Mathematical modelling of monotonic and cyclic behavior of polycrystalline freshwater ice.
|Title:||Mathematical modelling of monotonic and cyclic behavior of polycrystalline freshwater ice.|
|Abstract:||The objective of the present work is to develop and evaluate a three dimensional mathematical model for fresh water ice. The model serves as a mathematical base that can be extended to include the mechanical behaviour of sea-ice. A series of creep compression tests were carried out on columnar grained S-2 fresh water ice samples. The objective of this experimental work is to investigate the rate of accumulation of the permanent strains generated in ice undergoing creep deformations for non-cracking conditions. New equations for Poisson's ratio for columnar grained ice are proposed. A three dimensional mathematical model for polycrystalline fresh water ice is developed on the basis of analysis of the experimental results obtained in this study as well as experimental results taken from the literature. The model describes the mechanical behaviour of ice subjected to any loading path in the three dimensional stress space, including cyclic loading. The model formulations take into account the observed material non-linearity, time and temperature dependency, plasticity, material anisotropy, stress path dependency, and hysteresis behaviour of ice subjected to cyclic loading. The model is made up of the sum of two sub-models: A Non-cracking model and a Crack-activity model. Upon loading, ice undergoes both elastic and plastic deformations simultaneously. The total strains are presented as the sum of four strain components. A three dimensional visco-plastic constitutive relation is developed on the basis of the concepts of the classical theory of plasticity. However, modifications of the classical theory of plasticity were made so that the theory could be used to model the behaviour of ice and accommodate time, temperature, and material anisotropy in the constitutive equations. A comprehensive evaluation of the proposed mathematical model is conducted to verify the versatility and accuracy of the model in predicting the observed ice behaviour. The model predictions of the results of the monotonic uniaxial and triaxial tests are in excellent agreement with the measured stress strain curves, the cyclic tests, and the creep tests. Additional evaluation of the model includes theoretical predictions of tensile tests and predictions of the effect of stress rate and initial confining pressure on the behaviour of ice. In the light of all these predictions, recommendations for future research are suggested. (Abstract shortened by UMI.)|
|Collection||Thèses, 1910 - 2010 // Theses, 1910 - 2010|