Fractal balls

Bevilácqua, Luiz

doi:10.1016/j.apm.2003.10.017

Cited by 6 publications

(11 citation statements)

References 1 publication

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“…[38], dashed line: power-law asymptotic (2), and solid curve is calculated by Eqs. (35) and (36) with A = 6.776 MPa, a = 10.08, (10) D = 2.64, and ip = 0.817. For visual appreciation of the fit quality we use the same scales as in Fig.…”

Section: Pressure-packing Density Relationshipmentioning

confidence: 99%

“…(35) and (36) can be used to fit experimental data available in the range (3) and then extrapolate them to higher pressures and larger packing densities. Figure 7 illustrates that Eq.…”

Section: Pressure-packing Density Relationshipmentioning

confidence: 99%

“…As the compaction ratio K -L / R in creases, the packing density increases up to p = 1 at = ( n L / 6 h ) l/3. Experiments [12][13][14][15], theoretical con siderations [9][10][11][12][13]15,22,28,36], and numerical simulations [29][30][31]35,36,37] suggest that once K exceeds the threshold value K lh ( K lh & 1.7 [29,30]) the sheet packing density exhibits a power-law dependence on P. That is,…”

Section: Introductionmentioning

confidence: 99%

“…The crumpling behavior of thin sheets is strongly dependent on the confinement mode [15,22] and sheet geometry [22,34], One of the basic modes is the crumpling of a thin sheet subjected to isotropic confinement [22,[29][30][31]35], Under increasing hydrostatic pressure (P ) an initially flat square sheet is folded into an approximately spherical ball of diameter R with the packing density 6 hL? where h and L are the sheet thickness and edge size, respectively. As the compaction ratio K -L / R in creases, the packing density increases up to p = 1 at = ( n L / 6 h ) l/3.…”

Section: Introductionmentioning

confidence: 99%

“…Log-log plots of normalized pressure (P/A) versus packing density (1) along with the energetic (2) and entropic(3)contributions into P(p) behavior(35) for an elastic self-avoiding sheet with a = 5.2 (D = 22/9 and ip = 2/3).…”

mentioning

confidence: 99%

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Edwards's statistical mechanics of crumpling networks in crushed self-avoiding sheets with finite bending rigidity

Balankin

Flores-Cano

2015

Phys. Rev. E

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This paper is devoted to the crumpling of thin matter. The Edwards-like statistical mechanics of crumpling networks in a crushed self-avoiding sheet with finite bending rigidity is developed. The statistical distribution of crease lengths is derived. The relationship between sheet packing density and hydrostatic pressure is established. The entropic contribution to the crumpling network rigidity is outlined. The effects of plastic deformations and sheet self-contacts on crumpling mechanics are discussed. Theoretical predictions are in good agreement with available experimental data and results of numerical simulations. Thus, the findings of this work provide further insight into the physics of crumpling and mechanical properties of crumpled soft matter.

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Section: Pressure-packing Density Relationshipmentioning

confidence: 99%

“…(35) and (36) can be used to fit experimental data available in the range (3) and then extrapolate them to higher pressures and larger packing densities. Figure 7 illustrates that Eq.…”

Section: Pressure-packing Density Relationshipmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Edwards's statistical mechanics of crumpling networks in crushed self-avoiding sheets with finite bending rigidity

Balankin

Flores-Cano

2015

Phys. Rev. E

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Mechanical properties in crumple-formed paper derived materials subjected to compression

Hanaor

Flores‐Johnson

Wang

et al. 2017

Heliyon

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The crumpling of precursor materials to form dense three dimensional geometries offers an attractive route towards the utilisation of minor-value waste materials. Crumple-forming results in a mesostructured system in which mechanical properties of the material are governed by complex cross-scale deformation mechanisms. Here we investigate the physical and mechanical properties of dense compacted structures fabricated by the confined uniaxial compression of a cellulose tissue to yield crumpled mesostructuring. A total of 25 specimens of various densities were tested under compression. Crumple formed specimens exhibited densities in the range 0.8–1.3 g cm−3, and showed high strength to weight characteristics, achieving ultimate compressive strength values of up to 200 MPa under both quasi-static and high strain rate loading conditions and deformation energy that compares well to engineering materials of similar density. The materials fabricated in this work and their mechanical attributes demonstrate the potential of crumple-forming approaches in the fabrication of novel energy-absorbing materials from low-cost precursors such as recycled paper. Stiffness and toughness of the materials exhibit density dependence suggesting this forming technique further allows controllable impact energy dissipation rates in dynamic applications.

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Topological crossovers in the forced folding of self-avoiding matter

Balankin

Matamoros

León

et al. 2009

Physica A: Statistical Mechanics and its Applications

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We study the scaling properties of forced folding of thin materials of different geometry. The scaling relations implying the topological crossovers from the folding of three-dimensional plates to the folding of two-dimensional sheets and further to the packing of one-dimensional strings are derived for elastic and plastic manifolds. These topological crossovers in the folding of plastic manifolds were observed in experiments with predominantly plastic aluminum strips of different geometry. Elasto-plastic materials, such as paper sheets during the (fast) folding under increasing confinement force, are expected to obey the scaling force-diameter relation derived for elastic manifolds. However, in experiments with paper strips of different geometry we observed the crossover from packing of one-dimensional strings to folding two dimensional sheets only, because the fractal dimension of the set of folded elasto-plastic sheets is the thickness dependent due to the strain relaxation after a confinement force is withdrawn.

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Fractal balls

Cited by 6 publications

References 1 publication

Edwards's statistical mechanics of crumpling networks in crushed self-avoiding sheets with finite bending rigidity

Edwards's statistical mechanics of crumpling networks in crushed self-avoiding sheets with finite bending rigidity

Mechanical properties in crumple-formed paper derived materials subjected to compression

Topological crossovers in the forced folding of self-avoiding matter

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