Growth of a viscoplastic blister underneath an elastic sheet

Abstract

Inspired by the formation of geological structures as earth's crust deforms by magmatic intrusions, we investigate the elastohydrodynamic growth of a viscoplastic blister under an elastic sheet. By combining experiments, scaling analysis and numerical simulations we reveal a new regime for the growth of the blister's height $\sim t^{5/9}$ and radius $\sim t^{2/9}$. A plug like flow inside the blister dictates its dynamics, whereas the blister takes a quasi-static self-similar shape given by a balance in the pressure gradient induced by bending of the elastic sheet and the fluid's yield stress.