Advertisement

Mechanics of Random Media as a Tool for Scale Effects in Ice Fields

  • Martin Ostoja-Starzewski
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 94)

Abstract

The need to account for scale dependence of mechanical responses of ice fields is being noticed ever more often, e.g. (Overland et al., 1995; Dempsey, 2000). This challenge brings with it the need to study mechanics bridging different scales, and the exigency to deal with non-deterministic phenomena. In this respect, powerful tools are being offered by the fields of (i) spatio-temporal stochastic models, (ii) mechanics of random media, (iii) stochastic finite elements, and (iv) wave propagation in random media. In this paper we review some advantages offered by each of these areas as well as the possible applications they offer in mechanics of ice fields. Due to space limitations the presentation is, of necessity, brief and selective, but we hope it offers a perspective on powerful tools that exist for further research.

Keywords

Shear Band Representative Volume Element Random Medium Mathematical Morphology IUTAM Symposium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alzebdeh, K., Al-Ostaz, A., Jasiuk, I. and Ostoja-Starzewski, M., 1998, Fracture of random matrix-inclusion composites: scale effects and statistics, Intl. J. Solids Struct. 35(19), 2537–2566.zbMATHCrossRefGoogle Scholar
  2. Beran, M.J., 1974, Application of statistical theories for the determination of thermal, electrical, and magnetic properties of heterogeneous materials, in Mechanics of Composite Materials 2 (G.P. Sendeckyj, ed.), Academic Press, 209–249.Google Scholar
  3. Dempsey, J.P., 2000, Research trends in ice mechanics, in Research Trends in Solid Mechanics, Intl. J. Solids Struct. 37(1–2), 131–153.MathSciNetzbMATHCrossRefGoogle Scholar
  4. Greeley, R., 2000, The icy crust of the Jupiter moon, Europa, IUTAM Symposium on Scaling Laws in Ice Mechanics and Ice Dynamics, this volume.Google Scholar
  5. Grigoriu, M., 1999, Stochastic mechanics, in Research Trends in Solid Mechanics, Intl. J. Solids Struct. 37(1–2), 197–214.MathSciNetCrossRefGoogle Scholar
  6. Hazanov, S., 1999, On apparent properties of nonlinear heterogeneous bodies smaller than the representative volume, Acta Mech. 134, 123–134.MathSciNetzbMATHCrossRefGoogle Scholar
  7. Hill, R., 1963, Elastic properties of reinforced solids: some theoretical principles, J. Mech. Phys. Solids 11, 357–372.ADSzbMATHCrossRefGoogle Scholar
  8. Hopkins, M.A., 1996, On the mesoscale interaction of lead ice and floes. J. Geophys. Res. 101 (C8), 18,315–18,326.CrossRefGoogle Scholar
  9. Hopkins, M.A., 1998, Four stages of pressure ridging. J. Geophys. Res. 103(C10), 21,883–21,891.CrossRefGoogle Scholar
  10. Huet, C., 1990, Application of variational concepts to size effects in elastic heterogeneous bodies, J. Mech. Phys. Solids 38, 813–841.MathSciNetADSCrossRefGoogle Scholar
  11. Huet, C., 1999, Coupled and size boundary-condition effects in viscoelastic heterogeneous composite bodies, Mech. Mater. 31(12), 787–829.CrossRefGoogle Scholar
  12. Jeulin, D., 1997, Advances in Theory and Applications ofRandom Sets, World Scientific.Google Scholar
  13. Jeulin, D. and Ostoja-Starzewski, M., 2000, Shear bands in elasto-plastic response of random composites by geodesics, 8th ASCE Spec. Conf. Probabilistic Mech. Struct. Reliability, Notre Dame, IN.Google Scholar
  14. Jeulin, D. and Ostoja-Starzewski, M. (eds.), 2001, Mechanics of Random and Multiscale Microstructures, CISM Courses and Lectures, Springer-Verlag, Wien, in press.zbMATHGoogle Scholar
  15. Jiang, M., Ostoja-Starzewski, M. and Jasiuk, I., 2000, Scale-dependent bounds on effective elastoplastic response of random composites, J. Mech. Phys. Solids 49(3), 655–673.CrossRefGoogle Scholar
