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

Ville Pekka Lilja*, Arttu Polojärvi, Jukka Tuhkuri, Jani Paavilainen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)


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.

Original languageEnglish
Article number106107
Number of pages19
JournalComputers and Structures
Early online date9 Sep 2019
Publication statusPublished - Nov 2019
MoE publication typeA1 Journal article-refereed


  • Beam lattice network
  • Centroidal Voronoi tessellation
  • Effective material properties
  • Finite element-discrete element method
  • Ice
  • Size effect


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