Finite Viscoelastic Modeling of Ice Shelves Using Glen's Flow Law and Depth‐Dependent Material Properties

Source abstract

ABSTRACT Ice shelves are floating seaward extensions of glaciers that form where land‐based ice flows into the ocean. Recent observations suggest that their mechanical behavior is suitably described by a viscoelastic Maxwell model, as this framework captures both the instantaneous elastic response and the time‐dependent viscous flow of ice. The constitutive framework in this contribution is formulated within a finite strain framework based on a multiplicative decomposition of the deformation gradient into elastic and viscous parts. In addition, an exponential map is employed for the update of the viscous internal variables, which inherently preserves incompressible viscous flow during the entire simulation. The nonlinear viscous behavior of ice is incorporated by Glen's flow law, in which the viscosity depends on both deviatoric stress state and temperature, such that higher stress levels and temperatures lead to lower viscosities. The model is applied to an ice shelf benchmark problem subjected to self‐weight and hydrostatic pressure acting on the submerged parts. In this context, inhomogeneous material properties are considered across the shelf thickness, with density and Young's modulus increasing with depth as firn gradually densifies and transforms into glacier ice. Furthermore, a parameterized temperature field is prescribed across the thickness, reflecting the fact that the thermal state of an ice shelf is generally non‐uniform. The resulting stress distributions and displacements are evaluated and discussed.