Finite Element Formulation of a Piezoelectric Continuum and Performance Studies of Laminar PZT-Patch-Modules
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Finite Element Formulation of a Piezoelectric Continuum and Performance Studies of Laminar PZT-Patch-Modules Monika Gall1, Bärbel Thielicke1, Christophe Poizat1, Sven Klinkel2 1 Fraunhofer Institute for Mechanics of Materials IWM, Woehlerstrasse 11, 79108 Freiburg, Germany, Contact: [email protected] 2 Institute for Structural Analysis, University of Karlsruhe (TH), Kaiserstrasse 12, 76131 Karlsruhe, Germany
ABSTRACT Efficient application of piezoelectric sensors and actuators requires extensive investigations of their loading limits, failure-behavior and life-span under service conditions. Here the performance of laminar PZT-patch-modules is studied, applying a combined approach of experimental and numerical tests. Four-point bending tests are used to evaluate the sensor performance. Linear electro-mechanical coupling is implemented in an 8-node brick user element of the research finite element code FEAP to develop a flexible FE-tool for piezoelectric problems. Comparative FE-analyses of the bending test are carried out in order to assess the capability of the implemented FEAP user element versus the commercially available FE-code ABAQUS. FE-results show good agreement with the experimental tests, different element types yield slight deviations which are discussed.
INTRODUCTION Piezoelectric patch modules made of PZT ceramics (called PZT-patch-modules or PZTmodules in the following) have been developed in the frame of the German leading project “Adaptronics” [1, 2]. These modules can be used as sensors and actuators in adaptive systems where they have to withstand the operational demands of the structures on which they are applied. This requires studies towards durability and loading limits under relevant thermoelectro-mechanical loading situations. By conceiving and conducting tests in conjunction with FE-simulations, a good transferability of the results to different geometries and applications is achieved. Using four-point bending tests, the loading limits (maximum strain, electric field, number of cycles under load, temperature) and life-span of the PZT-patch-modules are investigated. As a step towards the development of a flexible FE-tool for complex piezoelectric material models that will allow to predict the life-span of piezoelectric sensors and actuators, linear electro-mechanical coupling is implemented into a FEAP [3] user element. This simulation tool is validated by comparison of FE-results to experimental data and comparative analyses with other FE-elements. First experimental and numerical results are presented and discussed here.
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EXPERIMENTAL DETAILS Design of the PZT-patch-modules The flexible, thin PZT-patch-modules (total thickness 0.43 mm) consist of thin monolithic piezoceramic wafers which are pre-encapsulated in a polymer (see figure 1). This improves the handling of the brittle PZT material while providing mechanical stabilization and electrical insulation. The PZT wafers’ surfaces are uniformly electroded to operate in the lateral d31 mode. The surfaces ele
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