Structural Modeling of Metamaterials

Ерофеев, В. И.; Pavlov, I. S.

doi:10.1007/978-3-030-60330-4

Cited by 8 publications

(11 citation statements)

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“…The solution of it is that the potential energy of the springs must be stationary for equilibrium, and a minimum for stable equilibrium, but the constitutive properties are dictated, besides the nature of intermolecular forces, by pure geometric consideration of kinematic compatibility. This interpretation of the macroscopic properties of a crystal, defined by the geometry of the constituent members, the nature of their contact and the type of intermolecular forces, is mesoscopic [2], being halfway between the microscopic level of detail, where particles can be taken into account through quantum physics, and the macroscopic level of continuum mechanics.…”

Section: Introductionmentioning

confidence: 99%

“…In order to account for ‘rotational’ effects and, specifically, torsional vibrations of the lattice members, it is common to conceive mass-spring models where additional eccentric springs connect the body of two adjacent meso-constituents, with anchoring points different from their centroids [2]. This approach is followed for the representation of chiral metamaterials, when the connectors are not symmetrically placed [13,14].…”

Section: Introductionmentioning

confidence: 99%

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Flextegrity simple cubic lattices

Boni

Royer-Carfagni

2023

Proc. R. Soc. A.

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Flextegrity lattices are spatial grids composed of stiff segments kept in contact by compliant pre-tensioned tendons. The kinematic skeleton is sensible to the orientation of the segments, since their relative rotation produces the straining of the tendons to an amount that depends upon the angle of rotation and the shape of the pitch surfaces of the contact joints: these dictate the constitutive properties of the lattice in response to external actions. Two- and three-dimensional lattices are investigated, in which the contact pitch surfaces, obtained with axial-symmetric toothed conjugate profiles, mimic the kinematics of spheres, centred at the nodes of a simple cubic lattice, in pure rolling motion. The allowed mechanisms are discussed under infinitesimal deformation, to recognize possible eigenstress states in the lattice. The response under finite deformations is worked out for two-dimensional lattices under symmetric and asymmetric loading. The theoretical predictions are compared with experimental results on 3D-printed physical models. Possible extensions are discussed for lattices with segments of varying size, different arrangements and multi-stable contact joints. The flextegrity microstructure can represent a mesoscopic model for homogeneous crystals composed of non-pointwise molecules, but it could actually be manufactured in metamaterials with peculiar properties.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Flextegrity simple cubic lattices

Boni

Royer-Carfagni

2023

Proc. R. Soc. A.

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“…However, these theories include a large number of material constants that require experimental determination and the connection of which with the structure of the material is not clear. An alternative direction, structural modeling, is devoid of such a drawback [2].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Mathematical Models of Metamaterials Defined as “Mass-in-Mass” and “Damper-in-Mass” Chains

Kolesov¹

2022

Materials Research Proceedings

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Abstract. To describe dynamic processes in an acoustic (mechanical) metamaterial, there are proposed models that are a one-dimensional chain containing the same masses connected by linearly elastic (or nonlinearly elastic) elements (springs) with the same stiffness. In this case, it is assumed that each mass contains inside itself a series connection of another mass and an elastic element or viscous element (damper).

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“…One-component nonlinear waves of the modified BBM equation have been widely studied [6][7][8][9][10]. However, the properties and methods for studying a two-component vector breather oscillating at the SDFs of the modified BBM equation are qualitatively different from the properties and methods for studying one-component soliton and breather of this equation.…”

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confidence: 99%

“…≠ 0 and we obtain the equation (7) where (8) The solution of Eq. ( 5) is sought in the form (see, e.g., [3][4][5]) (9) where K ± , k ± , and ω ± are real constants and V 0 is the velocity of the nonlinear wave. We assume the inequalities (10) to be satisfied.…”

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confidence: 99%

Two-Component Vector Breather

Adamashvili

2021

Tech. Phys. Lett.

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A two-component solution of the modified Benjamin-Bona-Mahoney equation is considered. Using a generalized perturbative reduction method, the equation is transformed to coupled nonlinear Schrödinger equations for auxiliary functions. An explicit analytical expression is obtained for the shape and parameters of a two-component vector breather, the components of which oscillate at the sum and difference frequencies and wavenumbers.

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Structural Modeling of Metamaterials

Cited by 8 publications

References 0 publications

Flextegrity simple cubic lattices

Flextegrity simple cubic lattices

Nonlinear Mathematical Models of Metamaterials Defined as “Mass-in-Mass” and “Damper-in-Mass” Chains

Two-Component Vector Breather

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