Effective elastic behavior of some models for perfect cellular solids

Grenestedt, Joachim L.

doi:10.1016/s0020-7683(98)00048-1

Cited by 116 publications

(55 citation statements)

References 16 publications

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“…Many analytical models have been proposed for the elastic stiffness of cellular materials, and with each there is associated a specific set of assumptions about the architecture of the foam and appropriate deformation mechanisms [18,19,[21][22][23][24][25][26]. In summary, for open-cell foams where elastic deformation is dominated by stretching of the beams, the stiffness is a linear function of the relative density.…”

Section: Elastic Propertiesmentioning

confidence: 99%

Deformation of open-cell aluminum foam

2001

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Abstract-The mechanical properties of high-purity aluminum foams produced by replication from salt precursors are measured in compression. These foams have homogeneous open-porosity, cell sizes equivalent to the particle size of the precursor salt (ෂ500 µm in this case) and relative densities near 25%. Deformation is uniform and strain hardening similar to the bulk material is observed without a plateau stress. A simple analytical model based on beam theory is employed to describe the flow stress and the change in stiffness of the foams as a consequence of compression. This model leads to a modified scaling law for the flow stress of metallic foams. 

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Section: Elastic Propertiesmentioning

confidence: 99%

Deformation of open-cell aluminum foam

2001

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“…When loaded macroscopically, closed cell materials develop tensile membrane stresses that efficiently utilize material volume independent of the macroscopic loading direction 24 . This stretched material contributes maximally to the macroscopic stiffness 24,11 . The geometric complexity of ordered 3D closed cell materials has historically made their study and utilization impractical, from both an analytical predictive, and a manufacturing standpoint.…”

mentioning

confidence: 99%

“…The ordinate intercepts at zero relative density in FIG.3, which we denote SE, SG, and SK for the plots of ( ̅ ⁄ )/( ̅ ⁄ ), ( ̅ ⁄ )/( ̅ ⁄ ) and ( ̅ ⁄ )/( ̅ ⁄ ) respectively, quantify this volume, being the fractional modulus of an equivalent effective continuum. As relative density increases, 2 nd and 3 rd order contributions, associated with the bending of struts and plates respectively 11 , become significant. In the case of the bulk modulus, the theoretical bounds are sensitive to the Poisson ratio,  of the constituent material.…”

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confidence: 99%

Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness

Berger

Wadley

McMeeking

2017

Nature

581

280

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A wide variety of high-performance applications require materials for which shape control is maintained under substantial stress, and that have minimal density. Bio-inspired hexagonal and square honeycomb structures and lattice materials based on repeating unit cells composed of webs or trusses, when made from materials of high elastic stiffness and low density, represent some of the lightest, stiffest and strongest materials available today. Recent advances in 3D printing and automated assembly have enabled such complicated material geometries to be fabricated at low (and declining) cost. These mechanical metamaterials have properties that are a function of their mesoscale geometry as well as their constituents, leading to combinations of properties that are unobtainable in solid materials; however, a material geometry that achieves the theoretical upper bounds for isotropic elasticity and strain energy storage (the Hashin-Shtrikman upper bounds) has yet to be identified. Here we evaluate the manner in which strain energy distributes under load in a representative selection of material geometries, to identify the morphological features associated with high elastic performance. Using finite-element models, supported by analytical methods, and a heuristic optimization scheme, we identify a material geometry that achieves the Hashin-Shtrikman upper bounds on isotropic elastic stiffness. Previous work has focused on truss networks and anisotropic honeycombs, neither of which can achieve this theoretical limit. We find that stiff but well distributed networks of plates are required to transfer loads efficiently between neighbouring members. The resulting low-density mechanical metamaterials have many advantageous properties: their mesoscale geometry can facilitate large crushing strains with high energy absorption, optical bandgaps and mechanically tunable acoustic bandgaps, high thermal insulation, buoyancy, and fluid storage and transport. Our relatively simple design can be manufactured using origami-like sheet folding and bonding methods.

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“…In this figure dashed lines indicate the results for reference structures with flat cell walls, whereas the solid lines give the density dependence of the structures based on the dry foams' geometries. Values for Ã reported by Grenestedt 3) for flat-celled tetrakaidecahedra structures are given for comparison. They fit very well with the values found for the respective structures in the present investigation.…”

Section: Resultsmentioning

confidence: 99%

Space-Filling Polyhedra as Mechanical Models for Solidified Dry Foams

2006

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The simulation of the mechanical behavior of idealized cellular structures is important as it gives insight into the principal deformation mechanisms that govern the mechanical behavior of real cellular structures, such as polymer foams or metallic foams, making accessible at least qualitative information about properties that are difficult to determine otherwise, for example the effective strength under hydrostatic loading. For capturing the mechanics of a closed-cell foam material in a meaningful way, three-dimensional models are employed in the context of the Finite Element method. The modeling approach presented in this paper employs generic, periodic unit cell models with the extension of providing physically sound microstructures by basing these models on surfaces of minimal energy calculated with the program Surface Evolver. This program is able to minimize the energy of a surface subject to given constraints, for example a prescribed initial geometry and, where required, periodicity. Accordingly, space-filling polyhedra with cells being separated by walls of minimal total area can be predicted, such as Lord Kelvin's tetrakaidecahedra or the Weaire-Phelan partition, the latter being energetically more favorable. These physics-based configurations are good representations of solidified (dry) foams. The results obtained by Finite Element stress and deformation analyses comprise the full tensor of elasticity and its dependence on the effective density; the non-planar faces resulting from the surface energy minimization are shown to influence the behavior for very low effective densities. By studying the behavior up to the onset of yielding on the effective, macro-mechanical level including the effects of multi-axial loading conditions, valuable information for the homogenized representation of closed-cell foams is obtained.

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Effective elastic behavior of some models for perfect cellular solids

Cited by 116 publications

References 16 publications

Deformation of open-cell aluminum foam

Deformation of open-cell aluminum foam

Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness

Space-Filling Polyhedra as Mechanical Models for Solidified Dry Foams

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