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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 88
PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and M. Papadrakakis
Paper 33

Material Forces for Simulation of Brittle Crack Propagation in Functionally Graded Materials

R. Mahnken

Chair of Engineering Mechanics, University of Paderborn, Germany

Full Bibliographic Reference for this paper
R. Mahnken, "Material Forces for Simulation of Brittle Crack Propagation in Functionally Graded Materials", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 33, 2008. doi:10.4203/ccp.88.33
Keywords: material forces, finite elements, crack propagation, Delaunay triangulation, J-integral.

Summary
Functionally graded materials (FGMs) are advanced materials that possess continuously graded properties [1]. Unlike homogeneous materials, the propagation of cracks is strongly dependent on the gradation of the material. In this work a thermodynamic consistent framework for crack propagation in FGMs is presented. Following Miehe et al. [3] we exploit a global Clausius Planck inequality, where the direction of crack propagation is obtained in terms of material forces. Some modifications to the approach in [3] are outlined.

Exploiting additional kinematical relations and a balance equation for equilibrium of forces finally a coupled initial-boundary value problem is obtained, which accounts for both, evolution of deformation and evolution of crack propagation.

In the numerical implementation a staggered algorithm - deformation update for fixed geometry followed by geometry update for fixed deformation - is employed within each time increment, [3]. The geometry update is a result of the incremental crack propagation, which is driven by material forces. The corresponding mesh is generated by combining the Delaunay triangulation with local mesh refinement. In order to improve the accuracy for the vectorial J-integrals a domain integral method is used [2].

References
1
Surush S., Mortensen A., "Fundamentals of functionally graded materials", Institute of Materials, London, 1998
2
Mahnken R., "Material forces for crack analysis of functionally graded materials in adaptively refined meshes", Int. J. Fracture., 2008. doi:10.1007/s10704-008-9175-9
3
Miehe C., Gürses E., "A robust algorithm for configurational-force-driven brittle crack propagation with r-adaptive mesh alignement", Int. J. Num. Meths. Eng., 72, 127-155, 2007. doi:10.1002/nme.1999

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