Nonlinear Simulation of Piezoceramic Materials Using Micromechanical Approach

Delibas, Bülent; Seemann, Wolfgang

doi:10.2514/6.2004-1811

Cited by 3 publications

(7 citation statements)

References 7 publications

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“…However, it also diminishes the ability to describe the behavior under complex and multi-axial loading conditions (Landis, 2004;Kushnir and Rabinovitch, 2007). The second group of constitutive models adopts a micromechanical approach (Hwang et al, 1995;Hwang et al, 1998;Lu et al, 1999;Hwang and McMeeking, 1999;Huber et al, 1999;Rodel and Kreher, 2000;Delibas et al, 2004;Huber and Fleck, 2004;Kamlah et al, 2005). A = 1000 mm 2 L = 1.0 mm In this case, the material point is represented by a set of grains whose spatial orientation is randomly distributed.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Non-linear Piezoelectric and Ferroelectric Actuators — Analysis and Potential Advantages

Kushnir

Rabinovitch

2008

Journal of Intelligent Material Systems and Structures

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The ability to enhance and to improve the efficiency of piezoelectric actuators through extending their operational range into the non-linear regime is analytically investigated. Motivated by the limited strain actuation capabilities of the existing piezoelectric actuators, it is proposed to take advantage of the non-linear ferroelectric regime, which involves large remanent strains. In order to examine this hypothesis, an analytical model for the one-dimensional electro mechanical behavior of a ferroelectric structure operated in the non-linear range is developed. The model is applicable to rod actuators, to an active layer in a stack actuator, or to an active fiber in a Micro-Fiber-Composite actuator. The governing equations and the boundary conditions, the non-linear, hysteretic, and history-dependent constitutive relations, and the solution procedure are developed and discussed. Illustrative examples that examine an active layer operating against a dead load, against a linear spring, and against a uniformly distributed load are presented and discussed. The non-linear response is also compared with the response to electrical loads in the linear range and with the prediction of the linear piezoelectric theory. Emphasis is placed on the potential advantages that can be achieved through the operation in the non-linear range.

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Section: Mathematical Formulationmentioning

confidence: 99%

Non-linear Piezoelectric and Ferroelectric Actuators — Analysis and Potential Advantages

Kushnir

Rabinovitch

2008

Journal of Intelligent Material Systems and Structures

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“…Therefore, it is required to discretize the space of grain orientation according to a uniform distribution function. To date, the grain orientation scattering used for the electro-micromechanical modeling of piezoelectric materials is a random one (Hwang et al, 1995(Hwang et al, , 1998Hwang and McMeeking, 1999;Huber et al, 1999;Rodel and Kreher, 2000;Delibas et al, 2004;Huber and Fleck, 2004;Kamlah et al, 2005). In the random grain set, the Euler angles are generated in the following manner:…”

Section: Deterministic Grain Setsmentioning

confidence: 99%

“…The second group of constitutive computational models adopts a micro-electromechanical approach (Hwang et al, 1995(Hwang et al, , 1998Lu et al, 1999;Hwang and McMeeking, 1999;Huber et al, 1999;Rodel and Kreher, 2000;Delibas et al, 2004;Huber and Fleck, 2004;Kamlah et al, 2005). In this case, the material point is represented by a set of grains whose spatial orientation is randomly distributed.…”

Section: Introductionmentioning

confidence: 99%

“…The response of each grain is calculated separately, and the response of the material point is determined by averaging over all grains (Hwang et al, 1995). Effects such as grain interaction (Hwang et al, 1998;Hwang and McMeeking, 1999;Huber et al, 1999;Rodel and Kreher, 2000;Delibas et al, 2004;Huber and Fleck, 2004;Kamlah et al, 2005) and rate dependency (Huber et al, 1999;Rodel and Kreher, 2000;Huber and Fleck, 2004;Kamlah et al, 2005) can also be taken into account. The micro-electromechanical models are able to quantify and describe the behavior of piezoelectric materials subjected to complex multi-axial electromechanical loading conditions and can provide insight into the physical phenomena at the material point level.…”

Section: Introductionmentioning

confidence: 99%

“…Although the micromechanical approach provides a powerful tool for the assessment of the response of the ferroelectric-piezoelectric material, to date no attempts were made to improve the efficiency of the model and to make it available for structural analysis. It seems that the main effort carried out in the field of the constitutive modeling of piezo-ceramics is to improve the reliability of the model and its ability to quantify the constitutive behavior of the material point (Hwang et al, 1998;Hwang and McMeeking, 1999;Huber et al, 1999;Lu et al, 1999;Rodel and Kreher, 2000;Delibas et al, 2004;Huber and Fleck, 2004;Kamlah et al, 2005). Yet, the challenge of improving the efficiency of the model still has to be faced.…”

Section: Introductionmentioning

confidence: 99%

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Grain Orientation Scattering in Nonlinear Constitutive Modeling of Piezoelectric-ferroelectric Materials

Kushnir

Rabinovitch

2007

Journal of Intelligent Material Systems and Structures

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The ability to enhance and to improve the efficiency of micromechanical models for the coupled electromechanical constitutive behavior of piezoelectric materials in the nonlinear regime is investigated. Motivated by the limited strain actuation capabilities of the existing piezoelectric materials and structures, it is recognized that the nonlinear regime has to be explored. However, due to the complex, strongly coupled, and hysteretic behavior of the material, the quantitative prediction of its nonlinear response requires complex and time-consuming algorithms. In this study, the ability to improve the efficiency of the micromechanical algorithm by using a deterministic set of directions as a representative of the scattering of grain's orientation within the piezoelectric polycrystal is investigated. Various types of deterministic grain sets that include an equal area, a spiral, and Fekete grain sets are examined. The constitutive micromechanical model for the piezoelectric material and the algorithms for the generation of the various grain sets are presented and discussed. Numerical results that compare the capabilities of the model that uses the deterministic scattering approach and those that adopt a random scattering, which is commonly used today, are presented and discussed. Emphasis is placed on the ability to predict the complex nonlinear material response and on the computational efficiency. The article closes with a summary and conclusions.

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