Abstract
A theoretical framework that provides a general representation of two-dimensional nonlinear constitutive relations is proposed. The theory is based upon minimization of maximum shear stress that links functional forms of energy dissipation and constitutive relation. Its application to a polynomial energy dissipation function leads to a power-law relationship between strain rate and stress magnitudes. On the basis of this relationship, a general categorization model for constitutive relations is developed and used to analyze forms commonly encountered in ice studies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alley, R. B., 1992. Flow-law hypotheses for ice-sheet modeling. J. Glaciol. 38: 245–256.
Bagnold, R. A., 1954. Experiments on a gravity free dispersion of large solid sphere in a Newtonian fluid under shear. Proc. R. Soc. London, Ser. A 225: 49–63.
Glen, J. W., 1958. The flow law of ice. A discussion of the assumptions made in glacier theory, their experimental foundations and consequences. IASH 47: 171–183.
Hibler, W. D. 1979. A dynamic thermodynamic model of sea ice. J. Phys. Oceanogr. 9: 815–846.
Jaeger, H. M. and S. R. Nagel, 1992. Physics of granular flow. Science 255: 1523–1531.
Landau, L. D. and E. M. Lifshitz, 1959. Fluid Mechanics. Trans. by J. B. Sykes and W. H. Reid, London, Pergamon Press; Reading, Mass., Addison-Wesley Pub. Co.
Moritz, R. E. and J. Ukita, 2000. Geometry and the deformation of pack ice, Part I: A simple kinematic model. Ann. Glaciol. 31: 313–322.
Overland, J. E. and J. Ukita, 2000. Arctic sea ice dynamics workshop. EOS Trans. AGU 81: 309, 314.
Parmerter, R. R. and M. D. Coon, 1972. Model of pressure ridge formation in sea ice. J. Geophys. Res. 77: 6565–6575.
Paterson, W. S. B., 1981. The Physics of Glaciers. Oxford, Pergamon Press (2nd Ed.).
Rothrock, D. A., 1975. The energetics of the plastic deformation of pack ice by ridging. J. Geophys. Res. 80: 4514–4519.
Shen, H. H., W. D. Hibler and M. Lepparanta, 1987. The role of floe collisions in sea ice rheology. J. Geophys. Res. 92: 7085–7096.
Stern, H. L., D. A. Rothrock and R. Kwok, 1995. Open water production in Arctic sea ice: satellite measurements and model parameterizations. J. Geophys. Res. 100: 20,601–20,612.
Thorndike, A. S., D. A. Rothrock, G. A. Maykut and R. Colony, 1975. The thickness distribution of sea ice. J. Geophys. Res. 80: 4501–4513.
Ukita, J. and R. E. Moritz, 1995. Yield curves and flow rules of pack ice. J. Geophys. Res. 95: 4545–4557.
Ukita, J. and R. E. Moritz, 2000. Geometry and the deformation of pack ice, Part II: Simulation with a random isotropic model and implication in sea ice rheology. Ann. Glaciol. 31: 323–326.
Ziegler, H and W. Wehrli, 1987. The derivation of constitutive relations from the free energy and the dissipation function. Adv. App. Mech. 25: 183–238.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Ukita, J. (2001). Two Dimensional Minimax Theory on Shear Stress and a General Classification Model for Nonlinear Constitutive Relations. In: Dempsey, J.P., Shen, H.H. (eds) IUTAM Symposium on Scaling Laws in Ice Mechanics and Ice Dynamics. Solid Mechanics and Its Applications, vol 94. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9735-7_39
Download citation
DOI: https://doi.org/10.1007/978-94-015-9735-7_39
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5890-4
Online ISBN: 978-94-015-9735-7
eBook Packages: Springer Book Archive