Abstract
The graph model presented in Part I of this series provides the basis for development of a computer simulation of tightly packed ice fields taken as ensembles of square-shaped ice floes with random physical properties. A program based on an alternating-direction scheme is developed to model the time evolution of a field of ice floes in a rectangular domain. The simulation of a field in an Arctic channel shows that there is a strong tendency for an earlier onset of microscale plastic flows and formation of irregular clusters of ice floes and openings in a field with spatially random properties versus a field with deterministic spatially homogeneous properties. A special study is conducted of an elastic-plastic transition in a field of 101×101 floes. The transition to macroscopically plastic flow is possible only with a percolation of inelastic regions through the entire domain of the ice field. The fact that this percolation is characterized by a noninteger fractal dimension uncovers a (possibly principal) generation mechanism of ice field morphologies, and points to scale dependence in mechanics of ice fields for certain ranges of loads.
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References
Colony, R., andThorndike, A. S. (1985),Sea Ice Motion as a Drunkard's Walk, J. Geophys. Res.90 C1, 965–974.
Coon, M. D., Maykut, G. A., Pritchard, R. S., andRothrock, D. A. (1974),Modelling the Pack Ice as an Elastic-Plastic Material, AIDJEX Bull.24, 1–105.
Douglas, J., Jr., andGunn, J. E. (1964),A General Formulation of Alternating-Direction Methods, Part I. Parabolic and Hyperbolic Problems, Num. Math.,6, 428–453.
Kadanoff, L. P. (1986),Fractals: Where's the Physics?, Physics Today39 (2), 6–7.
Konovalov, A. N. (1962),The Fractional Step Method for Solving the Cauchy Problem for an N-dimensional Oscillation Equation, Dokl. Akad. Nauk.147, 25–27.
Mandelbrot, B. B.,The Fractal Geometry of Nature (W.H. Freeman, New York 1983).
Matsushita, M. (1985),Fractal Viewpoint of Fracture and Accretion., J. Phys. Soc. Japan54 (3), 857–860.
Mellor, M. (1983),Mechanical Behavior of Sea Ice, CRREL Monograph 83-1.
Ostoja-Starzewski, M. (1984),Micromechanics Model of the Stochastic Evolution of the Ice Fields, Report to Atmospheric Environment Service of Canada.
Ostoja-Starzewski, M. (1985),A Stochastic Micromechanics Model of the Ice Fields, Report to Atmospheric Environment Service of Canada.
Ostoja-Starzewski, M. (1987),Morphology, Microstructure and Micromechanics of Ice Fields, NATO Adv. Res. Workshop on Structure and Dynamics of Partially Solidified Systems, South Lake Tahoe, CA, 1986; NATO Adv. Sci. Inst. Series E125 (ed.Loper, D.) pp 437–451.
Ostoja-Starzewski, M., andJessup, R. G. (1990),Micromechanics Model of Ice Fields—I: Microscale Constitutive Laws, Pure Appl. Geophys.132 (4), 781–802.
Ostoja-Starzewski, M. (1989),Mechanics of Damage in a Random Granular Microstructure: Percolation of Inelastic Phases Lett. Appl. Engng. Sci. (Int. J. Engng. Sci.)27 (3), 315–326.
Rothrock, D. A. andThorndike A. S. (1980),Geometric Properties of the Underside of Sea Ice, J. Geophys. Res.85C, 3955–3963.
Thorndike, A. S. (1986),Diffusion of Sea Ice, J. Geophys. Res.91C6, 7691–7696.
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Ostoja-Starzewski, M. Micromechanics model of ice fields—II: Monte Carlo simulation. PAGEOPH 133, 229–249 (1990). https://doi.org/10.1007/BF00877161
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DOI: https://doi.org/10.1007/BF00877161