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# Constitutive Model of Piezoelectric Material

Introduction to piezoelectric material, derivation of the constitutive model, example application and conclusion.
by

## Tim Pollock

on 9 July 2014

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#### Transcript of Constitutive Model of Piezoelectric Material

By: Tim Pollock Constitutive Model
-Piezoelectric Material What does Piezoelectric mean? The peizoelectric effect is described as the linear coupling between mechanical and electrical state variables. Piezoelectric Relationships Direct Piezoelectric Effect: Creation of polarization caused by mechanical stress on a dielectric material. Agenda: Introduction to piezoelectric material
Material Characteristics
Mechanical Relationship
Electrical Relationship
Piezoelectric Relationships
A look at the Constitutive Model
Example application problem
Conclusion/Questions Piezoelectric material is a type of "smart" material that is capable of performing both sensor and actuator functions by exhibiting coupling between multiple physical domains. Mechanical Relationship Electrical Relationship Dielectric materials (insulators) can be defined similarly to a linear elastic material in a Cartesian coordinate system as follows. Typically described using a linear elastic model where behaviour can be modeled using Hooks Law. Converse Piezoelectric Effect: Strain on a material caused by application of an external electric field. Consitutive Model - Linear Approxamation Total Electric Displacement Total Mechanical Strain Linear Elastic: Linear Piezoelectric: Linear Dielectric: Linear Piezoelectric: Example - Piezoelectric Sensor Material Properties - PZT 5H Operating in "33" Mode A piezoelectric sensor has stress applied in the direction of polarization equal to 3 MPa. Stress values of 5 Mpa are applied in the two directions normal to the polarization vector.

Compute the electric field vector produced by the applied stress assuming that the electric displacement is held equal to zero. Assume the material properties of PZT-5H. Problem Statement: Conclusion: A Set of Constitutive Equations Strain-Charge Form Shown as coupled matrix Top and bottom partition represent the converse and direct pieozelectric effect respectively.
On diagonal terms represent the constitutive relationships of mechanical and electrical material.
Off diagonal terms represent the electromechanical coupling between the two domains.
As 'd' approaches zero we are left with a material that exhibits very little electromechanical behaviour.
'd' is very important when determining the relative strength between different piezoelectric materials. Questions Equivalant Alternative Formulations Strain-Charge Form Stress-Charge Form Strain-Voltage Form Stress-Voltage Form Direct Piezoelectric CM Converse Piezoelectric CM References: [1] Newnham, R.E., Ruschau, G.R., 1992, “Electromechanical properties of smart materials,” Recent Advances in Adaptive and Sensory Materials and Their Applications, Edited by C.A. Rogers, Technomic Publishing, Lancaster, U.K.
[2]Leo, Donald J. Engineering analysis of smart material systems. Hoboken, NJ: John Wiley & Sons, 2007.
[3]Chee, Clinton Yat Kuan. STATIC SHAPE CONTROL OF LAMINATED COMPOSITE PLATE SMART STRUCTURE USING PIEZOELECTRIC ACTUATORS. Thesis. Sydney, 2000. Sydney: University of Sydney. Aeronautical Engineering, 2006. Print
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