A Fully Coupled Constitutive Model for Electrostrictive Ceramic Materials

Hom, Craig L.; Shankar, Nachiket

doi:10.1177/1045389x9400500610

Cited by 94 publications

(53 citation statements)

References 13 publications

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“…Remark: A nonlinear model for the electrostriction for relaxor ferroelectrics has been proposed in [6]. It includes the main characteristic of this effect, namely the rise of strain proportional to the square of the electric field strength, and describes the saturation of polarization at high fields.…”

Section: Invariant Formulationmentioning

confidence: 99%

Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials

Schröder

Groß

2004

Archive of Applied Mechanics (Ingenieur Archiv)

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Theoretical and numerical aspects of the formulation of electromechanically coupled, transversely isotropic solids are discussed within the framework of the invariant theory. The main goal is the representation of the governing constitutive equations for reversible material behaviour based on an anisotropic electromechanical enthalpy function, which automatically fulfills the requirements of material symmetry. The introduction of a preferred direction in the argument list of the enthalpy function allows the construction of isotropic tensor functions, which reflect the inherent geometrical and physical symmetries of the polarized medium. After presenting the general framework, we consider two important model problems within this setting: i) the linear piezoelectric solid; and ii) the nonlinear electrostriction. A parameter identification of the invariant-and the common coordinate-dependent formulation is performed for both cases. The tensor generators for the stresses, electric displacements and the moduli are derived in detail, and some representative numerical examples are presented. IntroductionIn certain crystals with unsymmetric structures, mechanical deformation leads to polarization producing electric voltage, which is called the piezoelectric effect. Another important phenomenon occurs, which is the higher-order electromechanical coupling effect, called electrostriction. It is observed in all dielectrics, irrespective of their symmetry, see e.g. [23], which describes the rise of strain proportional to the square of the applied electric field strength. In unsymmteric crystals this effect is usually neglected. Piezoelectric and electrostrictive ceramic devices have a wide range of applications as sensors and actuators in intelligent systems and smart structures, which are e.g. able to realize and to operate in actual environmental conditions within a closed-loop controlled system.For an introduction to the foundations of the linear theory of piezoelectricity, established by W. Voigt at the end of the 19th century, we refer to [13] and the references therein. A general framework of the electrodynamics of continua at finite strains is presented in detail in [4] and [5]; in this context see also the extensive list of references therein. In most formulations, the piezoelectric response is described with respect to an appropriate local orientation of the crystal axis. This is common for the treatment of linear problems. A Taylor series expansion

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Section: Invariant Formulationmentioning

confidence: 99%

Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials

Schröder

Groß

2004

Archive of Applied Mechanics (Ingenieur Archiv)

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“…It is also important to simulate the ferroelectric devices with non-uniform field. Some researchers have proposed several numerical methods to simulate the nonlinear behavior of ferroelectrics structure [34][35][36][37][38][39][40]. However, some of these works only deal with the simplified non-linear constitutive relation in which the domain-switching nonlinear behavior can not be completely represented, while the other works only simply substitute the electromechanical field into domain-switching criteria without noting that the domain distribution and the electromechanical field are fully coupled and they should be determined simultaneously, therefore these simulation results are only first-order approximations.…”

Section: Introductionmentioning

confidence: 99%

Domain-switching embedded nonlinear electromechanical finite element method for ferroelectric ceramics

Liu

Fang

2011

Sci. China Phys. Mech. Astron.

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To simulate the nonlinear behavior of ferroelectric structures and devices under non-uniform electromechanical loadings, a domain-switching embedded electromechanical finite element method is developed in this paper. Following continuum assumption, the electromechanical behavior of each representative material point can be obtained by averaging the behavior of the local corresponding microstructure, e.g. 42 domains used in this work. A new Double Gibbs free energy criterion for domain-switching is proposed to ensure the convergence and stability of the simulations on ferroelectrics under non-uniform field.Several computational examples are given to demonstrate that this nonlinear finite element method can yield reasonable and stable simulation results which can be used to explain some experimental results and assist the design of ferroelectric devices. ferroelectric material, domain-switching, finite element method, nonlinear electromechanical coupling, crack and fracture PACS: 77.80.Dj, 85.50.-n, 07.05.Tp

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“…Joshi [5] presented a concise formulation of relevant nonlinear constitutive relations of PZT, which can be used in dynamic modeling of the stator. Hom et al [6] used the electrostriction model [7] to study the superharmonic resonance of a piezoelectric actuator. Von Wagner and Hagedorn [8] observed not only nonlinearity of Duffing type (cubic) but also quadratic nonlinearity in the responses of a piezoceramic rod subjected to weak electric fields by experiments.…”

Section: Introductionmentioning

confidence: 99%

Second-order approximation of primary resonance of a disk-type piezoelectric stator for traveling wave vibration

Gao

Cao

2010

Nonlinear Dyn

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Considering the quadratic nonlinear constitutive relations of piezoelectric materials, a traveling wave dynamic model for a lead zirconate titanate stator of a traveling wave ultrasonic motor is established using Hamilton's principle and the RayleighRitz method. Applying the method of multiple scales, the second-order approximation of the primary resonance for traveling wave vibration of the stator is investigated. The second harmonic component is found in the primary response of the stator, which arises from the quadratic stiffness in the condition of weak excitation. In the region of the resonance, the two coupled modals are split and the lower-order peak bends to the left, hence a jump and delay exist in the response. In this way numerical results are given to verify the feasibility of the analytical approach. The results provide a theoretical foundation for further nonlinear dynamic analysis and design of the traveling wave ultrasonic motor.

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A Fully Coupled Constitutive Model for Electrostrictive Ceramic Materials

Cited by 94 publications

References 13 publications

Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials

Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials

Domain-switching embedded nonlinear electromechanical finite element method for ferroelectric ceramics

Second-order approximation of primary resonance of a disk-type piezoelectric stator for traveling wave vibration

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