A damage mechanics approach to the three dimensional constitutive modelling of ice deformation

Uncertainties in existing ice models come primarily from the incomplete modelling of the deformation behavior of ice in various loading states. In this study constitutive equations characterizing microcrack damage behavior of polycrystalline ice are developed based on continuum damage mechanics. The principal goal of the thesis is the formulation of a three dimensional damage model for the description of ice deformation, where damage evolution is formulated on the basis of a mathematical description of the physical aspects of microcracking. The specific objectives include: 1)Development of rate-dependent constitutive equations describing ice deformation for uniaxial and multiaxial stress states. Total strain is composed of three components, instantaneous elastic, delayed elastic and viscous strain. Each strain component is incorporated with material damage growth through a damage parameter. The mathematical nature of damage parameter is selected as a tensor based on the anisotropic behavior of microcrack fields. 2)Development of a physically based damage model associated with two microcracking mechanisms, grain boundary and transgranular cracking. The main contribution of the thesis lies in the formulation of damage evolution laws where the damage growth rate is expressed by resolved normal strain, normal stress, and strain-rate for each damage mechanism. Applications are directed to constant stress and constant strain-rate tests under uniaxial, biaxial, and confining pressure conditions. Cyclic behavior is also examined. The constitutive modelling is compared with available experimental results. The model is capable of predicting several important features of ice deformation behavior over a wide range of deformation regimes. The difference in tensile and compressive behavior and damage induced anisotropy can be predicted.

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