Fundamental solutions to contact problems of a magneto-electro-elastic half-space indented by a semi-infinite punch

Li, Xiangyu; Zheng, R.-F.; Chen, W.-Q.

doi:10.1016/j.ijsolstr.2013.09.020

Cited by 31 publications

(10 citation statements)

References 28 publications

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“…The coefficients Ai and Bi, (i = 1,…,4) in Eqs. (10)(11)(12)(13)(14) and (28)(29)(30)(31)(32) are the unknowns, which will be determined from the boundary conditions of the contact problem which solution has to satisfy.…”

Section: Statement and Mathematical Formulation Of The Problemmentioning

confidence: 99%

“…Bagault et al [31] developed a semi-analytical method for the contact problem of anisotropic elastic materials with an anisotropic coating. Li et al [32] present the fundamental contact solutions of a magneto-electro-elastic half-space indented by a smooth and rigid half-infinite punch. Zhou and Lee [33] investigated the frictional sliding contact problem in monoclinic piezoelectric materials subjected to a rigid punch.…”

Section: Introductionmentioning

confidence: 99%

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Computational contact mechanics for a medium consisting of functionally graded material coating and orthotropic substrate

Öner¹

2021

JSEAM

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This paper presents a semi-analytical method to investigate the frictionless contact mechanics between a functionally graded material (FGM) coating and an orthotropic substrate when the system is indented by a rigid flat punch. From the bottom, the orthotropic substrate is completely bonded to the rigid foundation. The body force of the orthotropic substrate is ignored in the solution, while the body force of the FGM coating is considered. An exponential function is used to define the smooth variation of the shear modulus and density of the FGM coating, and the variation of Poisson’s ratio is assumed to be negligible. The partial differential equation system for the FGM coating and the orthotropic substrate is solved analytically through Fourier transformations. After applying boundary and interface continuity conditions to the mixed boundary value problem, the contact problem is reduced to a singular integral equation. The Gauss–Chebyshev integration method is then used to convert the singular integral equation into a system of linear equations, which are solved using an appropriate iterative algorithm to calculate the contact stress under the rigid flat punch. The parametric analyses presented here demonstrate the effects of normalized punch length, material inhomogeneity, dimensionless press force, and orthotropic material type on contact stresses at interfaces, critical load factor, and initial separation distance between FGM coating and orthotropic substrate. The developed solution procedures are verified through the comparisons made to the results available in the literature. The solution methodology and numerical results presented in this paper can provide some useful guidelines for improving the design of multibody indentation systems using FGMs and anisotropic materials.

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Section: Statement and Mathematical Formulation Of The Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computational contact mechanics for a medium consisting of functionally graded material coating and orthotropic substrate

Öner¹

2021

JSEAM

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“…For example, this coupling effect can be employed in the information storage to electronically write the data and consequently read them magnetically without needing to the creation of a powerful local magnetic field (Wang and Weng, 2016). Thus, a plenty of research community efforts have been made on the investigation of the material properties of multiferroic composites as well as the mechanical characteristics of beam, plate, and shell-type structures and devices made of multiferroic composites, such as crack (Chen et al, 2004; Zhao et al, 2013), contact (Chen et al, 2010; Li et al, 2014a), small and large deflection (Li et al, 2008; Sladek et al, 2013; Zhou and Zhu, 2016), and vibrations (Shooshtari and Razavi, 2015; Wang et al, 2011), to name a few.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal large-amplitude vibration of embedded higher-order shear deformable multiferroic composite rectangular nanoplates with different edge conditions

Gholami

Ansari

Gholami

2017

Journal of Intelligent Material Systems and Structures

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Based on the nonlocal elasticity theory, a unified nonlocal, nonlinear, higher-order shear deformable nanoplate model is developed to investigate the size-dependent, large-amplitude, nonlinear vibration of multiferroic composite rectangular nanoplates with different boundary conditions resting on an elastic foundation. By considering a unified displacement vector and using von Kármán’s strain tensor, the strain–displacement components are obtained. Using coupled nonlocal constitutive relations, the coupled ferroelastic, ferroelectric, ferromagnetic, and thermal properties of multiferroic composite materials and small-scale effect are taken into account. The electric and magnetic potential distributions in the nanoplate are calculated via Maxwell’s electromagnetic equations. Furthermore, Hamilton’s principle is utilized to obtain the mathematical formulation associated with the coupled governing equations of motions and boundary conditions. The developed model enables us to consider the effects of rotary inertia and transverse shear deformation without using any shear correction factor. Also, it can be degenerated to the models based on the Kirchhoff and existing shear deformation plate theories. To solve the large-amplitude vibration problem, an efficient multistep numerical solution approach is utilized. Effects of various important parameters such as the type of the plate theory, and parameters of nonlocality and coupled fields on the nonlinear frequency response are investigated.

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“…Rogowski (2012) utilized four potential functions to investigate the indentation of a magneto-electro-elastic half space or of the layer lying on a two-parameter elastic foundation under the action of an axially symmetric rigid punch. Li et al (2014) obtained the exact and complete fundamental solutions of frictionless contact problem for the magneto-electro-elastic half-space subject to a half-infinite punch. Elloumi et al (2013) presented the exact solutions of a perfectly conducting rigid flat punch frictionally sliding over the surface of a homogeneous magneto-electro-elastic half-plane.…”

Section: Introductionmentioning

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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Fundamental solutions to contact problems of a magneto-electro-elastic half-space indented by a semi-infinite punch

Cited by 31 publications

References 28 publications

Computational contact mechanics for a medium consisting of functionally graded material coating and orthotropic substrate

Computational contact mechanics for a medium consisting of functionally graded material coating and orthotropic substrate

Nonlocal large-amplitude vibration of embedded higher-order shear deformable multiferroic composite rectangular nanoplates with different edge conditions

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

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