Frictional contact of an anisotropic piezoelectric plate

Figueiredo, Isabel N.; Stadler, Georg

doi:10.1051/cocv:2008022

Cited by 6 publications

(6 citation statements)

References 24 publications

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“…Actually, the scalings used for the unknowns and data are those adopted in (3.1) and (3.2) of [16]. In a future theoretical asymptotic analysis, with thinner thicknesses for the piezoelectric patches, it can be considered an analogous study, like the one conducted in [26], for three different layered elastic strips.…”

Section: Asymptotic Methodsmentioning

confidence: 99%

“…The mathematical justification of the two asymptotic models (for PSBP and PIP) presented in this paper, strongly relies on the arguments reported on the papers [13,14,16,25], for the piezoelectric patches (which have the geometry of plates) and [7] for the elastic plates. In reality the mathematical reasoning, that leads to the asymptotic models for PSBP and PIP, is a judicious combination of the proofs presented in these above mentioned works.…”

Section: Introductionmentioning

confidence: 95%

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Plate-Like Smart Structures: Reduced Models and Numerical Simulations

2009

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In this paper asymptotic models describing the mechanical and electric equilibrium state of two types of smart structures are presented and justified. The first structure consists of an anisotropic elastic thin plate with two surface bonded anisotropic piezoelectric patches and the second one is an anisotropic elastic sandwich thin plate with an inserted anisotropic piezoelectric patch. The two unknowns of the corresponding asymptotic models, the mechanical displacements of the structures and the electric potentials of the patches, are partially decoupled. The former are the solution of modified Kirchhoff-Love plate models, while the latter can be derived as explicit functions of the mechanical displacements. Moreover, different formulas for the electric potential arise as a consequence of diverse electric boundary conditions. We report numerical simulations with these asymptotic models.

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Section: Asymptotic Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Plate-Like Smart Structures: Reduced Models and Numerical Simulations

2009

Self Cite

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“…Problems of anisotropic piezoelectric/piezomagnetic materials under contact loading were also concerned. For anisotropic piezoelectric materials, on kind of single phase piezoelectric/piezomagnetic materials, Figueiredo and Stadler proposed an asymptotic model for the equilibrium state of a thin anisotropic piezoelectric plate in frictional contact with a rigid obstacle. Chung constructed the Green's function for an anisotropic piezoelectric half‐space bonded to a thin piezoelectric layer under the action of a generalized line force and a generalized line dislocation.…”

Section: Introductionmentioning

confidence: 99%

The multiple fields created by two perfectly‐conducting punches on piezoelectric/piezomagnetic materials with anisotropy

Lee

Jang

Li³

2017

Z Angew Math Mech

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This article proposes an analytical model of two perfectly conducting punches acting on piezoelectric/piezomagnetic materials with anisotropy. For six types of distinct or repeated roots, related auxiliary function are obtained. The closedform solutions of the reduced integral equations are derived for two electrically-conducting and magnetically-conducting flat punches. The stress, electric displacement and magnetic induction intensity factors at both edges of each punch are given explicitly in terms of the distance between the two punches and the width of each punch. Numerical test is done to demonstrate the contributions of the distances between the two flat punches and various material properties on the contact behaviors. The obtained results delineate that at the outer edges, there has stronger strength for the singularities of the surface contact stress, surface electric displacement and surface magnetic induction compared with that at the inner edges.Most materials exhibit anisotropic behavior [1], either due to crystalline structure or because the material possesses more complex structural composition at the nanoscale. Evolution of anisotropy has a significant impact on material properties [2]. Indentation technique is a powerful tool to study materials properties, which is widely used in the semiconductor, biomedical, and magnetic recording industries [3][4][5][6], and etc. Developing indentation technique needs the solution of contact problem of anisotropic materials, which is an important and interesting subject concerned by many researchers. Clements and Ang [7] solved generalized plane contact problems for an anisotropic half-space and layer in which the elastic moduli vary quadratically with the spatial variables. Kuchytsky-Zhyhailo and Rogowski [8] investigated the rigid spherical indenter contacting with an anisotropic linear elastic layer bonded to a rigid substrate. Boffy et al.[9] performed a contact analysis of deformable bodies loaded normally and tangentially against graded layers bonded to heterogeneous substrates. Recently, Barber and Ciavarella [10] proposed an approximate JKR solution for the adhesive contact of anisotropic materials, and found that the dimensionless degree of anisotropy can significantly increase the pull-off force.The growing application of new and especially anisotropic composite materials in modern engineering gives rise to new challenges in mechanics. For example, because of exhibiting a remarkable cross-coupling between the electric and magnetic ferroic orders [11][12][13], piezoelectric/piezomagnetic materials have great potentials to be widely used in smart materials/intelligent structures. The effect of anisotropy on the performances of piezoelectric/piezomagnetic materials is of interest. Zhao et al. [14] derived the analytical solutions in an anisotropic piezoelectric/piezomagnetic bi-material to reveal the effect of different non-uniform loadings (dislocations and tractions) on the induced fields. Problems of anisotropic piezoelectric/piezomagnetic materials...

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“…Therefore, some important results in this field were successfully obtained by applying two different modelling techniques: homogenization and asymptotic analysis (see Miara et al [8] for a review of the state of the art). See, in particular, Castillero et al [9], Ghergu et al [10] and Miara et al [11] for homogenization of piezoelectric plates and shells and Bellis and Imperiale [5], Collard and Miara [12], Sabu [13], Weller and Licht [14] and Figueiredo and Stadler [15] (and references therein) for formal asymptotic analysis to justify lower dimensional constitutive laws for piezoelectric plates, shells and rods. Recently, pioneering work for modelling of thin linearly piezoelectric beams including convergence results has been presented [16–18].…”

Section: Introductionmentioning

confidence: 99%

Mathematical and numerical analysis of an obstacle problem for elastic piezoelectric beams

Rodríguez-Arós

Cao-Rial

2017

Mathematics and Mechanics of Solids

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We consider a mathematical model that describes the equilibrium of an electro-elastic beam in contact with an electrically conductive foundation (an obstacle). The model is constructed by coupling the beam equation with a system of equations describing one-dimensional piezoelectricity. We state the unique weak solvability of the model as well as the continuous dependence of the weak solution with respect to the data. We also introduce a discrete scheme for which we perform numerical analysis, including convergence and error estimate results. Finally, we present numerical simulations in the study of a test problem.

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Frictional contact of an anisotropic piezoelectric plate

Cited by 6 publications

References 24 publications

Plate-Like Smart Structures: Reduced Models and Numerical Simulations

Plate-Like Smart Structures: Reduced Models and Numerical Simulations

The multiple fields created by two perfectly‐conducting punches on piezoelectric/piezomagnetic materials with anisotropy

Mathematical and numerical analysis of an obstacle problem for elastic piezoelectric beams

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