Elastostatic bounds for the stiffness of an elliptical disc inclusion embedded at a transversely isotropic bi-material interface

Selvadurai, A. P. S.

doi:10.1007/bf00945172

Cited by 19 publications

(3 citation statements)

References 19 publications

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“…A four-concentric circular cylindrical model was used by for the stress analysis of coated fiber composites subjected to thermomechanical loadings. Selvadurai (1985) developed a set of bounds which can be used to estimate the asymmetric rotational stiffness of a rigid elliptical disc inclusion which is embedded in bonded contact at an isotropic bi-material elastic interface. They obtained explicit expressions for the stress field and strain energy under a given symmetry of the anisotropy of materials and the orientation of the inclusion.…”

Section: Inclusions Precipitates and Compositesmentioning

confidence: 99%

Micromechanics of defects in solids

Mura¹,

Barnett

1987

Mechanics of Elastic and Inelastic Solids

3,016

1,372

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PrefaceThis book stems from a course on Micromechanics that I started about fifteen years ago at Northwestern University. At that time, micromechanics was a rather unfamiliar subject. Although I repeated the course every year, I was never convinced that my notes have quite developed into a final manuscript because new topics emerged constantly requiring revisions, and additions. I finally came to realize that if this is continued, then I will never complete the book to my total satisfaction. Meanwhile, T. Mori and I had coauthored a book in Japanese, entitled Micromechanics, published by Baifu-kan, Tokyo, in 1975. It received an extremely favorable response from students and researchers in Japan. This encouraged me to go ahead and publish my course notes in their latest version, as this book, which contains further development of the subject and is more comprehensive than the one published in Japanese.Micromechanics encompasses mechanics related to microstructures of materials. The method employed is a continuum theory of elasticity yet its applications cover a broad area relating to the mechanical behavior of materials: plasticity, fracture and fatigue, constitutive equations, composite materials, polycrystals, etc. These subjects are treated in this book by means of a powerful and unified method which is called the 'eigenstrain method.' In particular, problems relating to inclusions and dislocations are most effectively analyzed by this method, and therefore, special emphasis is placed on these topics. When this book is used as a text for a graduate course, Sections 3, 11, and 22 should be emphasized.

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Section: Inclusions Precipitates and Compositesmentioning

confidence: 99%

Micromechanics of defects in solids

Mura¹,

Barnett

1987

Mechanics of Elastic and Inelastic Solids

3,016

1,372

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“…Selvadurai (2001) and Selvadurai & Willner (2006) examined problems related to surface-reinforced half-spaces loaded internally by localized forces that are axisymmetric and non-axisymmetric. Of related interest are investigations that deal with the mechanics of rigid disc-shaped inclusions embedded at the interface of bi-material elastic regions, where either kinematic constraints are invoked to develop convenient analytical solutions or the governing integral equations are solved in a numerical fashion (Selvadurai, 1984a(Selvadurai, , 1994a(Selvadurai, ,b,c, 2000b(Selvadurai, ,c, 2009aSelvadurai & Au, 1986). In this paper, we examine a generalization of the Kelvin force problem to include a bi-material region, which is separated by a bonded flexural constraint in the form of either a Germain-Poisson-Kirchhoff thin plate or a Reissner thick plate that accounts for shear deformation effects.…”

Section: Introductionmentioning

confidence: 99%

Mechanics of contact between bi-material elastic solids perturbed by a flexible interface

Selvadurai

2014

IMA Journal of Applied Mathematics

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This paper generalizes the classical result of R.D. Mindlin for the axisymmetric problem related to the action of a concentrated force at the interior of an isotropic elastic half-space to include a bi-material region that is perturbed by an interface exhibiting flexural behaviour. The flexural behaviour of the interface is described by a Germain-Poisson-Kirchhoff thin plate theory. A Hankel integral transform technique is used to obtain an explicit result for the deflection of the flexural interface. The reduction of the solution to conventional results associated with both half-space problems and infinite space problems is indicated. Formal results are also presented for the case where the flexural behaviour of the plate is modelled by the plate theory proposed by E. Reissner.

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“…The problems of bimaterial full space subjected to internal loadings are considered fundamental in interface mechanics and have various ranges of applications, including the interactions between interface and dislocations [30,31], eigenstrain [32,33], and interfacial inclusion [34][35][36]. The mechanics of bimaterial models are useful to provide reliable first approximations to the performances of many composite structures, e.g.…”

Section: Literature Reviewmentioning

confidence: 99%

Response of bimaterials with interfacial tension subjected to axisymmetric body force

Chen

Yue

2019

Mathematics and Mechanics of Solids

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This paper presents an analytical treatment of the boundary value problem of an isotropic elastic bimaterial full space with interfacial tension subjected to an axisymmetric body force. The interfacial tension is modeled as the residual stress in the pre-tensed interfacial atom membrane on the basis of Gurtin and Murdoch's surface theory. The generality of the present model is justified with several degenerated cases (e.g. classical bimaterials with bonded and unsinkable interface, homogeneous full space with interfacial tension, and half space with surface tension). By virtue of classical Hankel or Fourier transforms, the unconventional boundary value problems are addressed in a concise and systematic manner. The final solutions are all given in the form of a semi-infinite line integral. Particularly, the solutions for the interfacial response induced by interfacial point load can be obtained in exact closed form in terms of Struve and Bessel functions. Numerical results are presented to show the influence of interfacial tension on the induced responses. It is shown that the existence of interfacial tension can significantly influence the induced elastic fields and reduce the point load singularity. The results presented in this paper are useful and meaningful to the studies of nanocomposites, soft solids, and biological tissue, where the effects of surface/interface tension could be dominant.

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Elastostatic bounds for the stiffness of an elliptical disc inclusion embedded at a transversely isotropic bi-material interface

Cited by 19 publications

References 19 publications

Micromechanics of defects in solids

Micromechanics of defects in solids

Mechanics of contact between bi-material elastic solids perturbed by a flexible interface

Response of bimaterials with interfacial tension subjected to axisymmetric body force

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