An Energetic Study of a One-Dimensional Model of a Liquid-Filled Crack.

Abstract:

Formation of dykes through magma ascent is a difficult problem with complex fluid-structure interaction. We present here an energetic framework for the study of the propagation of liquid-filed cracks in a solid. We consider a one-dimensional example of an inextensible membrane bonded to a rigid substrat. This simplified toy model allows to focus on the physics of fracture and fluid-structure interaction. The evolution problem is formulated in terms of two principles: a stability criterion which consists in minimizing the total energy of the system (potential energy + fracture surface energy) and an energy balance condition which enforces the continuity of the total energy with respect to the loading. Different cases are analyzed, whether by considering the crack propagation horizontal or vertical. In this latter case, we measure the impact of the fluid's buoyancy on the results. We also investigate how viscosity of the fluid modifies the framework and its consequences on the crack's evolution compared to a quasi-static approach. Those preliminary results are essential milestones toward a 3-D resolution of the problem.