A contact problem for electro‐elastic materials

Hüeber, S.; Matei, Andaluzia; Wohlmuth, Barbara

doi:10.1002/zamm.201200235

Cited by 20 publications

(11 citation statements)

References 28 publications

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“…being κ * the conductivity parameter similar to [32]. So, according to (17), the electrical contact condition (7) shows that when there is no contact (i.e.…”

Section: Electrical Contact Conditionsmentioning

confidence: 99%

“…Alternatively, the variational formulation of the problem (e.g. [32] for frictionless PE contact) could be considered for nonsymmetrical BEM frictional contact based on [45]. In what follows, we are going to present the system of non-linear equations for each quasi-static PE contact load step.…”

Section: Pe Contact Discrete Formulationmentioning

confidence: 99%

“…[29], Barboteu and Sofonea [30,31]. More recently Hüeber et al [32] studied the quasistatic 2D frictionless contact problems for electro-elastic materials, based on the assumption that the foundation is electrically conductive.…”

Section: Introductionmentioning

confidence: 99%

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3D BEM for orthotropic frictional contact of piezoelectric bodies

2015

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A numerical methodology to model the threedimensional frictional contact interaction of piezoelectric materials in presence of electric fields is presented in this work. The boundary element method (BEM) is used in order to compute the electro-elastic influence coefficients. The proposed BEM formulation employs an explicit approach for the evaluation of the corresponding fundamental solutions, which are valid for general anisotropic behaviour meanwhile mathematical degeneracies in the context of the Stroh formalism are allowed. The contact methodology is based on an augmented Lagrangian formulation and uses an iterative Uzawa scheme of resolution. An orthotropic frictional law is implemented in this work so anisotropy is present both in the bulk and in the surface. The methodology is validated by comparison with benchmark analytical solutions. Some additional examples are presented and discussed in detail, revealing the importance of considering orthotropic frictional contact conditions in the electro-elastic analysis of this kind of problems.

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“…being κ * the conductivity parameter similar to [32]. So, according to (17), the electrical contact condition (7) shows that when there is no contact (i.e.…”

Section: Electrical Contact Conditionsmentioning

confidence: 99%

Section: Pe Contact Discrete Formulationmentioning

confidence: 99%

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3D BEM for orthotropic frictional contact of piezoelectric bodies

2015

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“…Wu et al [16] investigated frictionless contact of a transversely isotropic piezoelectric multilayered half-space pressed by insulating or conducting rigid solids with various shapes like a flat-ended cylinder, a cone, and a sphere. Hüeber et al [17] examined the unilateral contact problem of an electro-elastic body under the action of a rigid electrically conductive foundation by applying the Signorini condition with nonzero gap. The effects of anisotropy of piezoelectric materials [18,19] on the contact behavior were also considered.…”

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confidence: 99%

A general solution approach to dynamic contact between a sinusoidal rigid solid and piezoelectric materials with anisotropy

Kim

2015

Acta Mech

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Applying the operator method, general solutions for dynamic governing equations involving anisotropic piezoelectric materials are derived. Based on the general solutions, a rigid solid with a sinusoidal surface moving along the surface of anisotropic piezoelectric materials is concerned. Dual series equations are obtained and solved analytically. Then, the electro-elastic fields are determined in series forms. A full contact problem leads to more simple forms. Numerical analysis is performed for the anisotropic piezoelectric material 0 • Graphite-epoxy, in which an illustrative example concerning the vertical mechanical displacement on the surface is displayed to validate the present approach. Results demonstrate that the contact behavior is considerably affected by both the velocity and material properties.

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“…Mathematical models in variational form for coupled electro-elastic frictional contact problems have been proposed (e.g. [20,21]); and some numerical schemes based in the Finite Element Method (FEM) have been implemented. Quasistatic 2D contact problems between solid-foundation and a PE material and an electro-visco-elastic material have been studied, for instance, by Sofonea et al [22,23,24,25] under frictionless conditions; and by Sofonea et al [26] incorporating isotropic frictional contact conditions.…”

Section: Introductionmentioning

confidence: 99%

3D coupled multifield magneto-electro-elastic contact modelling

Rodríguez-Tembleque

Buroni

Sáez

2016

International Journal of Mechanical Sciences

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Highlights-A numerical procedure for the three-dimensional frictional contact modelling of anisotropic coupled magneto-electro-elastic materials in presence of both electric and magnetic fields is presented.-An orthotropic frictional law is considered, so anisotropy is present both in the bulk and in the surface.-The methodology uses the boundary element method with explicit evaluation of the fundamental solutions in order to compute the magneto-electro-elastic influence coefficients.-The contact model is based on an augmented Lagrangian formulation and it uses an iterative Uzawa scheme of resolution.-Conducting, semi-conducting and insulated electric and/or magnetic indentation conditions, as well as orthotropic frictional contact conditions are considered.-The methodology is validated by comparison with benchmark analytical solutions. Then, additional exploration examples are presented and discussed in detail, revealing that magnetoelectric material coupling, conductivity contact conditions lead to a significant effect on the indentation force and contact pressure distributions.-The influence of friction in electric and magnetic potential responses has been also proved to be very significant. Moreover, tangential loads exhibit an important influence both on the maximum values of the electric and magnetic potentials as well as on their distributions. AbstractThe present work deals with the general contact problem for coupled magnetoelectro-elastic materials. Despite of the relevant technological applications, this topic of research has been treated only in some analytical works. But analytical solutions lack the generality of numerical methodologies, being restricted typically to simple geometries, loading conditions, idealized contact conditions and mostly taking into account transversely isotropic material symmetry with the symmetry axis normal to the contact surface. In this work, a numerical procedure for the three-dimensional frictional contact modelling of anisotropic coupled magneto-electro-elastic materials in presence of both electric and magnetic fields is presented for the first time. An orthotropic frictional law is considered, so anisotropy is present both in the bulk and in the surface. The methodology uses the boundary element method with explicit evaluation of the fundamental solutions in order to compute the magneto-electro-elastic influence coefficients. The contact model is based on an augmented Lagrangian formulation and it uses an iterative Uzawa scheme of resolution. Conducting, semi-conducting and insulated electric and/or magnetic indentation conditions, as well as orthotropic frictional contact conditions are considered. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 coupling, conductivity contact conditions lead to a significant effect on the indentation force and contact pressure dis...

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A contact problem for electro‐elastic materials

Cited by 20 publications

References 28 publications

3D BEM for orthotropic frictional contact of piezoelectric bodies

3D BEM for orthotropic frictional contact of piezoelectric bodies

A general solution approach to dynamic contact between a sinusoidal rigid solid and piezoelectric materials with anisotropy

3D coupled multifield magneto-electro-elastic contact modelling

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