Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling

Chen, Weiqiu

doi:10.1007/s10409-015-0509-3

Cited by 35 publications

(4 citation statements)

References 236 publications

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“…In the framework of magneto-electro-elasticity, the constants ζ ki included in (14) have the following symmetric properties 4 15…”

Section: Methods Of the Generalized Potential Theorymentioning

confidence: 99%

“…The multi-ferroic composite materials, which consist of a piezoelectric phase and a piezomagnetic phase, have drawn more and more attention in recent years. Owing to the strong coupling effects among the elastic, electric and magnetic fields and the admirable physical properties of high strength and light weight, the materials are widely used as sensors, actuators, transducers and energy storage in numerous industrial fields [1][2][3][4][5]. However, those materials are brittle.…”

Section: Introductionmentioning

confidence: 99%

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Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

Zheng¹,

Wu²,

Li³

et al. 2018

Smart Mater. Struct.

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The problem of a penny-shaped crack embedded in an infinite space of transversely isotropic multi-ferroic composite medium is investigated. The crack is assumed to be subjected to uniformly distributed mechanical, electric and magnetic loads applied symmetrically on the upper and lower crack surfaces. The semi-permeable (limited-permeable) electro-magnetic boundary condition is adopted. By virtue of the generalized method of potential theory and the general solutions, the boundary integro-differential equations governing the mode I crack problem, which are of nonlinear nature, are established and solved analytically. Exact and complete coupling magneto-electro-elastic field is obtained in terms of elementary functions. Important parameters in fracture mechanics on the crack plane, e.g., the generalized crack surface displacements, the distributions of generalized stresses at the crack tip, the generalized stress intensity factors and the energy release rate, are explicitly presented. To validate the present solutions, a numerical code by virtue of finite element method is established for 3D crack problems in the framework of magneto-electro-elasticity. To evaluate conveniently the effect of the medium inside the crack, several empirical formulae are developed, based on the numerical results.

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“…In the framework of magneto-electro-elasticity, the constants ζ ki included in (14) have the following symmetric properties 4 15…”

Section: Methods Of the Generalized Potential Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

Zheng¹,

Wu²,

Li³

et al. 2018

Smart Mater. Struct.

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show abstract

“…Especially, applying the general solutions developed by Chen et al [12] or similar ones for transversely isotropic materials, Karapetian and Kalinin [14] and Yang and Jin [15] analyzed the effects of heat distributions on indentation problems. Only some representative works are listed in this paper; for more researches on contact problems for transversely isotropic materials in coupling fields, see review articles by Chen and his coauthors [18,19]. Furthermore, Krenev et al [20] utilized Hankel’s integral transformation to study the indentation of a nonhomogeneous half infinite elastic body under thermo-mechanical coupling fields, whose material properties varied along its depth.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional analytical solutions to the half infinite thermo-elastic body pressed by a rigid cylindrical structure in thermal environment

Yang

2023

Mathematics and Mechanics of Solids

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The novelty of this paper is to propose exact three-dimensional analytical solutions to the half infinite thermo-elastic body pressed by a rigid cylindrical structure for the first time, in which uniform heat flux flowing from rigid structure into the half infinite body is considered. Using recent general solutions expressed by four harmonic functions and extending potential theory method to consider heat effect, the governing integral equations are first derived. Then, the equations are analytically solved and displacement, stress, and temperature field components expressed by elementary functions are obtained. To validate the presented solutions, the correctness of the solutions is exactly examined, and normal contact displacement and stress without heat effect are compared with those in literatures. Furthermore, a numerical example which is the stainless steel thermo-elastic body pressed by a displacement restrictor is studied. Displacement, stress, and temperature distributions are analyzed, and the influence of heat flux on the pressed depth is also discussed in detail. The analytical solutions presented in this paper are rather important in engineering practice and can provide a basis for indentation analysis, displacement restrictor design, foundation settlement calculation, and so on.

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“…For the axisymmetric contact of homogeneous piezoelectric materials, extensive works can be found by Giannakopoulos and Suresh (1999), Chen (2000), Giannakopoulos and Parmaklis (2007), Yang (2008), and Berndt and Sevostianov (2016) for the frictionless contact problem; Xiong et al (2005) for the Reissner–Sagoci problem; Chen and Yu (2008) for the partial slip contact problem; and Chen and Yu (2005) and Rogowski and Kalinński (2007) for the adhesive contact problem. Chen (2015) gave an extensive review on recent advances in the three-dimensional (3D) analyses of crack and contact problems of multifunctional materials with multifield coupling.…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric partial slip contact of a functionally graded piezoelectric coating under a conducting punch

Wang

2016

Journal of Intelligent Material Systems and Structures

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This article considered the axisymmetric partial slip contact problem of a functionally graded piezoelectric coated half-space indented by a rigid spherical punch subjected to a normal load. It is assumed that the punch within the contact region is a perfect conductor with a constant electric potential. The electro-mechanical properties of the functionally graded piezoelectric materials vary exponentially along the thickness direction. The whole contact region consists of an inner circular stick region surrounded by an outer annular slip region obeying Coulomb’s law of friction. The problem is reduced to a set of coupled Cauchy singular integral equations by employing the Hankel integral transform. An iterative method is used to determine the unknown stick/slip region, normal contact pressure, electric charge, and radial tangential traction. The effects of the resultant electric charge, friction coefficient, and gradient index on the surface electro-mechanical fields are presented in detail.

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Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling

Cited by 35 publications

References 236 publications

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

Three-dimensional analytical solutions to the half infinite thermo-elastic body pressed by a rigid cylindrical structure in thermal environment

Axisymmetric partial slip contact of a functionally graded piezoelectric coating under a conducting punch

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