Contact problem for magneto-electro-elastic half-plane materials indented by a moving punch. Part I: Closed-form solutions

Zhou, Yue‐Ting; Lee, Kang Yong

doi:10.1016/j.ijsolstr.2012.08.017

Cited by 39 publications

(8 citation statements)

References 28 publications

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“…When two perfectly conducting flat punches integrates as a single flat punch, the expressions in Eq. are the same as those for a single flat punch with contact region

x \in (- r_{2}, r_{2})

and external loadings

2 P_{k} false(k = 1, 2, 3 false)

given in .…”

Section: Results Reduced To a Single Flat Punchmentioning

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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“…When two perfectly conducting flat punches integrates as a single flat punch, the expressions in Eq. are the same as those for a single flat punch with contact region

x \in (- r_{2}, r_{2})

and external loadings

2 P_{k} false(k = 1, 2, 3 false)

given in .…”

Section: Results Reduced To a Single Flat Punchmentioning

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

Self Cite

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“…Thus, the eigenvalues have the properties that (i) complex roots occur in conjugate pairs and (ii) opposite roots emerge simultaneously (Zhou and Lee, 2012). Since magneto-electro-elastic materials are placed in z > 0 plane, the eigenvalues with negative real part, i.e.…”

Section: Eigenvalue Distribution and General Solutionmentioning

confidence: 99%

“…Further, with consideration of the eigenvalues' properties mentioned above, one may conjecture that in Case A, the eigenvalues may be real or conjugate imaginary numbers, and there are nine cases (please refer to Zhou and Lee, 2012); in Case B, t 1 should be a real number, and t 3 and t 4 should be real or conjugate imaginary numbers; in Case C, t 1 and t 3 should be real or conjugate imaginary numbers; and in Case D and Case E, all eigenvalues are real numbers.…”

Section: Eigenvalue Distribution and General Solutionmentioning

confidence: 99%

Constructing potentials to evaluate magneto-electro-elastic materials in contact with periodically rough surface

Zhou

Kim

2015

European Journal of Mechanics - A/Solids

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“…Both works are based on Fabrikant's method of potential theory for elastic materials [4]. Moving rigid punch solutions in two-dimensions (2D) have been considered by Zhou et al, both for frictionless [5,6] and frictional contact [7,8,9,10,11]. 2D graded materials are further considered in [12] .…”

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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Contact problem for magneto-electro-elastic half-plane materials indented by a moving punch. Part I: Closed-form solutions

Cited by 39 publications

References 28 publications

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

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

Constructing potentials to evaluate magneto-electro-elastic materials in contact with periodically rough surface

3D coupled multifield magneto-electro-elastic contact modelling

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