Neutrality of the elliptic inhomogeneity in the case of non-uniform loading

Schiavone, Peter

doi:10.1016/s0020-7225(03)00201-5

Cited by 15 publications

(9 citation statements)

References 14 publications

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“…Following [12,13,36,38], an infinite class of boundary conditions for out-of-plane problems is considered through the following polynomial expression of m-th order (m ∈ N) for the remote displacement applied to an infinite elastic plane. Considering a polar coordinate system (r, θ) centered at the origin of the x 1 -x 2 axes, the polynomial displacement boundary conditions can be written as…”

Section: Out-of-plane Elasticity and Nonuniform Remote Conditionsmentioning

confidence: 99%

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Shahzad

Corso

Bigoni

2016

J Elast

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Stress field solutions and Stress Intensity Factors (SIFs) are found for n-cusped hypocycloidal shaped voids and rigid inclusions in an infinite linear elastic plane subject to nonuniform remote antiplane loading, using complex potential and conformal mapping. It is shown that a void with hypocycloidal shape can lead to a higher SIF than that induced by a corresponding star-shaped crack; this is counter intuitive as the latter usually produces a more severe stress field in the material. Moreover, it is observed that when the order m of the polynomial governing the remote loading grows, the stress fields generated by the hypocycloidal-shaped void and the star-shaped crack tend to coincide, so that they become equivalent from the point of view of a failure analysis. Finally, special geometries and loading conditions are discovered for which there is no stress singularity at the inclusion cusps and where the stress is even reduced with respect to the case of the absence of the inclusion. The concept of Stress Reduction Factor (SRF) in the presence of a sharp wedge is therefore introduced, contrasting with the well-known definition of Stress Concentration Factor (SCF) in the presence of inclusions with smooth boundary. The results presented in this paper provide criteria that will help in the design of ultra strong composite materials, where stress singularities always promote failure. Furthermore, they will facilitate finding the special conditions where resistance can be optimized in the presence of inclusions with non-smooth boundary.

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Section: Out-of-plane Elasticity and Nonuniform Remote Conditionsmentioning

confidence: 99%

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Shahzad

Corso

Bigoni

2016

J Elast

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“…Since that pioneering study, the idea of neutrality has drawn the interest of many researchers both from a practical and theoretical point of view. Several aspects of neutral holes were studied, for example, by Richards and Bjorkman [2], Budiansky et al [3] and Senocak and Waas [4], and neutral inhomogeneities in several settings were investigated by Ru [5], Benveniste and Miloh [6], Milton and Serkov [7], Benveniste and Chen [8], Chen et al [9], Schiavone [10], Van Vliet et al [11], Mahboob and Schiavone [12], Vasudevan and Schiavone [13,14], and Bertoldi et al [15]. For a concise introduction to the subject of neutral inhomogeneities see Section 7.11 in Milton [16].…”

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confidence: 99%

Soft Neutral Elastic Inhomogeneities with Membrane-type Interface Conditions

Benveniste

Miloh

2007

J Elasticity

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A foreign body, called an "inhomogeneity," when introduced in a host solid disturbs the stress field which is present in it. One can explore the possibility of modifying the contact mechanism between the inhomogeneity and the host body so as to leave the stress field in the host solid undisturbed. If such a procedure succeeds, then the inhomogeneity is called "neutral." Modification of the contact mechanism between the inhomogeneity and the host solid can be achieved, for example, by a suitably designed thick or thin interphase between them. When the interphase is thin, it can be represented by an "imperfect interface" model. In the present study we consider "soft" inhomogeneities which are more compliant than the host body. A "membrane-type interface" which models a thin and stiff interphase is used in rendering such inhomogeneities neutral. Illustrative examples are constructed for cylindrical neutral inhomogeneities of elliptical cross section under a triaxial loading, and for spheroidal inhomogeneities subjected to an axisymmetric loading.

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“…For further details, the reader is referred to [29,18,7,26,27,22,17,10,11] and to the reference therein. Concerning the case of inclusions, a method allowing to find the stresses set up in an elastic body was originally introduced in [13] and later on developed in [14,28,19,20,4,30,25] for various inclusions shape. On the other hand, the reconstruction techniques of small inclusions using only boundary measurements are described in [2].…”

Section: Introductionmentioning

confidence: 99%

A thick‐point approximation of a small body embedded in an elastic medium: justification with an asymptotic analysis

et al. 2021

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The present paper proposes an approximation of the influence of a small inclusion, having different stiffness, in an elastic medium restricting its cinematics to a finite dimensional space. The problem, for the unknown displacement, is written in accordance of transmission conditions between elastic medium and inclusion. The multi-scale asymptotic expansions techniques, by using some corrective terms, are introduced to model the inclusion influence in both initial and approximated problems. Finally, some error estimates for asymptotic expansions are presented and different strategies are compared.

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Neutrality of the elliptic inhomogeneity in the case of non-uniform loading

Cited by 15 publications

References 14 publications

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Soft Neutral Elastic Inhomogeneities with Membrane-type Interface Conditions

A thick‐point approximation of a small body embedded in an elastic medium: justification with an asymptotic analysis

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