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Research Papers

# Exact Two-Dimensional Contact Analysis of Piezomagnetic Materials Indented by a Rigid Sliding Punch

[+] Author and Article Information
Yue Ting Zhou

School of Mechanical Engineering, Yonsei University, Seoul 120-749, Republic of Koreazhouyueting@yeah.net

Kang Yong Lee1

School of Mechanical Engineering, Yonsei University, Seoul 120-749, Republic of Korea; Department of Engineering Mechanics, Dalian University of Technology, DaLian 116024, PR ChinaKYL2813@gmail.com

1

Corresponding author.

J. Appl. Mech 79(4), 041011 (May 09, 2012) (12 pages) doi:10.1115/1.4006239 History: Received July 14, 2011; Revised October 31, 2011; Posted February 28, 2012; Published May 09, 2012; Online May 09, 2012

## Abstract

The aim of the present paper is to investigate the two-dimensional moving contact behavior of piezomagnetic materials under the action of a sliding rigid punch. Introduction of the Galilean transformation makes the constitutive equations containing the inertial terms tractable. Eigenvalues analyses of the piezomagnetic governing equations are detailed, which are more complex than those of the commercially available piezoelectric materials. Four eigenvalue distribution cases occur in the practical computation. For each case, real fundamental solutions are derived. The original mixed boundary value problem with either a flat or a cylindrical punch foundation is reduced to a singular integral equation. Exact solution to the singular integral equation is obtained. Especially, explicit form of the stresses and magnetic inductions are given. Figures are plotted both to show the correctness of the derivation of the exact solution and to reveal the effects of various parameters on the stress and magnetic induction.

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## Figures

Figure 1

The distribution of the normalized surface contact stress σYY(X/a,0)/σ* [ σ*=P/(aπ)]

Figure 4

The distribution of the normalized magnetic induction BY(X/a,Y/a)/B* [B*=B0/(aπ)] in the direction parallel to the surface: (a) Y/a=-0.1 and (b) Y/a=-0.2

Figure 5

The distribution of the normalized magnetic induction BY(X/a,Y/a)/B* [B*=B0/(aπ)] in the direction vertical to the surface: (a) X/a=0 and (b) X/a=0.4

Figure 6

The half-width of contact region for a cylindrical punch versus the mechanical loading P

Figure 7

The half-width of contact region for a cylindrical punch versus the radius R

Figure 8

The half-width of contact region for a cylindrical punch versus the dimensionless moving speed c

Figure 9

The influences of mechanical loading P on the surface contact stress σYY(X,0)

Figure 10

The influences of cylindrical punch radius R on the surface contact stress σYY(X,0)

Figure 11

The influences of dimensionless moving speed c on the surface contact stress σYY(X,0)

Figure 12

The distribution of the near surface magnetic induction BY(X,Y) in the direction parallel to the surface: (a) Y=-0.025 and (b) Y=-0.05

Figure 2

The distribution of the normalized normal stress σYY(X/a,Y/a)/σ* [σ*=P/(aπ)] in the direction parallel to the surface: (a) Y/a=-0.1 and (b) Y/a=-0.2

Figure 3

The distribution of the normalized normal stress σYY(X/a,Y/a)/σ* [σ*=P/(aπ)] in the direction vertical to the surface: (a) X/a=0 and (b) X/a=0.3

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