Effective material properties of a finite element-discrete element model of an ice sheet

Abstract

A three-dimensional finite element-discrete element model of an ice sheet is presented. The model consists of an in-plane beam lattice of co-rotational, viscously damped Timoshenko beam finite elements connected with the mass centroids of rigid discrete elements that form the actual ice sheet. A sheet is generated and meshed via a centroidal Voronoi tessellation procedure. Due to the internally damped, lattice-based construction, the mechanical response becomes both strain rate- and size-dependent, the examination of which forms a central part of the present study. Four displacement-controlled, in-plane, constitutive tests are thus performed to compute the effective, quasi-static, in-plane Young’s (in tension and compression); shear (in simple shear); and bulk (in equi-biaxial tension) moduli E,G, and K, respectively, of a modelled ice sheet. Examined is a set of square, self-similar (plan view) ice sheet samples with the side lengths of L=10, 20, 40, 80, and 160 m; thicknesses of h=0.5, 1.0, and 1.5 m; and the discrete element sizes of l=2h and 3h. The moduli are computed as functions of a relative sheet size parameter Lrel (Lrel=L/l) and the applied strain rate. The results indicate that the samples exhibit a moderately strong size dependence, whereas the strain rate has only a minor effect. In each test the size effect approximately vanishes if the relative sheet size parameter Lrel⪆25.