Cracks in Tension-Field Elastic Sheets

O. Mahmood , B. Audoly (1) , S. Roux (2)

1 IJLRDA-MISES - Mécanique et Ingénierie des Solides Et des Structures
2 LMPS - Laboratoire de Mécanique Paris-Saclay

We consider the deformation of a thin elastic sheet which is stiff in traction but very soft in compression, as happens in presence of wrinkling. We use the tension-field material model and explore numerically the response of a thin sheet containing multiple cracks of different geometries, when subjected to applied tension. With a single crack, the stress concentrates along a St-Andrew's cross-shaped pattern, whose branches extend from the crack tips to the corners of the domain; at a (small) distance r from the crack tip, the stress displays the usual $r^{−1/2}$ stress singularity but with an unusual and non-universal angular dependence. A strong interaction between multiple cracks is reported and discussed: in particular, for certain configurations of the cracks, the tensile stiffness of a cracked sheet can be zero even though the sheet is made up of a single component.

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Physique mathématique [math-ph]

O. Mahmood, B. Audoly, S. Roux. Cracks in Tension-Field Elastic Sheets. Physical Review Letters, 2018, 121 (14), ⟨10.1103/PhysRevLett.121.144301⟩. ⟨hal-01898155⟩