Spherically layered inclusions in a homogeneous elastic medium

Kanaun, S. K.; Kudryavtseva, L. T.

doi:10.1016/0021-8928(86)90013-4

Cited by 32 publications

(6 citation statements)

References 1 publication

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“…A complete solution of the static problem for a many layered inclusion is obtained in [23], where the detailed expression for tensor A(x) is presented.…”

Section: Versions II and Iii Of The Emm In The Long-wave Regionmentioning

confidence: 99%

Propagation of elastic waves in composites with random set of spherical inclusions (effective medium approach)

2004

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“…A complete solution of the static problem for a many layered inclusion is obtained in [23], where the detailed expression for tensor A(x) is presented.…”

Section: Versions II and Iii Of The Emm In The Long-wave Regionmentioning

confidence: 99%

Propagation of elastic waves in composites with random set of spherical inclusions (effective medium approach)

2004

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“…Another class of analytical solutions may be constructed for a spherically symmetric inclusion subjected to a constant external field E 0 [12]. Let us consider an isotropic medium with a spherical and isotropic inclusion centered at the origin of the Cartesian coordinate system.…”

Section: Some Analytical Solutions Of the Integral Equation (21)mentioning

confidence: 99%

A numerical method for the solution of thermo- and electro-static problems for a medium with isolated inclusions

Kanaun

Kochekseraii

2003

Journal of Computational Physics

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“…The alignment of fibers, and how different plies are stacked up, causes the anisotropy as well as values of effective parameters at the macroscale [23][24][25][26][27]. Porous materials are frequently modeled as a full material with voids as given inclusions at the microscale, we refer to [28][29][30][31][32][33]. Additive manufacturing is capable of building metamaterials as demonstrated in [34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization

Abali

Barchiesi

2020

Continuum Mech. Thermodyn.

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Metamaterials exhibit materials response deviation from conventional elasticity. This phenomenon is captured by the generalized elasticity as a result of extending the theory at the expense of introducing additional parameters. These parameters are linked to internal length scales. Describing on a macroscopic level, a material possessing a substructure at a microscopic length scale calls for introducing additional constitutive parameters. Therefore, in principle, an asymptotic homogenization is feasible to determine these parameters given an accurate knowledge on the substructure. Especially in additive manufacturing, known under the infill ratio, topology optimization introduces a substructure leading to higher-order terms in mechanical response. Hence, weight reduction creates a metamaterial with an accurately known substructure. Herein, we develop a computational scheme using both scales for numerically identifying metamaterials parameters. As a specific example, we apply it on a honeycomb substructure and discuss the infill ratio. Such a computational approach is applicable to a wide class substructures and makes use of open-source codes; we make it publicly available for a transparent scientific exchange.

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Spherically layered inclusions in a homogeneous elastic medium

Cited by 32 publications

References 1 publication

Propagation of elastic waves in composites with random set of spherical inclusions (effective medium approach)

Propagation of elastic waves in composites with random set of spherical inclusions (effective medium approach)

A numerical method for the solution of thermo- and electro-static problems for a medium with isolated inclusions

Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization

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