Growth of a viscoplastic blister underneath an elastic sheet

Abstract

Inspired by geological structures formed by magmatic intrusions that deform the Earth's crust, we investigate the elastohydrodynamic growth of a viscoplastic blister under an elastic sheet resting on a prewetted substrate. By combining experiments, scaling analysis and numerical simulations, we reveal new regimes for the elastoviscoplastic growth dynamics of the blister. The blister height and its apparent radius grow as $h(0,t) \sim t^{5/9}$ and $R(t) \sim t^{2/9}$ if the fluid pressure is set by bending of the sheet, and as $h(0,t) \sim t^{5/13}$ and $R(t) \sim t^{4/13}$ if the fluid pressure is set by stretching of the sheet. A plug-like flow inside the blister dictates its dynamics, whereas the blister takes a self-similar shape given by a balance of the fluid's yield stress and the pressure gradient induced by the deformation of the elastic sheet.