  16. Kerman, B., 1998, A damage mechanics model for sea ice imagery, Global Atmos. Ocean Sys. 6, 1–34.Google Scholar
  17. Kerman, B.R. and Johnson, K., 1998, Properties of a probability measure for sea ice imagery, Global Atmos. Ocean Sys. 6, 35–92.Google Scholar
  18. Lacy, T.E., McDowell, D.L. and Talreja, R., 1999, Gradient concepts for evolution of damage, Mech. Mater. 31(12), 831–860.CrossRefGoogle Scholar
  19. MicroMorph, 1997, Center of Mathematical Morphology, Ecole des Mines de Paris, France.Google Scholar
  20. Ostoja-Starzewski, M., 1987, Morphology, microstructure and micromechanics of ice fields, in Structure and Dynamics of Partially Solidified Systems, NATO Advanced Science Institutes E125, (D. Loper, Ed.), 437–451, Martinus Nijhoff, Doordrecht.CrossRefGoogle Scholar
  21. Ostoja-Starzewski, M., 1998, Random field models of heterogeneous materials, Intl. J. Solids Struct., 35(19), 2429–2455.zbMATHCrossRefGoogle Scholar
  22. Ostoja-Starzewski, M., 1999a, Scale effects in materials with random distributions of needles and cracks, Mech. Mater. 31(12), 883–893.CrossRefGoogle Scholar
  23. Ostoja-Starzewski, M., 1999b, Microstructural disorder, mesoscale finite elements, and macroscopic response, Proc. Roy. Soc. Lond. A455, 3189–3199.MathSciNetADSzbMATHCrossRefGoogle Scholar
  24. Ostoja-Starzewski, M., 2001 a, Microstructural randomness versus representative volume element in thermomechanics, ASME J. Appl. Mech., in press.Google Scholar
  25. Ostoja-Starzewski, M., 2001b, Crack patterns in plates with randomly placed holes: A maximum entropy approach, Mech. Res. Comm. 28(2), 193–198.zbMATHCrossRefGoogle Scholar
  26. Ostoja-Starzewski, M. and Ilies, H., 1996, The Cauchy and characteristic boundary value problems for weakly random rigid-perfectly plastic media, Intl. J. Solids Struct. 33(8), 1119–1136.zbMATHCrossRefGoogle Scholar
  27. Ostoja-Starzewski, M. and Trebicki, J., 1999, On the growth and decay of acceleration waves in random media, Proc. Roy. Soc. Lond. A455, 2577–2614.MathSciNetADSzbMATHCrossRefGoogle Scholar
  28. Ostoja-Starzewski, M. and A. Woods, 2000, Spectral finite elements for structural dynamics of randomly inhomogeneous media, 8th ASCE Spec. Conf. Probab. Mech. Struct. Reliability, Notre Dame, IN.Google Scholar
  29. Overland, J.E., Walter, B.A., Curtin, T.B. and Turet, P., 1995, Hierarchy and sea ice mechanics, J. Geophys. Res. 100, 4559–4571.ADSCrossRefGoogle Scholar
  30. Poliakov, A.N.B., H.J. Herrmann, Y.Y. Podladchikov and S. Roux, 1994, Fractal plastic shear bands, Fractals 2, 567–581.zbMATHCrossRefGoogle Scholar
  31. Sab, K., 1992. On the homogenization and the simulation of random materials, Eur. J. Mech. A/Solids 11, 585–607.MathSciNetzbMATHGoogle Scholar
  32. Sanchez-Palencia, E. and Zaoui, A. (eds.), 1987, Homogenization Techniques for Composite Media, Lecture Notes in Physics 272.Google Scholar
  33. Schreyer, H.L., 2000, Modeling failure initiation in sea ice based on loss of ellipticity, IUTAM Symposium on Scaling Laws in Ice Mechanics and Ice Dynamics, this volume.Google Scholar
  34. Schulson, E.M., 2000, Fracture of ice on scales large and small, IUTAM Symposium on Scaling Laws in Ice Mechanics and Ice Dynamics, this volume.Google Scholar
  35. Serra, J.P., 1982, Image Analysis and Mathematical Morphology, Academic Press.zbMATHGoogle Scholar
  36. Sobczyk, K., 1985, Stochastic Wave Propagation, Elsevier.zbMATHGoogle Scholar
  37. Willis, J.R., 1981, Variational and related methods for the overall properties of composites, Adv. Appl. Mech. 21, 2–78.MathSciNetADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Martin Ostoja-Starzewski
    • 1
  1. 1.Department of Mechanical EngineeringMcGill UniversityMontréal, QuébecCanada

Personalised recommendations