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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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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	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 doi:10.4203/ccp.88.33 purchase the full-text of this paper 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 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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