By redistributing stresses, curvature provides a geometric tool for controlling how materials fracture. In particular, curvature can guide where fracture initiates and how it evolves. At the Chicago MRSEC, Irvine and MRSEC international collaborator Vitelli from the University of Leiden, demonstrated this using thin elastic sheets confined to geometries with positive (shown in red in the images) and negative (blue) Gaussian curvature.
The team’s experiments and simulations show, for the first time, how curvature can be used to stimulate or suppress the growth of cracks, and steer or arrest their propagation. Since stresses from curvature are independent of material parameters, the results have general implications and open up new opportunities for fracture control from the nanoscale to geological strata.
N. Mitchell, V. Koning, V. Vitelli and W.T.M. Irvine, accepted, Nature Materials (2016). DOI:10.1038/NMAT4733
Gaussian curvature—positive for caps and negative for saddles—governs the behaviour of cracks. In the experimental setup, an initially ﬂat PDMS sheet conforms to a curved 3D-printed surface. A small incision nucleates the crack.
On spherical caps, cones, and bumps, the positive integrated curvature from the centre to the crack’s position directs cracks towards the azimuthal direction, while the negative curvature saddle inverts this behaviour.