A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb’s problem and plane wave nonlinear propagation.
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May 04 2012
A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation
Olivier Bou Matar;
Olivier Bou Matar
a)
International Associated Laboratory LEMAC, IEMN, UMR CNRS 8520, PRES Lille Nord de France, ECLille, 59652 Villeneuve d’Ascq,
France
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Pierre-Yves Guerder;
Pierre-Yves Guerder
International Associated Laboratory LEMAC, IEMN, UMR CNRS 8520, PRES Lille Nord de France, ECLille, 59652 Villeneuve d’Ascq,
France
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YiFeng Li;
YiFeng Li
College of Electronics and Information Engineering,
NanJing University of Technology
, NanJing, 210009, People’s Republic of China
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Bart Vandewoestyne;
Bart Vandewoestyne
Wave Propagation and Signal Processing Research Group, K.U. Leuven Campus Kortrijk, E. Sabbelaan 53, B-8500 Kortrijk,
Belgium
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Koen Van Den Abeele
Koen Van Den Abeele
Wave Propagation and Signal Processing Research Group, K.U. Leuven Campus Kortrijk, E. Sabbelaan 53, B-8500 Kortrijk,
Belgium
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a)
Author to whom correspondence should be addressed. Electronic mail: olivier.boumatar@iemn.univ-lille1.fr
J. Acoust. Soc. Am. 131, 3650–3663 (2012)
Article history
Received:
June 16 2011
Accepted:
February 18 2012
Citation
Olivier Bou Matar, Pierre-Yves Guerder, YiFeng Li, Bart Vandewoestyne, Koen Van Den Abeele; A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation. J. Acoust. Soc. Am. 1 May 2012; 131 (5): 3650–3663. https://doi.org/10.1121/1.3693654
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