title: Intertwined Multiple Spiral Fracture in Perforated Sheets.
abstract: We study multiple tearing of a thin, elastic, brittle sheet indented with a rigid cone. The n cracks initially prepared symmetrically propagate radially for n≥4. However, if n<4 the radial symmetry is broken and fractures spontaneously intertwine along logarithmic spiral paths, respecting order n rotational symmetry. In the limit of very thin sheets, we find that fracture mechanics is reduced to a geometrical model that correctly predicts the maximum number of spirals to be strictly 4, together with their growth rate and the perforation force. Similar spirals are also observed in a different tearing experiment (this time up to n=4, in agreement with the model), in which bending energy of the sheet is dominant.
authors.affiliation: Departamento de Física, Universidad de Santiago de Chile, Avenida Ecuador 3493, 9170124 Estación Central, Santiago, Chile.
authors.forename: Juan-Francisco
authors.initials: JF
authors.lastname: Fuentealba
authors.affiliation: Departamento de Física, Universidad de Santiago de Chile, Avenida Ecuador 3493, 9170124 Estación Central, Santiago, Chile.
authors.forename: Eugenio
authors.initials: E
authors.lastname: Hamm
authors.affiliation: PMMH, CNRS UMR 7636, UPMC, Université Paris 6 and Université Paris Diderot Paris 7, ESPCI Paris, 10 rue Vauquelin, 75231 Paris Cedex 05, France.
authors.forename: Benoît
authors.initials: B
authors.lastname: Roman