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Research Papers

Frictional Indentation of Anisotropic Magneto-Electro-Elastic Materials by a Rigid Indenter

[+] Author and Article Information
Yue-Ting Zhou

School of Aerospace Engineering
and Applied Mechanics,
Tongji University,
Shanghai 200092, China

Zheng Zhong

School of Aerospace Engineering
and Applied Mechanics,
Tongji University,
Shanghai 200092, China
e-mail: zhongk@tongji.edu.cn

1Corresponding author.

Manuscript received December 27, 2013; final manuscript received February 5, 2014; accepted manuscript posted February 10, 2014; published online March 6, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(7), 071001 (Mar 06, 2014) (12 pages) Paper No: JAM-13-1520; doi: 10.1115/1.4026795 History: Received December 27, 2013; Accepted February 01, 2014; Revised February 05, 2014

An exact analysis on frictional contact between a rigid punch and anisotropic magneto-electro-elastic materials is performed, within the framework of the fully coupled theory. The indenter moves relative to magneto-electro-elastic materials, and Coulomb friction law is used. The mixed boundary value problem is reduced to singular integral equations of the second kind with analytical solution presented. For a triangular or semiparabolic indenter, explicit expression for surface physical in-plane stress, electrical displacement and magnetic induction are obtained. Influences of the friction coefficient and the volume fraction on contact behaviors are detailed under the prescribed contact loading conditions. Under either a triangular or semiparabolic indenter, the surface in-plane stress, electric displacement and magnetic induction are discontinuous and unbounded around the leading edge, and such a serious near-edge response can be relieved through adjusting the values of the friction coefficient or the volume fraction.

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Figures

Grahic Jump Location
Fig. 1

A sliding indenter with (a) a triangular profile and (b) a semiparabolic profile over the surface of anisotropic magneto-electro-elastic (MEE) materials. P denotes the resultant normal force, Q the frictional tangential force, μf the friction coefficient, 0 and a the contact edges, W0 the indentation depth, and R the radius.

Grahic Jump Location
Fig. 2

The influences of: (a) the friction coefficient μf and (b) the volume fraction κ on powers of stress singularity at the edges of a triangular indenter, where solid line is for ρ and dashed line for ϑ

Grahic Jump Location
Fig. 3

The influences of: (a) the friction coefficient μf and (b) the volume fraction κ on the normalized surface contact stress σzz(x,0)/p* (p*=-Ts/ℏ11(0.5)) under a triangular indenter

Grahic Jump Location
Fig. 4

The influences of: (a) the friction coefficient μf and (b) the volume fraction κ on the normalized surface in-plane stress σxx(x,0)/p* (p*=-Ts/ℏ11(0.5)) under a triangular indenter

Grahic Jump Location
Fig. 5

The influences of: (a) the friction coefficient μf and (b) the volume fraction κ on the normalized surface electric displacement Dx(x,0)/D* (D*=p*e33c(0.5)/c33c(0.5)) under a triangular indenter

Grahic Jump Location
Fig. 6

The influences of: (a) the friction coefficient μf and (b) the volume fraction κ on the normalized surface magnetic induction Bx(x,0)/B* (B*=p*h33c(0.5)/c33c(0.5)) under a triangular indenter

Grahic Jump Location
Fig. 7

The influences of: (a) the friction coefficient μf and (b) the volume fraction κ on the normalized surface contact stress σzz(x,0)/p* (p*=P/R) under a semiparabolic indenter

Grahic Jump Location
Fig. 8

The influences of: (a) the friction coefficient μf and (b) the volume fraction κ on the normalized surface in-plane stress σxx(x,0)/p* (p*=P/R) under a semiparabolic indenter

Grahic Jump Location
Fig. 9

The influences of: (a) the friction coefficient μf and (b) the volume fraction κ on the normalized surface electric displacement Dx(x,0)/D* (D*=e33c(0.5)·P/(c33c(0.5)·R)) under a semiparabolic indenter

Grahic Jump Location
Fig. 10

The influences of: (a) the friction coefficient μf and (b) the volume fraction κ on the normalized surface magnetic induction Bx(x,0)/B* (B*=h33c(0.5)·P/(c33c(0.5)·R)) under a semiparabolic indenter

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