, Volume 51, Issue 2, pp 329–339 | Cite as

Mathematical modeling of three equal collinear cracks in an orthotropic solid

  • T. Sadowski
  • E. M. Craciun
  • A. Răbâea
  • L. Marsavina
Computational Micromechanics of Materials


We consider a homogeneous elastic, orthotropic solid containing three equal collinear cracks, loaded in tension by symmetrically distributed normal stresses. Following Guz’s representation theorem and solving Riemann–Hilbert problems we determine the expressions of the complex potentials. Using the asymptotic analysis, we obtain the asymptotic values of the incremental stress and displacement fields. We determine the tangential stresses near the crack tips. Using the maximum tangential stress criterion and numerical computations we study the interaction problem for a Graphite-epoxy fiber reinforced composite material.


Three equal collinear cracks Riemann–Hilbert problem  Maximum tangential stress criterion Cracks interaction 



Financial support of Structural Funds in the Operational Programme - Innovative Economy (IE OP) financed from the European Regional Development Fund - Project "Modern material technologies in aerospace industry", No POIG.0101.02-00-015/08 is gratefully acknowledged (RT-15: Unconventional technologies of joining elements of aeronautical constructions). E.M.C. acknowledges financial support from the ERC Advanced Grant ‘Instabilities and nonlocal multiscale modelling of materials’ FP7-PEOPLE-IDEAS-ERC-2013-AdG (2014-2019). Support by Polish Ministry of Science and Education within the statutory research No S/20/2015 is also acknowledged.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • T. Sadowski
    • 1
  • E. M. Craciun
    • 2
  • A. Răbâea
    • 3
  • L. Marsavina
    • 4
  1. 1.Lublin University of TechnologyLublinPoland
  2. 2.Faculty of Mathematics and Informatics“Ovidius” University of ConstantaConstantaRomania
  3. 3.Faculty of SciencesTechnical University of Cluj-Napoca, N.U.C.B.M.Cluj-NapocaRomania
  4. 4.Politehnica University of TimisoaraTimisoaraRomania

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