TY - JOUR
T1 - Topological crossovers in the forced folding of self-avoiding matter
AU - Balankin, Alexander S.
AU - Matamoros, Daniel Morales
AU - Pineda León, Ernesto
AU - Rangel, Antonio Horta
AU - Martínez Cruz, Miguel Ángel
AU - Samayoa Ochoa, Didier
N1 - Funding Information:
We wish to thank Professor T.A. Witten for the comments concerning the density of folding energy stored in the fractal balls. This work was supported by the Government of Mexico City under Project PICCT08-38.
PY - 2009/5/1
Y1 - 2009/5/1
N2 - 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of folded elasto-plastic sheets is the thickness dependent due to the strain relaxation after a confinement force is withdrawn.
AB - 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.
KW - Forced folding
KW - Fractal dimension
KW - Scaling
KW - Topological crossover
UR - http://www.scopus.com/inward/record.url?scp=60449095580&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2009.01.021
DO - 10.1016/j.physa.2009.01.021
M3 - Artículo
SN - 0378-4371
VL - 388
SP - 1780
EP - 1790
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 9
ER -