Cracks in Cosserat Continuum—Macroscopic Modeling

  • Arcady V. Dyskin
  • Elena Pasternak
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 21)


Modeling of particulate and layered materials (e.g., concrete and rocks, rock masses) by Cosserat continua involves characteristic internal lengths which can be commensurate with the microstructural size (the particle size or layer thickness). When fracture propagation in such materials is considered, the criterion of their growth is traditionally based on the parameters of the crack-tip stress singularities referring to the distances to the crack tip smaller than the characteristic lengths and hence smaller than the microstructural size. This contradicts the very notion of continuum modeling which refers to the scales higher than the microstructural size. We propose a resolution of this contradiction by considering an intermediate asymptotics corresponding to the distances from the crack tip larger than the microstructural sizes (the internal Cosserat lengths) but yet smaller than the crack length. The approach is demonstrated using examples of shear crack in particulate and bending crack in layer materials.


Shear Crack Stress Singularity Macroscopic Modeling Crack Line Cosserat Continuum 
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  1. 1.
    Dyskin, A.V., Pasternak, E.: Rotational mechanism of in-plane shear crack growth in rocks under compression. In: Potvin, Y., Carter, J., Dyskin, A., Jeffrey, R. (eds.) 1st Southern Hemisphere International Rock Mechanics Symposium SHIRMS 2008, vol. 2, pp. 111–120. Australian Centre for Geomechanics, Crawley (2008) Google Scholar
  2. 2.
    Gourgiotis, P., Georgiadis, H.: Distributed dislocation approach for cracks in couple-stress elasticity: shear modes. Int. J. Fract. 147, 83–102 (2007) MATHCrossRefGoogle Scholar
  3. 3.
    Landau, L., Lifshitz, E.: Theory of Elasticity. Braunschweig, Oxford (1959) Google Scholar
  4. 4.
    Morozov, N.: Mathematical Issues of the Crack Theory. Nauka, Moscow (1984). In Russian Google Scholar
  5. 5.
    Nowacki, W.: The linear theory of micropolar elasticity. In: Nowacki, W., Olszak, W. (eds.) Micropolar Elasticity, pp. 1–43. Springer, Berlin (1974) Google Scholar
  6. 6.
    Pasternak, E., Dyskin, A., Mhlhaus, H.B.: Cracks of higher modes in Cosserat continua. Int. J. Fract. 140, 189–199 (2006) MATHCrossRefGoogle Scholar
  7. 7.
    Pasternak, E., Mhlhaus, H., Dyskin, A.: On the possibility of elastic strain localisation in a fault. Pure Appl. Geophys. 161, 2309–2326 (2004) CrossRefGoogle Scholar
  8. 8.
    Tada, H., Paris, P., Irwin, G.: The Stress Analysis of Cracks. Handbook, 3rd edn. ASME Press, New York (1985) Google Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.The University of Western AustraliaPerthAustralia

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