International Journal of Fracture

, Volume 147, Issue 1–4, pp 269–283 | Cite as

Material forces for crack analysis of functionally graded materials in adaptively refined FE-meshes

  • Rolf Mahnken
Original Paper


This work describes the computation of fracture parameters in functionally graded materials (FGMs) with stationary cracks. To this end the continuum concept of material forces is employed, such that the corresponding balance equation can be discretized with a standard Galerkin finite element procedure. A domain-type formulation is used for evaluation of a vectorial J-integral, where in the practical implementation the material nodal forces of the finite element discretization are summed up in a finite region of the crack-tip. In this way the numerical calculation is completely independent from the alignment of the finite element mesh or any selected integration contour, which is most attractive for adaptively refined finite element meshes. For illustrative purpose the accuracy of the method is discussed for two examples based on comparison with available theoretical and numerical solutions.


Material forces Finite elements Stress intensity factor J-integral 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Engineering Mechanics (LTM)University of PaderbornPaderbornGermany

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