Multi-scale modelling of ice fracture patterns on the surface of Europa using computationally derived tidal boundary conditions

The smallest of Jupiter’s Galilean satellites, Europa has one of the smoothest surfaces of our solar system. This is due to the comparative youth of its ice crust which is believed to resurface over time. This ice crust is observed to be crisscrossed with a multitude of linae, thought to be large-scale fractures, as well as dotted with numerous regions of lenticulae and chaos. Tidal stresses on Europa are modelled according to Wahr (2009) and are evaluated over periods of 1e3-1e6 years. The nucleation, growth and interaction of fractures is modelled using a three-dimensional finite element-based fracture simulator which assumes that the material is linear, isotropic and homogeneous. Other material properties are drawn from Selvans (2009). Nucleation of fractures is assumed to occur only in tension, and sub-scale nucleation modelled by a damage criterion models the weakening of the ice matrix. Stress intensity factors at the fracture tips are computed with the displacement correlation method. Fracture growth is modelled geometrically as a function of the accumulation of stresses on the fracture tips. The simulator evaluates how tidal stresses are expected to induce the nucleation and growth of fractures on the surface of Europa. Nucleation and growth are modelled in two regions, an equatorial region and a sub-polar region, representative of deformation scenarios on the satellite surface. The simulation runs at two different scales. Tidal forces are computed at the satellite scale using Wahr (2009). These are applied as boundary conditions of smaller scale 100km x 100km x 20km cuboidal regions, in which the nucleation and growth of fractures is modelled. Within each region, a number of three dimensional non-planar fractures grow and interact. Resulting patterns are compared against observational data.