A Prony-series type viscoelastic solid coupled with a continuum damage law for polar ice modeling

Abstract

Predicting the time-dependent behavior of polar ice is a significant challenge especially when damage effects are considered. In the present work, ice is modeled by a generalized Maxwell type viscoelastic solid and coupled to a continuum damage model. Viscoelastic behavior is obtained by a Prony-series expansion where the shear components of the deviatoric stress are time dependent while the volumetric part remains purely elastic. A semi-analytical integration scheme of the convolution integral allow for fast computation of stresses. Damage initiation and propagation is captured by a Murakami rate dependent damage law, where the state of damage is updated at each time step based on the current values of stress. The model is shown to be thermodynamically consistent.A rigorous gradient-based constrained optimization approach is employed to calibrate the model parameters against some published experimental data. Validation tests which include tensile creep, compressive creep and biaxial failure contours under compression are then carried out and good agreement is demonstrated. Furthermore, the model is implemented in a finite element code and is used to investigate surface crevasse propagation in grounded marine-terminating glaciers. The simulations, on idealized rectangular ice slabs in contact with the ocean, examine the depth and rate of damage propagation with increasing seawater depth near the terminus. The predictions and computational efficiency of the proposed model are highlighted when compared to another recently published ice model.