Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state

Haghpanah, Babak; Papadopoulos, Jim; Mousanezhad, Davood; Nayeb-Hashemi, Hamid; Vaziri, Ashkan

doi:10.1098/rspa.2013.0856

Cited by 81 publications

(62 citation statements)

References 58 publications

(128 reference statements)

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“…Similar buckling phenomena are generically observed in many systems that are subjected to external or internal stresses, for example in elastic films and sheets [52,70] and in geometrically confined cellular networks [71,72]. The ALCs experience an effective compressive stress due to the extensile 'growth' of the filament pairs in a confined geometry, which arises from their motor-induced shear dynamics.…”

Section: Theorysupporting

confidence: 55%

“…The ALCs experience an effective compressive stress due to the extensile 'growth' of the filament pairs in a confined geometry, which arises from their motor-induced shear dynamics. Application of such a compressive stress leads to buckling of the network's constituents [71,72]. It has been shown that out-of-plane buckling of an elastic sheet due to an effective compressive stress may be quantitatively modeled by a Swift-Hohenberg-type equation with g > 0 2 in the corresponding free energy [52].…”

Section: Theorymentioning

confidence: 99%

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Antipolar ordering of topological defects in active liquid crystals

Oza

Dunkel

2016

New J. Phys.

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ATP-driven microtubule-kinesin bundles can self-assemble into two-dimensional active liquid crystals (ALCs) that exhibit a rich creation and annihilation dynamics of topological defects, reminiscent of particle-pair production processes in quantum systems. This recent discovery has sparked considerable interest but a quantitative theoretical description is still lacking. We present and validate a minimal continuum theory for this new class of active matter systems by generalizing the classical Landau-de Gennes free-energy to account for the experimentally observed spontaneous buckling of motor-driven extensile microtubule bundles. The resulting model agrees with recently published data and predicts a regime of antipolar order. Our analysis implies that ALCs are governed by the same generic ordering principles that determine the non-equilibrium dynamics of dense bacterial suspensions and elastic bilayer materials. Moreover, the theory manifests an energetic analogy with strongly interacting quantum gases. Generally, our results suggest that complex nonequilibrium pattern-formation phenomena might be predictable from a few fundamental symmetry-breaking and scale-selection principles.Active materials [1] assembled from intracellular components, such as DNA [2], microtubules and motor proteins [3-5] promise innovative biotechnological applications, from microscale transport and medical devices [2] to artificial tissues [1] and programmable soft materials [6][7][8]. Beyond their practical value, these systems challenge theorists to generalize equilibrium statistical mechanics to far-from-equilibrium regimes [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Recent experimental advances in the self-assembly and manipulation of colloids with DNA-mediated interactions [27][28][29] have stimulated theoretical analysis that may eventually help clarify the physical principles underlying self-replication [30-32] and evolution in viruses [33][34][35] and other basic biological systems. Yet, despite some partial progress [10,18,19,[36][37][38][39], our conceptual understanding of active materials, and living matter in general, remains far from complete. We do not know whether, or under which conditions, 'universality' ideas [40] that have proved powerful in the description of equilibrium systems can be generalized to describe collective dynamics of active matter not just qualitatively but also quantitatively. This deficit may be ascribed to the fact that mathematical models have been successfully tested against experiments in only a few instances [3,4,15,[41][42][43].Recently discovered 2D active liquid crystal (ALC) analogs [5,[44][45][46][47] comprise an important class of nonequilibrium systems that allows further tests of general theoretical concepts [40] and specific models. ALCs are assemblies of rod-like particles that exhibit non-thermal collective excitations due to steady external [44,45] or internal [5, 47] energy input. At high concentrations, ALCs form an active nematic phase characterized by...

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Section: Theorysupporting

confidence: 55%

Section: Theorymentioning

confidence: 99%

Antipolar ordering of topological defects in active liquid crystals

Oza

Dunkel

2016

New J. Phys.

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“…This geometrical change results in an increase in multiple scattering of the propagating waves at the cell walls and consequently opening up the Bragg-type band gaps [31]. The alterations of the band structure indicate a hierarchy-dependent transition, which parallels the effect of hierarchy on mechanical behavior in other contexts [10][11][12][13][14].…”

mentioning

confidence: 87%

“…Examples include collagen [1], bone [2,3], tooth [2], tendon [3], wood [3,4], nacre [5], gecko foot pads [6], Asteriscus plant [7], Euplectella sponge [8], and water-repellent biological systems [9]. The purely structural role of hierarchy in boosting mechanical performance is now well known [10][11][12][13][14]. In addition to hierarchy, periodic organizations aimed at influencing the wave-propagation behavior, for instance in structural colorations, can also be found in nature [15][16][17].…”

mentioning

confidence: 99%

Honeycomb phononic crystals with self-similar hierarchy

et al. 2015

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We highlight the effect of structural hierarchy and deformation on band structure and wave-propagation behavior of two-dimensional phononic crystals. Our results show that the topological hierarchical architecture and instability-induced pattern transformations of the structure under compression can be effectively used to tune the band gaps and directionality of phononic crystals. The work provides insights into the role of structural organization and hierarchy in regulating the dynamic behavior of phononic crystals, and opportunities for developing tunable phononic devices.

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“…However, when all electromagnets are activated, axial buckling of the cell walls is suppressed, and the lattice material buckles at a higher load into an anti-chiral pattern observed in a regular triangular grid. [20] The stress corresponding to the onset of instability for the anti-chiral pattern was approximately 3.38 higher than that of the floral pattern. This is consistent with the theoretical prediction for the ratio of buckling strength of the periodic structure in the chiral s 0 ð Þ and symmetric s 1 ð Þ modes, s0 s1 ¼ 1 4 1 þ Iin Iout ¼ 3:25 (see part D of the Supporting Information for the analytical derivation of buckling strength).…”

Section: Programmable Nonlinear Elastic Responsementioning

confidence: 90%

Programmable Elastic Metamaterials

et al. 2015

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We introduce a novel concept for the design of programmable-elasticity metamaterials; materials whose elastic properties can be modified instantaneously and reversibly on demand. Real-time tunable linear and nonlinear elastic moduli are obtained in lattice materials by adjustment of strut connectivity via actuation of embedded electromagnetic locks. The Young's modulus and Poisson's ratio of prototype 2D materials are varied instantaneously by more than 2 orders of magnitude and between 0.15 and 0.9, respectively. The buckling strength of the structure is altered by an order of magnitude between two bifurcation states associated with a centrosymmetric and an anti-chiral buckling pattern.

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Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state

Cited by 81 publications

References 58 publications

Antipolar ordering of topological defects in active liquid crystals

Antipolar ordering of topological defects in active liquid crystals

Honeycomb phononic crystals with self-similar hierarchy

Programmable Elastic Metamaterials

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