Negative Poisson ratio in two-dimensional networks under tension

Boal, David H.; Seifert, Udo; Shillcock, Julian C.

doi:10.1103/physreve.48.4274

Cited by 86 publications

(95 citation statements)

References 22 publications

(15 reference statements)

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“…Crystalline 2d networks have been studied extensively in the past [14][15][16], partly because of their biological significance (e.g. as a simple model for the spectrin network in red blood corpuscles) [17,18].…”

Section: Introductionmentioning

confidence: 99%

Equilibrium and dynamic pleating of a crystalline bonded network

Ganguly

Nath

Horbach

et al. 2017

The Journal of Chemical Physics

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We describe a phase transition that gives rise to structurally non-trivial states in a two-dimensional ordered network of particles connected by harmonic bonds. Monte Carlo simulations reveal that the network supports, apart from the homogeneous phase, a number of heterogeneous "pleated" phases, which can be stabilised by an external field. This field is conjugate to a global collective variable quantifying "non-affineness", i.e. the deviation of local particle displacements from local affine deformation. In the pleated phase, stress is localised in ordered rows of pleats and eliminated from the rest of the lattice. The kinetics of the phase transition is unobservably slow in molecular dynamics simulation near coexistence, due to very large free energy barriers. When the external field is increased further to lower these barriers, the network exhibits rich dynamic behaviour: it transforms into a metastable phase with the stress now localised in a disordered arrangement of pleats. The pattern of pleats shows ageing dynamics and slow relaxation to equilibrium. Our predictions may be checked by experiments on tethered colloidal solids in dynamic laser traps.

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Section: Introductionmentioning

confidence: 99%

Equilibrium and dynamic pleating of a crystalline bonded network

Ganguly

Nath

Horbach

et al. 2017

The Journal of Chemical Physics

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“…Recent work indicates that flexible sheet-like structures, such as studied here, are characterized by a negative Poisson ratio ν, [71][72][73] that is, the material expands normal the direction of stretching, as opposed to normal materials which expand in the same direction as the stretching. The formation of a composite material with negative Poisson ratio ("auxetic" materials) is expected to lead to a reduction of the Poisson ratio of the composite as a whole.…”

Section: Relationship Of Structure To Tensile Strengthmentioning

confidence: 99%

The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

Knauert

Douglas

Starr

2007

J Polym Sci B Polym Phys

213

158

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Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity η and the tensile strength τ , which we determine via molecular dynamics simulations. Our simulations of compact (icosahedral), tube or rod-like, and sheet-like model nanoparticles, all at a volume fraction φ ≈ 0.05, indicate an order of magnitude increase in the viscosity η relative to the pure melt. This finding evidently can not be explained by continuum hydrodynamics and we provide evidence that the η increase in our model nanocomposites has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod-like nanoparticles and least for the sheet-like nanoparticles. Curiously, the enhancements of η and τ exhibit opposite trends with increasing chain length N and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in τ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite. The molecular dynamics simulations in the present work focus on the reference case where the modification of the melt structure associated with glass-formation and entanglement interactions should not be an issue. Since many applications require good particle dispersion, we also focus on the case where the polymer-particle interactions favor nanoparticle dispersion. Our simulations point to a substantial contribution of nanoparticle shape to both mechanical and processing properties of polymer nanocomposites.

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“…Their unusual macroscopic properties of expanding in the lateral direction when stretched and accompanying shape changes enable their use in a range of applications, from bioengineering stents to polymeric filters to mechanical energy storage, which require the structure to be able to move repeatedly without failure (Alderson et al, 2001;Ali and Rehman, 2011). Some natural materials are also auxetic and demonstrate these unusual properties through well-known mechanisms involving negative pressures and tension (Boal et al, 1993;Wojciechowski, 1995). Other auxetic designs include reentrant units (Gibson et al, 1982), chiral structures (Lakes, 1991;Prall and Lakes, 1997), interconnected polymeric nodules (Evans, 1989), or relative rotation of rigid units, such as squares, rectangles or triangles (Grima et al, 2005;Espinosa et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Low Fatigue Dynamic Auxetic Lattices With 3D Printable, Multistable, and Tuneable Unit Cells

et al. 2018

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Stress distribution has led to the design of both tough and lightweight materials. Truss structures distribute stress well and are commonly used to design lightweight materials for applications experiencing low strains. In 3D lattices, however, few structures allow high elastic compression and tunable deformation. This is especially true for auxetic material designs, such as the prototypical re-entrant honeycomb with sharp corners, which are particularly susceptible to stress concentrations. There is a pressing need for lightweight lattice designs that are dynamic, as well as resistant to fatigue. Truss designs based on hinged structures exist in nature and delocalize stress rather than concentrating it in small areas. They have inspired us to develop s-hinge shaped elastic unit cell elements from which new classes of architected modular 2D and 3D lattices can be printed or assembled. These lattices feature locally tunable Poisson ratios (auxetic), large elastic deformations without fatigue, as well as mechanical switching between multistable states. We demonstrate 3D printed structures with stress delocalization that enables macroscopic 30% cyclable elastic strains, far exceeding those intrinsic to the materials that constitute them (6%). We also present a simple semi-analytical model of the deformations which is able to predict the mechanical properties of the structures within <5% error of experimental measurements from a few parameters such as dimensions and material properties. Using this model, we discovered and experimentally verified a critical angle of the s-hinge enabling bistable transformations between auxetic and normal materials. The dynamic modeling tools developed here could be used for complex 3D designs from any 3D printable material (metals, ceramics, and polymers). Locally tunable deformation and much higher elastic strains than the parent material would enable the next generation of compact, foldable and expandable structures. Mixing unit cells with different hinge angles, we designed gradient Poisson's ratio materials, as well as ones with multiple stable states where elastic energy can be stored in latching structures, offering prospects for multi-functional designs. Much like the energy efficient Venus flytrap, such structures can store elastic energy and release it on demand when appropriate stimuli are present.

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Negative Poisson ratio in two-dimensional networks under tension

Cited by 86 publications

References 22 publications

Equilibrium and dynamic pleating of a crystalline bonded network

Equilibrium and dynamic pleating of a crystalline bonded network

The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

Low Fatigue Dynamic Auxetic Lattices With 3D Printable, Multistable, and Tuneable Unit Cells

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