Modeling of micropolar type chiral structures

Vasiliev, Aleksey A.

doi:10.22226/2410-3535-2013-3-248-251

Cited by 2 publications

(3 citation statements)

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“…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]. Another class is represented by lattice solid models [15], consisting of non-pointwise particles linked by bonds of various nature.…”

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]. Another class is represented by lattice solid models [15], consisting of non-pointwise particles linked by bonds of various nature.…”

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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“…В статьях [14,15] нами строятся модели и изучаются свойства квадратных решеток Коссера с хиральной микроструктурой с частицами конечного размера и сложными пружинными связями. В настоящей статье представлена структурная и дискретная модели треугольных решеток, отмечены их интересные свойства, а также строится микрополярная модель, выделяются ее особенности.…”

Section: Introductionunclassified

Models and some properties of Cosserat triangular lattices with chiral microstructure

Vasiliev¹,

Pavlov²

2019

LOM

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Structural, discrete and continual models of the Cosserat triangular lattice with a chiral microstructure are elaborated. The structural model is constructed on the base of particles of finite size with complex spring bonds. With symmetric diagonal bonds, one has the usual Cosserat triangular lattice, while with different diagonal bonds the Cosserat lattice with a chiral microstructure is realized. The choice of different variants enables one to compare the lattices with the ordinary and chiral microstructures and to select the specific properties caused by the chirality. For this purpose, the problems for the hexagonal cell are solved. In the first problem, the behaviour of the cell under a uniform compression (tension) of the cell is investigated. The ordinary lattice is compressed (elongated) in the direction of the force action. The particles of the chiral cell deviate from the direction of the force action during their displacements. The direction of the deviation is different for compressive (tensile) forces, i. e. the chiral lattice responds qualitatively differently to compression and tension. In the second problem, the top and bottom layers of the cell are rigidly compressed (stretched). The middle layer of the ordinary lattice is then stretched (compressed). This is a typical reaction of ordinary materials to tension (compression). The particles displace along the layer. In the chiral lattice, the middle layer is compressed under compression and is stretched under tension of the cell, i. e. chiral cell possesses the auxeticity property. In this case, the middle layer is inclined. The direction of inclination is different for compression or tension. Thus, the chirality effect is manifested. On the basis of the discrete model, equations of the continuum micropolar model are obtained. For symmetric connections, one has equations of the ordinary micropolar theory. The chiral lattice enables one to obtain equations of the chiral micropolar theory and to select the terms of the equations provided by chirality. Using the continuum model, one can find the values of the parameters, for which the second-order derivatives disappear in the rotational equations for the triangular lattice. Thus, it is possible to select a special case of parameters, for which the lattice is described by the equations of the reduced Cosserat theory.

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Modeling of micropolar type chiral structures

Cited by 2 publications

References 5 publications

Flextegrity simple cubic lattices

Flextegrity simple cubic lattices

Models and some properties of Cosserat triangular lattices with chiral microstructure

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