Skip to main content

Models: Micro-Macro

The Synthetic Paper

  • Chapter
Probabilities and Materials

Part of the book series: NATO ASI Series ((NSSE,volume 269))

Abstract

The problem of relating mechanical response of materials to their microstructure is common to many areas. It is relevant in mechanics of polycrystalline, granular (and other type) media, in problems of effective moduli and problems of crack propagation and damage formation/evolution. We thus have seven papers in this session. In the following, rather than providing here a review of each of these papers, we give a discussion of salient features and techniques common to various disciplines that these papers represent. This is accompanied by an account of state of the art and future challenges in micromechanics. It is hoped that the reader will see potential applications in study of other types of materials, e.g. cellular, fibrous, biological.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Auvinet, G (1993) Random stress fields within granular media, this book.

    Google Scholar 

  • Axelrad, D.R. (1978) Micromechanics of Solids, PWN/Elsevier, Warsaw/Amsterdam.

    Google Scholar 

  • Beran, M.J. (1968) Statistical Continuum Theories, J. Wiley, New York.

    Google Scholar 

  • Breysse, D., Fokwa, D. and Drahy, F. (1994) Spatial variability in concrete: nature, structure and consequences, in (Ostoja-Starzewski and Jasiuk, 1994).

    Google Scholar 

  • Chameau, J.L. and Muhunthan, B. (1993) Modelling granular fabric by tensors and their statistical test, this book.

    Google Scholar 

  • Chang, C.S. and Liao, C.L. (1994) Estimates of elastic modulus for media of randomly packed granules, in (Ostoja-Starzewski and Jasiuk, 1994).

    Google Scholar 

  • Chang, C.S. (1993) Micromechanical model for randomly packed granules, this book.

    Google Scholar 

  • Chudnovsky, A. (1977) The Principles of Statistical Theory of Long Term Strength, Novosibirsk (in Russian).

    Google Scholar 

  • Ghosh, S and Moorthy, S. (1993) A Voronoi cell finite element model for random heterogeneous media, this book.

    Google Scholar 

  • Hashin, Z. (1983) Analysis of composite materials — a survey, J. Appl. Mech., Vol. 50, pp. 481–505.

    Article  Google Scholar 

  • Herrmann, H.J. and Roux, S. (1990) Statistical models for the fracture of disordered media, Elsevier (North-Holland).

    Google Scholar 

  • Huet, C. (1990) Application of variational concepts to size effects in elastic heterogeneous bodies, J. Mech. Phys. Solids 38(6), 813–841.

    Article  Google Scholar 

  • Huet, C. (1993) Experimental characterization, micromechanical simulation and spatio-stochastic approach of concrete behaviors below the representative volume, this book.

    Google Scholar 

  • Jasiuk, I., Chen, J. and Thorpe, M.F. (1992) Elastic moduli of composites with rigid sliding inclusions, J. Mech. Phys. Solids, Vol. 40(2), pp. 373–391.

    Article  Google Scholar 

  • Jeulin, D. (1994) Fracture statistics models and crack propagation in random media, in (Ostoja-Starzewski and Jasiuk, 1994).

    Google Scholar 

  • Jeulin, D. (1986) Study of spatial distributions in multicomponent structures by image analysis, Acta Stereol. Vol. 5(2), pp. 232–239.

    Google Scholar 

  • Jeulin, D. (1989) Some aspects of mathematical morphology for physical applications, Physica A, Vol. 157, pp. 13–20.

    Article  Google Scholar 

  • Jeulin, D. (1993) Morphological models for random media, this book.

    Google Scholar 

  • Jeulin, D. (1994) Morphological Models of Random Structures, CRC Series on Continuum Modelling and Discrete Systems, in preparation.

    Google Scholar 

  • Kachanov, M. (1993) Elastic solids with many cracks and related problems, Adv. Appl. Mech. Vol. 30, in press.

    Google Scholar 

  • Kachanov, M., Tsukrov, I. and Shafiro, B. (1994) Effective moduli of solids with cavities of various shapes, in (Ostoja-Starzewski and Jasiuk, 1994).

