We seek to model arbitrary strong and weak discontinuities propagation in solid mediums such as cracks and phase fronts. We focus on the development of the eXtended Finite Element Method combined with Level Sets to achieve this goal. We are mainly focused on the development of new techniques to solve non-linear three-dimensionnal quasi-static and dynamic crack propagation. We propose particular non-linear solvers and time integrators within the X-FEM to perform fast and efficient computations and also develop ad-hoc experiments to validate our numerical methods.
Higher order functions such as B-Spline and NURBS functions, massively used in Computer Aided Design and that are built into the Isogeometric Analysis are promissing new basis for powerful numerical methods. Within the isogeometric analysis, we develop particular numerical scheme to simulate elastic-plastic incompressible solids at large strains, higher order shells and geometrically exact contact algorithms. The final goal is to obtain a NURBS-based framework to accurately simulate metal forming with an accurate geometric description and precise non-linear stress states. This work is done in collaboration with Professor Thomas J.R. Hughes' group at the University of Texas at Austin and Dr Yuri Bazilevs at the University of California San Diego.
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Work in collaboration with Anthony Gravouil and Hubert Maigre. Pictures and animations done using Paraview.
Simulation of Kalthoff's experiment
This example deals with the numerical simulation of Kalthoff's experiment of the failure mode transition under pure mode-2 loading. The experimental configuration is the following: a plate with two symmetrical edge cracks is impacted by a projectile at a given speed V0. By modifying the projectile's velocity, Kalthoff observed a transition in the type of failure. At low velocity, i.e. under low strain rate, brittle failure is observed with a simultaneous propagation of the two cracks with a global angle between 60° and 70°. If one increases the projectile's speed, a transition between brittle fracture and shear band propagation (with a propagation angle of approximatively -10°) occurs. We consider here only the brittle propagation with in impact velocity of 20m/s.
Compact Compression specimen
The Compact Compression Specimen experiment first introduced by Bui et al and further developed by Maigre and Rittel. The interest of the CCS experimentis that there is always a mixed-mode loading condition at the crack tip. The test rig is a Split Hopkinson Pressure Bar (Kolsky bar), the input bar is modelled by the experimental dynamic load.
Semi-infinite crack in an infinite medium
A semi-infinite mode I crack in an infinite medium submitted to a tensile stress wave is considered. The analytical solution for the mode I dynamic stress intensity factor was obtained by Freund. We consider a finite geometry, therefore we can only compare the results with the analytical solution until the tensile stress wave is reflected on the bottom side and reaches again the crack tip.
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Work in collaboration with Anthony Gravouil and Alain Combescure. Pictures and animations done using Gmsh and mencoder.
Closing effects due to plasticity in a Compact Tension specimen
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Work in collaboration with Yuri Bazilevs, Victor M. Calo and Thomas J.R. Hughes. Pictures done using GMV.
Pinching of an incompressible toroidal solid
This example exploits the ability of NURBS to exactly represent conic sections. It consists of the pinching of a toroidal solid. A nearly incompressible Neo-Hookean material model is considered (equivalent Poisson ratio of 0.4998). Because of symmetry, one quarter of the structure is considered, with a mesh of 4x16x2 elements with quadratic and cubic NURBS.
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- S. Lipton, J.A. Evans, Y. Bazilevs, T. Elguedj and T.J.R. Hughes, "Robustness of Isogeometric Structural Discretizations Under Severe Mesh Distortion", in preparation, 2008.
- T. Elguedj, A. Gravouil and H. Maigre, "An explicit dynamics extended finite element method. Part 1: mass lumping for arbitrary enrichment functions" , in preparation, 2008.
- T. Elguedj, A. Gravouil and H. Maigre, "An explicit dynamics extended finite element method. Part 2: element-by-element stable-explicit/explicit scheme" , in preparation, 2008.
- T. Elguedj, Y. Bazilevs, V.M. Calo and T.J.R. Hughes, "B-bar
and F-bar Projection Methods for Nearly Incompressible Linear and Nonlinear Elasticity and Plasticity using Higher-order NURBS Elements." Computer Methods in Applied Mechanics and Engineering, vol. 197, p. 2732-2762, 2008.
(Preprint avalaible as ICES report 0726)
- A. Gravouil, A. Combescure, T. Elguedj, É. Ferrié, JY. Buffière and W. Ludwig. "Application of X-FEM to 3D real cracks and elastic-plastic fatigue crack growth." In Proceedings of the IUTAM Symposium on Discretization Methods for Evolving Discontinuities, p. 213-232, A. Combescure, R. de Borst and T. Belytschko editors, Springer, Dordrecht, The Netherlands, 2007.
- T. Elguedj, A. Gravouil and A. Combescure. "A mixed augmented Lagrangian-extended finite element method for modelling elastic-plastic fatigue crack growth with unilateral contact." International Journal for Numerical Methods in Engineering, vol. 71, p. 1569-1597, 2007.
- T. Elguedj, A. Gravouil, A. Combescure. "Appropriate extended functions for X-FEM simulation of elastic-plastic fatigue crack growth with frictional contact."European Journal of Computational Mechanics, vol. 15 n° 1-2-3, p. 155-166, 2006.
