A Micromechanics-Based Constitutive Model for Polycrystalline Ice

In this paper a constitutive-model based on micromechanics is given to predict the time dependent ductile behavior of ice under compressive load. It is presumed creep and microcracking are the two dominant mechanisms in the ductile range. The proposed model is formulated on the idea that shear slip along the basal plane is the cause of the permanent deformation of ice, and that microcracking is caused by the local stress due to the mismatch strain. A single crystal is modeled as an inclusion constrained in a polycrystalline matrix with random orientation of the basal plane. Eshelby’s solution is used to estimate the local stress due to the mismatch strain. Maximum tensile stress criterion is adopted to predict microcracking and then crack density is predicted as a function of time. The stress-strain relation of the polycrystalline ice is calculated on the basis of single crystal property in which effect of internal structural changes is incorporated as the reduction of constraint of the surrounding matrix with increasing microcracking. The model predictions for constant load and constant strain rate tests are shown to demonstrate the validity of the model. The constitutive model is implemented in finite element analysis code and a small-scale indentation test is simulated as an example.