Chiral metamaterial predicted by granular micromechanics: verified with 1D example synthesized using additive manufacturing

Misra, Anil; Nejadsadeghi, Nima; Angelo, Michele De; Placidi, Luca

doi:10.1007/s00161-020-00862-8

Cited by 40 publications

(31 citation statements)

References 43 publications

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“…The microstructure is conceived in order to obtain chirality effects analogous to those already measured experimentally in [38], where the observation of an interesting and exotic stable equilibrium path is reported. Indeed, in extension tests performed by [38], a characteristic stable shaped deformed equilibrium configuration is found when clamping clamping conditions are applied.…”

Section: Introductionmentioning

confidence: 99%

Equilibria determination of elastic articulated duoskelion beams in 2D via a Riks-type algorithm

Barchiesi

Dell’Isola

Bersani

et al. 2021

International Journal of Non-Linear Mechanics

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The overall behavior of an articulated beam structure constituted by elements arranged according to a specific chirality is studied. The structure as a whole, due to its slenderness and geometry, is called duoskelion beam. The name duoskelion is a neologism which is inspired by the Greek word δύοσκέλιον (two-legged). A discrete model for shearable beams, formulated recently, is exploited to investigate its mechanics. A purposely designed numerical scheme, adapting the Riks rationale, is used to calculate large displacement and deformation equilibria of duoskelion beams. Aimed at computing the current step correction, the Riks arc-length method is modified and made more efficient by applying a specific orthogonality condition, defined via the stiffness matrix, to an adapted extrapolation step. The robustness of the resulting scheme and its capability to follow equilibrium branches allows, in principle, for the exploration of the whole set of local energy minima in the introduced space of configurations, by using suitably modulated perturbative external loads. The developed numerical tool can be used to understand the mechanics of duoskelion beams. It is proved that there exists a stable principal equilibrium branch in which only compression is observed for any compression load. Additional stable equilibrium branches are found in compression such that the clamped-clamped compressed beam assumes a characteristic shape which, upon reaching a critical load, is significantly amplified. A mechanically relevant stable equilibrium is also found in extension, being observed the-shaped configuration experimentally found in Misra et al. (2020).

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Section: Introductionmentioning

confidence: 99%

Equilibria determination of elastic articulated duoskelion beams in 2D via a Riks-type algorithm

Barchiesi

Dell’Isola

Bersani

et al. 2021

International Journal of Non-Linear Mechanics

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“…Athermal granular material systems exhibit many non-standard physical phenomena, such as that of negative group velocity, 24,25 frequency band gaps, [26][27][28][29] chirality 30 and load path dependency. The latter is the key physical phenomenon that underlies our results: collections of discrete athermal particles have the remarkable property that they can become rigid when assembled into certain arrangements.…”

Section: Mechanical Phasesmentioning

confidence: 99%

“…We also provide strong evidence that particle rotations are an essential kinematical quantity in the study of dense amorphous packings, as they are already in the field of active matter 6 and metamaterials. 30 More broadly, the spatial autocorrelation analysis of rotations that we employ may reveal essential features in materials science of a large variety of materials that exhibit the effects of intrinsic length scales.…”

Section: Rotational Dynamics Across the Phase Boundarymentioning

confidence: 99%

Rotational diffusion and rotational correlations in frictional amorphous disk packings under shear

Wang

Nejadsadeghi

et al. 2021

Soft Matter

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“…It is worth noting that this simplification may lose its applicability for materials that possess strong variations and discontinuities of stiffnesses or have highly disordered micro-geometries, which could be deliberately designed as in pantographic metamaterials [17,[43][44][45][46][47][48][49][50][51][52][53][54][55][56][57] or in granular (meta)materials [58]. In these cases, Taylor's series expansion is not representative and additional kinematic descriptors may be introduced to accurately describe the response as in Cosserat or micromorphic media [59,60].…”

Section: Relative Inter-granular Displacement and Related Continuum Deformation Measuresmentioning

confidence: 99%

“…The strain field is then used by means of ( 7)- (12) to compute the relative displacements u η , u τ , which depend on the space coordinates and on the angle θ. Such displacements are then given as input to the KKT conditions in (55), (56), and (58). The damage fields D η and D τ are recovered as an output of KKT conditions.…”

mentioning

confidence: 99%

Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution

Timofeev¹,

Barchiesi

Misra

et al. 2020

Mathematics and Mechanics of Solids

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Mechanical behavior of materials with granular microstructures is confounded by unique features of their grain-scale mechano-morphology, such as the tension–compression asymmetry of grain interactions and irregular grain structure. Continuum models, necessary for the macro-scale description of these materials, must link to the grain-scale behavior to describe the consequences of this mechano-morphology. Here, we consider the damage behavior of these materials based upon purely mechanical concepts utilizing energy and variational approach. Granular micromechanics is accounted for through Piola’s ansatz and objective kinematic descriptors obtained for grain-pair relative displacement in granular materials undergoing finite deformations. Karush–Kuhn–Tucker (KKT)-type conditions that provide the evolution equations for grain-pair damage and Euler–Lagrange equations for evolution of grain-pair relative displacement are derived based upon a non-standard (hemivariational) variational approach. The model applicability is illustrated for particular form of grain-pair elastic energy and dissipation functionals through numerical examples. Results show interesting damage-induced anisotropy evolution including the emergence of a type of chiral behavior and formation of finite localization zones.

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Chiral metamaterial predicted by granular micromechanics: verified with 1D example synthesized using additive manufacturing

Cited by 40 publications

References 43 publications

Equilibria determination of elastic articulated duoskelion beams in 2D via a Riks-type algorithm

Equilibria determination of elastic articulated duoskelion beams in 2D via a Riks-type algorithm

Rotational diffusion and rotational correlations in frictional amorphous disk packings under shear

Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution

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