A three dimensional anisotropic constitutive model for ductile behaviour of columnar grained sea ice

Abstract

A three dimensional constitutive model is developed for the ductile behaviour of columnar grained sea ice. Based on the sea ice microstructure, a geometric pattern for the distribution of brine pockets in a single grain of sea ice is idealized. An initial defect tensor for a single grain of sea ice is defined by using the geometric pattern. Subsequently, the initial defect tensor for polycrystalline ice is obtained from the initial defect tensor for a single grain of sea ice and the probability distribution of the c-axis. The effect of the brine pockets on the response of sea ice to different types of loading is expressed by introducing two additional tensors. One of these tensors is called the influence tensor for deviatoric stresses, and the other one is the influence tensor for hydrostatic stresses. With the two influence tensors, an effective stress tensor is defined. The effective stress is used in the sea ice constitutive equations. Comparisons between model predictions and laboratory test results under both uniaxial and multiaxial loading conditions show that the model predictions agree with the test data.