    Google Scholar 

  • Kachanov, M., Tsukrov, I. and Shafiro, B. (1993) Effective properties of solids with randomly located defects, this book.

    Google Scholar 

  • Kleiber, M. and Hien, T.D. (1992) The Stochastic Finite Element Method, J. Wiley, New York.

    Google Scholar 

  • Kumar, S., Kurtz, S.K., Banavar, J.R. and Sharma, M.G. (1992) Properties of a three-dimensional Poisson-Voronoi tessellation: a Monte Carlo study, J. Stat. Phys., Vol. 67(3/4), pp. 523–550.

    Article  Google Scholar 

  • Mathéron, G. (1967) Elements pour une Theorie des Milieux Poreux, Masson, Paris.

    Google Scholar 

  • Mathéron, G. (1975) Random Sets and Integral Geometry, J. Wiley, New York.

    Google Scholar 

  • Moorthy, S., Ghosh, S. and Liu, Y. (1994) Voronoi cell finite element model for thermoelastoplastic deformation in random heterogenous media, in (Ostoja-Starzewski and Jasiuk, 1994).

    Google Scholar 

  • Mura, T. (1982) Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, Hague.

    Google Scholar 

  • Nemat-Nasser, S and Horii, M. (1993) Micromechanics: Overall Properties of Heterogeneous Solids, Amsterdam, North-Holland.

    Google Scholar 

  • NSF Workshop (1993) on “The statistical characterization of material microstructure and its relation to material performance,” The Catholic University of America, Washington, D.C.; final report by M.J. Beran and J.J. McCoy.

    Google Scholar 

  • Ostoja-Starzewski, M. (1993) Micromechanics as a basis of random elastic continuum approximations, Probab. Engng. Mech., Vol. 8(2), pp. 107–114, 1993.

    Article  Google Scholar 

  • Ostoja-Starzewski, M. (1993) Micromechanics as a basis of stochastic finite elements and differences — an overview, Appl. Mech. Rev. (Special Issue: Mechanics Pan-America 1993, M.R.M. Crespo da Silva and C.E.N. Mazzilli, Eds.), Vol. 46 (11, Part 2), pp. S134–S147.

    Google Scholar 

  • Ostoja-Starzewski, M. (1994) Micromechanics as a basis of continuum random fields, Appl. Mech. Rev. (Special Issue: Micromechanics of Random Media), in press.

    Google Scholar 

  • Ostoja-Starzewski, M., and Jasiuk, I., Eds. (1994) Appl. Mech. Rev. (Special Issue: Micromechanics of Random Media), Vol. 47 (1, Part 2).

    Google Scholar 

  • Serra, J. (1982) Image Analysis and Mathematical Morphology, Academic Press, London.

    Google Scholar 

  • Serra, J., Ed. (1988) Image Analysis and Mathematical Morphology, Vol. 2, Academic Press, London.

    Google Scholar 

  • Shen, H.H., Satake, M., Mehrabadi, M., Chang, C.S. and Campbell, C.S. (1992) Advances in Micromechanics of Granular Materials, Proceedings of the 2nd US-Japan Seminar on Micromechanics of Granular Materials, Stud. Appl. Mech., Vol. 31, Elsevier; also Mech. Mater. (Special Issue: Mechanics of Granular Materials), Vol. 16 (1-2), 1993.

    Google Scholar 

  • Stoyan, D., Kendall, W.S. and Mecke, J. (1987) Stochastic Geometry and Applications, J. Wiley, New York.

    Google Scholar 

  • Torquato, S. (1991) Random heterogeneous media: microstructure and improved bounds on effective properties, Appl. Mech. Rev. Vol. 44(2), pp. 37–75.

    Article  Google Scholar 

  • Willis, J.R. (1981) Variational and Related Methods for the Overall Properties of Composites, Adv. Appl. Mech., Vol. 21, pp. 2–78.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Ostoja-Starzewski, M. (1994). Models: Micro-Macro. In: Breysse, D. (eds) Probabilities and Materials. NATO ASI Series, vol 269. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1142-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-1142-3_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4500-1

  • Online ISBN: 978-94-011-1142-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics