimizing the quadratic difference between the experimental and numerical electrical conductance and resistance curves (to consider resonance and antiresonance frequencies). To assure the convergence of the optimization procedure, this work proposes restarting the optimization loop whenever the procedure ends in an undesired or an unfeasible solution. Two experimental examples using PZ27 and APC850 samples are presented to test the precision of the method and to check the dependency of the frequency range used, respectively.

Numerical Characterization of Piezoceramics Using Resonance Curves

“…A more efficient computation can be obtained from the PDE equations with the appropriate analytical expressions [12,32]. Then, the next value of the parameter is: $p_{par}^{k+1}=p_{par}^k+\Delta p_{par}^k$ where the increment $\Delta p_{par}^k$ is computed from the error between the solution and the experimental data: $\nabla \left(\Im \left(p_{par}^k\right)\right)\Delta p_{par}^k=Z_{exp}-\Im \left(p_{par}^k\right)$…”

“…As a final remark, the efficiency of the FEM simulation can be improved by using customized finite element code. This code can be programmed to be coherent with the optimization algorithm and can use strategies, such as adaptive mesh or more elaborated elements [ 14 , 19 , 32 ].…”

“…There are many strategies to implement an optimization algorithm able to determine the material parameters. Several authors reported the details for implementing such algorithms [ 8 , 12 , 14 , 15 , 32 ]. The minimization problem to be solved is defined in Section 5.1 .…”

“…Another gradient-based algorithm uses the Method of Moving Asymptotes (MMA) [ 30 ]. Recently, Kiyono and co-authors used this method to obtain the full piezoelectric model [ 31 , 32 ]. In all the FEM iterative methods the reduction of the model to minimize the simulation time is critical.…”

Electromechanical Anisotropy at the Ferroelectric to Relaxor Transition of (Bi0.5Na0.5)0.94Ba0.06TiO3 Ceramics from the Thermal Evolution of Resonance Curves

“…This sample is thermally depolarized, producing changes in the resonance spectrum as a function of temperature. One alternative to do that is using an iterative methodology based in finite-element method (FEM) simulation [6][7][8]. The use of FEM based minimization techniques to obtain the parameters in the piezoelectric models was successfully implemented by several groups in recent years [9][10][11].…”