A new discontinuous Galerkin method for non-linear Mechanics

[en] A discontinuous Galerkin framework for large deformations of solids is established. The method is based on a general Hu-Washizu-de Veubeke functional allowing for displacement and stress discontinuities in the domain interior. The focus of this paper is on the treatment of large elasto-plastic deformations. The method is shown to possess the required numerical properties: consistency in the non-linear range and linearized stability. In order to demonstrate the versatility, accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided. Further developments of the method will lead to applications where physical discontinuities must be modeled like fragmentation or failure.

Disciplines :

Mechanical engineering

Author, co-author :

Noels, Ludovic ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Milieux continus et thermomécanique

Radovitzky, Raúl; Massachusetts Institute of Technology - MIT > Aeronautics & Astronautics

Language :

English

Title :

A new discontinuous Galerkin method for non-linear Mechanics

Publication date :

2006

Event name :

47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

Event organizer :

American Institute of Aeronautics and Astronautics

Event place :

Newport, United States

Event date :

du 1 au 4 mai 2006

Audience :

International

Publisher :

American Institute of Aeronautics and Astronautics, United States

Pages :

paper 2121

Additional URL :

http://pdf.aiaa.org/preview/CDReadyMSDM06_1172/PV2006_2122.pdf

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique
This research was supported by the U.S. Army through the Institute for Soldier Nanotechnologies, under Contract DAAD-19-02-D-0002 with the U.S. Army Research Office

Available on ORBi :

since 14 August 2008

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Bibliography

Nitsche, J., "Uber ein Variationsprinzip zur Lösung Dirichlet-Problemen bei Verwendung von Teilraumen, die Keinen Randbedingungen Uneworfen Sind," Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Vol. 36, 1971, pp. 9-15.
Cockburn, B., "Discontinuous Galerkin methods for convection-dominated problems," High-Order Methods for Computational Physics, edited by A. Quaterroni, Vol. 11 of Lecture Notes in Computational Sciences and Engineering, London, UK, 2003, pp. 69-213.
Zienkiewicz, O., Taylor, R., Sherwin, S., and Peiró, J., "On Discontinuous Galerkin Methods," International Journal of Numerical Methods in Engineering, Vol. 58, 2003, pp. 1119-1148.
Mergheim, J., Kuhl, E., and Steinmann, P., "A Hybrid Discontinuous Galerkin/Interface Method for the Computational Modelling of Failure," Communication in Numerical Method in Engeneering, Vol. 20, 2004, pp. 511-519.
Brezzi, F., Manzini, G., Marini, D., Pietra, P., and Russo, A., "Discontinuous Galerkin Approximations for Elliptic Problems," Numerical Methods for Partial Differential Equations, Vol. 16, No. 4, 2000, pp. 365-378.
Bassi, F. and Rebay, S., "A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations," Journal of Computational Physics, Vol. 131, 1997, pp. 267-279.
Arnold, D., Brezzi, F., Cockburn, B., and Marini, L., "Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems," SIAM Journal of Numerical Analysis, Vol. 39, No. 5, 2002, pp. 1749-1779.
Hansbo, P. and Larson, M., "Discontinuous Galerkin Methods for Incompressible and Nearly Incompressible Elasticity by Nitsche's Method," Computer Methods in Applied Mechanics and Engineering, Vol. 191, 2002, pp. 1895-1908.
Engel, G., Garikipati, K., Hughes, T., Larson, M., Mazzei, L., and Taylor, R., "Continuous/Discontinuous Finite Element Approximations of Fourth-Order Elliptic Problems in Structural and Continuum Mechanics with Applications to Thin Beams and Plates," Computer Methods in Applied Mechanics and Engineering, Vol. 191, 2002, pp. 3669-3750.
Lew, A., Neff, P., Sulsky, D., and Ortiz, M., "Optimal BV Estimates for a Discontinuous Galerkin Method for Linear Elasticity," Applied Mathematics Research eXpress, Vol. 3, 2004, pp. 73-106.
Noels, L. and Radovitzky, R., "A general discontinuous Galerkin method for finite hyperelasticity. Formulation and numerical applications." International Journal of Numerical Methods in Engineering, 2006, in Press.
Radovitzky, R. and Ortiz, M., "Error estimation and adaptative meshing in strongly nonlinear dynamics problems," Computer Methods in Applied Mechanic and Engineering, Vol. 172, 1999, pp. 203-240.
Ortiz, M. and Stainier, L., "The variational formulation of viscoplastic updates," Computer Methods in Applied Mechanics and Engineering, Vol. 171, 1999, pp. 419-444.