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Physical Argument for Nonlocality of Microcracking Damage in a Continuum

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Advances in Continuum Mechanics
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Abstract

The concept of nonlocal continuum, which was introduced into continuum mechanics by Eringen [1,2], Kröner [3] and others, has recently proven to be an effective approach to endow a continuum model for strain-softening damage with a localization limiter which prevents spurious localization instabilities [4–6]. Physical micromechanical justification of this concept, however, has been almost nonexistent.

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References

  1. Eringen, A.C., “Theory of micropolar continuum”, Proc., 9th Midwestern Mechanics Conference, held at University of Wisconsin (1965), 23–40.

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  2. Eringen, A.C., “A unified theory of thermomechanical materials”, Int. J. of Engineering Science 4 (1966), 179–202.

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  3. Kröner, E., “Elasticity theory of materials with long-range cohesive forces”, Int. J. of Solids and Structures 3 (1968), 731–742.

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  4. Baant, Z.P., and Pijaudier-Cabot, G., “Nonlocal continuum damage, localization instability and convergence”, J. of Applied Mechanics ASME 55 (1988), 287–293.

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  5. Pijaudier-Cabot, G., and Baant, Z.P., “Nonlocal damage theory”, J. of Engineering Mecanics ASCE 113 (1987), 1512–1533.

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  6. Bazant, Z.P., and Ozbolt, J., “Nonlocal microplane model for fracture, damage and size effect in structures”, J. of Engineering Mechanics ASCE 116 (1990), 2485–2505.

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  7. Baant, Z.P., “Why continuum damage is nonlocal: justification by microcrack array”, Mechanics Research Communications 14 (1987), 407–419.

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  8. S. Kachanov, L.M.,“Time of rupture process under creep conditions”, Izvestia Akadenii Nauk, USSR, 8 (1958), 26–31 (in Russian).

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  9. Kachanov, M., “Elastic solids with many cracks — a simple method of analysis”, Int. J. of Solids and Structures 23 (1987), 23–43.

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© 1991 Springer-Verlag Berlin, Heidelberg

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Bažant, Z.P. (1991). Physical Argument for Nonlocality of Microcracking Damage in a Continuum. In: Brüller, O.S., Mannl, V., Najar, J. (eds) Advances in Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48890-0_18

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  • DOI: https://doi.org/10.1007/978-3-642-48890-0_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53988-9

  • Online ISBN: 978-3-642-48890-0

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