- T. Menouillard, T. Elguedj and A. Combescure. "Mixed mode stress intensity factor evaluation for graded materials." International Journal of Solids and Structures, vol. 43, p. 1946-1959, 2006.
- T. Elguedj, A. Gravouil, and A. Combescure. "Appropriate extended functions for X-FEM simulation of plastic fracture mechanics."Computer Methods in Applied Mechanics and Engineering, vol. 195, p. 501-515, 2006.
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- A. Gravouil, A. Combescure, T. Elguedj, É. Ferrié, JY. Buffière and W. Ludwig. "Application of X-FEM to 3D real cracks and elastic-plastic fatigue crack growth." IUTAM Symposium on Discretization Methods for Evolving Discontinuities (Lyon, France), September 4-7, 2006, p. 213-232, Springer, Dordrecht, The Netherland.
- T. Elguedj, A. Gravouil and A. Combescure. "Simulation of plastic fatigue crack growth by a two-scale extended finite element method." 16th European Conference of Fracture (Alexandroupolis, Greece), July 3-7, 2006, p. 933-934, Springer, Dordrecht, The Netherland.
- T. Elguedj, A. Gravouil and A. Combescure. "Fonctions de forme étendues pour la mécanique élasto-plastique de la rupture par méthode X-FEM" (in French). 7ème Colloque National en Calcul de Structure (Giens, France), May 17-20, 2005, vol. 2, p. 617-622, Hermès-Lavoisier, Paris.
- T. Menouillard, T. Elguedj and A. Combescure. "Méthode de calcul des facteurs d'intensité des contraintes en mode mixte pour des matériaux à gradient de propriétés mécaniques" (in French). 7ème Colloque National en Calcul de Structure (Giens, France), May 17-20, 2005, vol. 2, p. 439-444, Hermès-Lavoisier, Paris.
- A. Combescure, A. Gravouil, MC. Baietto-Dubourg, T. Elguedj, R. Ribeaucourt and É. Ferrié. "Extended finite element method for numerical simulation of 3D fatigue crack growth." 31st Leeds-Lyon Symposium on Tribology (Leeds, United-Kingdom), September 7-9, 2004, p. 323-329, Elsevier.
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- T. Elguedj, Y. Bazilevs, V.M. Calo and T.J.R. Hughes. "F-bar projection method for finite deformation elasticity and plasticity using NURBS-based isogeometric analysis." 8th World Congres on Computational Mechanics / 5th European Congress on Computational Methods in Applied Sciences and Engineering (Venice, Italy), June 30 - July 4, 2008.
- T. Elguedj, Y. Bazilevs, V.M. Calo and T.J.R. Hughes. "F-bar projection method for finite deformation elasticity and plasticity using NURBS-based isogeometric analysis." 11th ESAFORM conference on material forming (Lyon, France), April 23-25, 2008.
- T. Elguedj, A. Gravouil, A. Combescure. "Simulation de la propagation de fissure de fatigue en élasto-plasticité par une méthode éléments finis étendus à deux échelles" (in French). 18ème Congrès Français de Mécanique (Grenoble, France), August 27-31, 2007.
- T. Elguedj, Y. Bazilevs, V.M. Calo and T.J.R. Hughes. " B/F-bar Projection Methods for Nearly Incompressible Analysis using Higher-order NURBS Elements." 9th US National Congress on Computational Mechanics (San Francisco, USA), July 23-26, 2007.
- T. Elguedj, Y. Bazilevs, V.M. Calo and T.J.R. Hughes. "A New F-bar Formulation for Nearly Incompressible Finite Strain Analysis." McMat 2007 - ASME Applied Mechanics and Materials Conference (Austin, USA), June 3-7, 2007.
- T. Elguedj, A. Gravouil and A. Combescure. "X-FEM simulation of plastic fatigue crack growth." 7th World Congress on Computational Mechanics (Los Angeles, USA), July 16-22, 2006.
- T. Elguedj, A. Gravouil and A. Combescure. "X-FEM method for elastic-plastic fatigue crack growth simulation." FatigueDesign (Senlis, France), November 16-18, 2005.
- T. Elguedj, A. Gravouil and A. Combescure. "Appropriate extended functions for X-FEM simulation of plastic fatigue crack growth." 11th International Conference on Fracture (Turin, Italy), March 20-25, 2005.
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"Fatigue crack growth simulation using the extended finite element method with plasticity and contact-friction." (in French)
"Simulation numérique de la propagation de fissure en fatigue par la méthode des éléments finis étendus: prise en compte de la plasticité et du contact-frottement."
(PDF )
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Laboratoire de Mécanique des Contacts et des Structures - Equipe Mécanique des Solides et des Endommagements
INSA de Lyon
20 avenue Albert Einstein
Bâtiment Joseph Jaquard
69621 Villeurbanne Cedex
France
office: +33 (0) 4 72 43 71 05
fax: +33 (0) 4 72 43 89 13
e-mail: thomasDOTelguedjATinsa-lyonDOTfr
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Last updated on August 6th, 2008.