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.
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References
Auvinet, G (1993) Random stress fields within granular media, this book.
Axelrad, D.R. (1978) Micromechanics of Solids, PWN/Elsevier, Warsaw/Amsterdam.
Beran, M.J. (1968) Statistical Continuum Theories, J. Wiley, New York.
Breysse, D., Fokwa, D. and Drahy, F. (1994) Spatial variability in concrete: nature, structure and consequences, in (Ostoja-Starzewski and Jasiuk, 1994).
Chameau, J.L. and Muhunthan, B. (1993) Modelling granular fabric by tensors and their statistical test, this book.
Chang, C.S. and Liao, C.L. (1994) Estimates of elastic modulus for media of randomly packed granules, in (Ostoja-Starzewski and Jasiuk, 1994).
Chang, C.S. (1993) Micromechanical model for randomly packed granules, this book.
Chudnovsky, A. (1977) The Principles of Statistical Theory of Long Term Strength, Novosibirsk (in Russian).
Ghosh, S and Moorthy, S. (1993) A Voronoi cell finite element model for random heterogeneous media, this book.
Hashin, Z. (1983) Analysis of composite materials — a survey, J. Appl. Mech., Vol. 50, pp. 481–505.
Herrmann, H.J. and Roux, S. (1990) Statistical models for the fracture of disordered media, Elsevier (North-Holland).
Huet, C. (1990) Application of variational concepts to size effects in elastic heterogeneous bodies, J. Mech. Phys. Solids 38(6), 813–841.
Huet, C. (1993) Experimental characterization, micromechanical simulation and spatio-stochastic approach of concrete behaviors below the representative volume, this book.
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.
Jeulin, D. (1994) Fracture statistics models and crack propagation in random media, in (Ostoja-Starzewski and Jasiuk, 1994).
Jeulin, D. (1986) Study of spatial distributions in multicomponent structures by image analysis, Acta Stereol. Vol. 5(2), pp. 232–239.
Jeulin, D. (1989) Some aspects of mathematical morphology for physical applications, Physica A, Vol. 157, pp. 13–20.
Jeulin, D. (1993) Morphological models for random media, this book.
Jeulin, D. (1994) Morphological Models of Random Structures, CRC Series on Continuum Modelling and Discrete Systems, in preparation.
Kachanov, M. (1993) Elastic solids with many cracks and related problems, Adv. Appl. Mech. Vol. 30, in press.
Kachanov, M., Tsukrov, I. and Shafiro, B. (1994) Effective moduli of solids with cavities of various shapes, in (Ostoja-Starzewski and Jasiuk, 1994).
Kachanov, M., Tsukrov, I. and Shafiro, B. (1993) Effective properties of solids with randomly located defects, this book.
Kleiber, M. and Hien, T.D. (1992) The Stochastic Finite Element Method, J. Wiley, New York.
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.
Mathéron, G. (1967) Elements pour une Theorie des Milieux Poreux, Masson, Paris.
Mathéron, G. (1975) Random Sets and Integral Geometry, J. Wiley, New York.
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).
Mura, T. (1982) Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, Hague.
Nemat-Nasser, S and Horii, M. (1993) Micromechanics: Overall Properties of Heterogeneous Solids, Amsterdam, North-Holland.
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.
Ostoja-Starzewski, M. (1993) Micromechanics as a basis of random elastic continuum approximations, Probab. Engng. Mech., Vol. 8(2), pp. 107–114, 1993.
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.
Ostoja-Starzewski, M. (1994) Micromechanics as a basis of continuum random fields, Appl. Mech. Rev. (Special Issue: Micromechanics of Random Media), in press.
Ostoja-Starzewski, M., and Jasiuk, I., Eds. (1994) Appl. Mech. Rev. (Special Issue: Micromechanics of Random Media), Vol. 47 (1, Part 2).
Serra, J. (1982) Image Analysis and Mathematical Morphology, Academic Press, London.
Serra, J., Ed. (1988) Image Analysis and Mathematical Morphology, Vol. 2, Academic Press, London.
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.
Stoyan, D., Kendall, W.S. and Mecke, J. (1987) Stochastic Geometry and Applications, J. Wiley, New York.
Torquato, S. (1991) Random heterogeneous media: microstructure and improved bounds on effective properties, Appl. Mech. Rev. Vol. 44(2), pp. 37–75.
Willis, J.R. (1981) Variational and Related Methods for the Overall Properties of Composites, Adv. Appl. Mech., Vol. 21, pp. 2–78.
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© 1994 Springer Science+Business Media Dordrecht
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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
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DOI: https://doi.org/10.1007/978-94-011-1142-3_4
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