The mechanics of three-dimensional cellular materials
08 Jul 1982-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (The Royal Society)-Vol. 382, Iss: 1782, pp 43-59
TL;DR: In this paper, the mechanical properties of two-dimensional cellular materials, or honeycombs, are analyzed and compared with experiments, in terms of bending, elastic buckling and plastic collapse of the beams that make up the cell walls.
Abstract: The mechanical properties (linear and nonlinear elastic and plastic) of two-dimensional cellular materials, or honeycombs, are analysed and compared with experiments. The properties are well described in terms of the bending, elastic buckling and plastic collapse of the beams that make up the cell walls.
Citations
More filters
TL;DR: A route is developed for fabricating extremely low-density, hollow-strut metallic lattices that exhibit complete recovery after compression exceeding 50% strain, and energy absorption similar to elastomers and attribute these properties to structural hierarchy at the nanometer, micrometer, and millimeter scales.
Abstract: Ultralight (<10 milligrams per cubic centimeter) cellular materials are desirable for thermal insulation; battery electrodes; catalyst supports; and acoustic, vibration, or shock energy damping. We present ultralight materials based on periodic hollow-tube microlattices. These materials are fabricated by starting with a template formed by self-propagating photopolymer waveguide prototyping, coating the template by electroless nickel plating, and subsequently etching away the template. The resulting metallic microlattices exhibit densities ρ ≥ 0.9 milligram per cubic centimeter, complete recovery after compression exceeding 50% strain, and energy absorption similar to elastomers. Young’s modulus E scales with density as E ~ ρ^2, in contrast to the E ~ ρ^3 scaling observed for ultralight aerogels and carbon nanotube foams with stochastic architecture. We attribute these properties to structural hierarchy at the nanometer, micrometer, and millimeter scales.
1,412 citations
TL;DR: The mechanical properties (elastic, plastic, creep, and fracture) of cellular solids or foams are related to the properties of the cell wall material and to the cell geometry.
Abstract: The mechanical properties (elastic, plastic, creep, and fracture) of cellular solids or foams are related to the properties of the cell wall material and to the cell geometry The properties are well described by simple formulae Such materials occur widely in nature and have many potential engineering applications
909 citations
TL;DR: The results of this previous study are applied to cancellous bone in an attempt to further understand its mechanical behaviour and the results agree reasonably well with experimental data available in the literature.
867 citations
TL;DR: The mechanics of a wide range of natural cellular materials and their role in lightweight natural sandwich structures and natural tubular structures are examined, as well as two examples of engineered biomaterials with a cellular structure, designed to replace or regenerate tissue in the body.
845 citations
TL;DR: The Young's modulus of elasticity, the calcium content and the volume fraction (1-porosity) of 23 tension specimens and 80 bending specimens, taken from compact bone of 18 species of mammal, bird and reptile, were determined.
818 citations
References
More filters
Book•
[...]
01 Jan 1934
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Abstract: Chapter 1: Stresses and Strains Chapter 2: Foundations of Plasticity Chapter 3: Elasto-Plastic Bending and Torsion Chapter 4: Plastic Analysis of Beams and Frames Chapter 5: Further Solutions of Elasto-Plastic Problems Chapter 6: Theory of the Slipline Field Chapter 7: Steady Problems in Plane Strain Chapter 8: Non-Steady Problems in Plane Strain
20,724 citations
Book•
[...]
01 Jan 1917
TL;DR: This book is an application of some of the concepts of physical science and sundry mathematical methods to the study of organic form and is like one of Darwin's books, well-considered, patiently wrought-out, learned, and cautious.
Abstract: Introduction John Tyler Bonner VII 1. Introductory 2. On magnitude 3. The forms of cells 4. The forms of tissues, of cell-aggregates 5. On spicules and spicular skeletons 6. The equiangular spiral 7. The shapes of horns and of teeth or tusks 8. On form and mechanical efficiency 9. On the theory of transformations, or the comparison of related forms 10. Epilogue Index.
4,470 citations
3,823 citations
01 Jan 1950
TL;DR: In this article, a self-consistent method for the estimation of the shear modulus and the bulk modulus is proposed, where each hole is surrounded by a spherical shell of real material, and the reaction of the rest of the material is estimated by replacing it by equivalent homogeneous material.
Abstract: The effective bulk and shear moduli are calculated by a self-consistent method due to Frohlich and Sack. The bulk modulus k is determined by applying a hydrostatic pressure, and the shear modulus μ by applying a simple homogeneous shear stress, to a large sphere. Each hole is surrounded by a spherical shell of real material, and the reaction of the rest of the material is estimated by replacing it by equivalent homogeneous material For consistency, both the density and the displacement of the outer spherical boundary must be the same whether the hole and its surrounding shell are replaced by equivalent material or not. The effective elastic constants calculated from these conditions are 1/k = 1/k0ρ + 3(1 - ρ)/4μ0ρ + O[(1 - ρ)3], (μ0 - μ)/μ0 = 5(1 - ρ)(3k0 + 4μ0)/(9k0 + 8μ0) + O[(1 - ρ)2], where k0 and μ0 refer to the real material and ρ is the density of the actual material relative to that of the real material, in the next approximation k depends on the standard deviation of the volumes of the holes. The dilatation due to a distribution of pressures in the holes is p(1/k - 1/k0), where p is the mean obtained when the pressure in each hole has a weight proportional to the volume of the hole. By using the hydrodynamic analogue of the elastic problem, the theory is briefly applied to the theory of sintering, and used to discuss the effective viscosity of a liquid containing small air bubbles.
748 citations