Nonlinear and Linear Elastodynamic Transformation Cloaking

Yavari, Arash; Golgoon, Ashkan

doi:10.1007/s00205-019-01389-2

Cited by 19 publications

(23 citation statements)

References 117 publications

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“…We mention in passing that Milton, Briane, and Willis have proven mathematically in 2006 that the Willis equations are form invariant under general curvilinear spatial coordinate transformations [29,30]. However, their discussion concerning the form invariance of linear Cauchy elasticity has raised some controversy in the literature [31][32][33]. Completely independent of this controversy, linear Willis elasticity remains an interesting generalization of linear Cauchy elasticity.…”

Section: Generalized Static Linear Cauchy Elasticitymentioning

confidence: 96%

Static chiral Willis continuum mechanics for three-dimensional chiral mechanical metamaterials

et al. 2019

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Recent static experiments on twist effects in chiral three-dimensional mechanical metamaterials have been discussed in the context of micropolar Eringen continuum mechanics, which is a generalization of linear Cauchy elasticity. For cubic symmetry, Eringen elasticity comprises nine additional parameters with respect to linear Cauchy elasticity, of which three directly influence chiral effects. Here, we discuss the behavior of the static case of an alternative generalization of linear Cauchy elasticity, the Willis equations. We show that in the homogeneous static cubic case, only one additional parameter with respect to linear Cauchy elasticity results, which directly influences chiral effects. We show that the static Willis equations qualitatively describe the experimentally observed chiral twist effects, too. We connect the behavior to a characteristic length scale.

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Section: Generalized Static Linear Cauchy Elasticitymentioning

confidence: 96%

Static chiral Willis continuum mechanics for three-dimensional chiral mechanical metamaterials

et al. 2019

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“…Clearly if one wants to cloak a large enough mass and moves the body far enough (one body length would suffice) then that mass will be felt through its inertial resistance. An indepth study of limitations to elastodynamic cloaking is in [133].…”

Section: Elastodynamic Equations At Constant Frequencymentioning

confidence: 99%

A unifying perspective on linear continuum equations prevalent in science. Part II: Canonical forms for time-harmonic equations

Milton¹

2020

Preprint

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“…Many researchers have tried to use the idea of transformation cloaking in other fields. In the case of elastodynamics, this has led to many inconsistent formulations that were critically reviewed in [Yavari and Golgoon, 2019] and [Golgoon and Yavari, 2020]. We should emphasize that the ideas related to elastodynamic cloaking are much older and go back to the works [Gurney, 1938, Reissner and Morduchow, 1949, Mansfield, 1953 on reinforced holes in elastic sheets, and [Hashin, 1962, Hashin and Shtrikman, 1963, Hashin, 1985, Hashin and Rosen, 1964, Benveniste and Milton, 2003] on neutral inhomogeneities.…”

Section: Introductionmentioning

confidence: 99%

“…Cloaking a hole in an elastic body can be formulated in terms of two equivalent boundary-value problems [Yavari and Golgoon, 2019]. The hole is covered by a cloak that needs to be designed.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of classical linear elasticity, generalized Cosserat elasticity, and centrosymmetric gradient elasticity, starting from a homogeneous and isotropic virtual body in which the balance of angular momentum is satisfied, it turns out that the balance of angular momentum cannot be satisfied in the physical problem unless the cloaking map is the identity map everywhere. In other words, the balance of angular momentum is the obstruction to exact transformation cloaking [Yavari and Golgoon, 2019]. In the case of elastic plates a set of cloaking compatibility equations obstruct transformation cloaking.…”

Section: Introductionmentioning

confidence: 99%

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Elastodynamic Transformation Cloaking for Non-Centrosymmetric Gradient Solids

Sozio,

Golgoon,

Yavari

2021

Preprint

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In this paper we investigate the possibility of elastodynamic transformation cloaking in bodies made of non-centrosymmetric gradient solids. The goal of transformation cloaking is to hide a hole from elastic disturbances in the sense that the mechanical response of a homogeneous and isotropic body with a hole covered by a cloak would be identical to that of the corresponding homogeneous and isotropic body outside the cloak. It is known that in the case of centrosymmetric gradient solids the balance of angular momentum is the obstruction to transformation cloaking. We will show that this is the case for non-centrosymmetric gradient solids as well.

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Nonlinear and Linear Elastodynamic Transformation Cloaking

Cited by 19 publications

References 117 publications

Static chiral Willis continuum mechanics for three-dimensional chiral mechanical metamaterials

Static chiral Willis continuum mechanics for three-dimensional chiral mechanical metamaterials

A unifying perspective on linear continuum equations prevalent in science. Part II: Canonical forms for time-harmonic equations

Elastodynamic Transformation Cloaking for Non-Centrosymmetric Gradient Solids

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