Affiliations: Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia | Department of Mathematics and Natural Sciences, Institute of Mathematics, University of Kassel, Germany
Note: [] Corresponding author: Martin Steigemann, Department of Mathematics and Natural Sciences, Institute of Mathematics, University of Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany. Tel.: +49 561 804 4285; Fax: +49 561 804 4646; E-mail: martin.steigemann@mathematik.uni-kassel.de
Abstract: A crack approaching a material interface between two elastic materials may stop or may advance by either penetrating the interface or deflecting into the interface (cf. N.Y. He and J.W. Hutchinson, Int. J. Solids Struct. 25 (1989), 1053–1067). Mathematical models for crack path prediction are based on the asymptotic behavior near the crack tip. In this work, an idea to compute the asymptotic expansion of the displacement field for structures composed of two dissimilar elastic anisotropic materials is shown, if the crack impinges the material interface. In contrast to the well-known case of isotropic materials, logarithmic terms can appear in the asymptotic decomposition of the displacement field in anisotropic composites. Based on this results, the energy release rate is calculated for different scenarios of crack propagation in composite structures.
