A velocity/stress mixed stabilized nodal finite element for elastodynamics: Analysis and computations with strongly and weakly enforced boundary conditions

Scovazzi, G.; Song, T.; Zeng, X.

doi:10.1016/j.cma.2017.07.018

Title: A velocity/stress mixed stabilized nodal finite element for elastodynamics: Analysis and computations with strongly and weakly enforced boundary conditions

Journal Article · Tue Jul 25 00:00:00 EDT 2017 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2017.07.018· OSTI ID:1538113

^[1]; Song, T. ^[1]; Zeng, X. ^[2]

Duke University, Durham, NC (United States)
University of Texas at El Paso, TX (United States)

A new nodal mixed finite element is proposed for the simulation of linear elastodynamics and wave propagation problems in time domain. Our method is based on equal-order interpolation discrete spaces for both the velocity (or displacement) and stress (or strain) tensor variables. The mixed form is derived using either the velocity/stress or velocity/strain pair of unknowns, the latter being instrumental in extensions of the method to nonlinear mechanics. The proposed approach works equally well on hexahedral or tetrahedral grids and, for this reason, it is suitable for time-domain engineering applications in complex geometry. The peculiarity of the proposed approach is the use of the rate form of the stress update equation, which yields a set of governing equations with the structure of a non-dissipative space/time Friedrichs’ system. We complement standard traction boundary conditions for the stress with strongly and weakly enforced boundary conditions for the velocity (or displacement). Weakly enforced boundary conditions are particularly suitable when considering complex geometrical shapes, because they do not require dedicated data structures for the imposition of the boundary degrees of freedom, but, rather, they utilize the structure of the variational formulation. Here we also show how the framework of weakly enforced boundary conditions can be used to develop variational forms for multi-domain simulations of heterogeneous media. A complete analysis including stability and convergence proofs is included, in the case of a space–time variational approach. A series of computational tests are used to demonstrate and verify the performance of the proposed approach.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); ExxonMobil Upstream Research Company; US Department of the Navy, Office of Naval Research (ONR)

Grant/Contract Number:: SC0012169; N00014-14-1-0311

OSTI ID:: 1538113

Alternate ID(s):: OSTI ID: 1549632

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Vol. 325, Issue C; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 26 works

Citation information provided by
Web of Science

References (107)

Remarks on the stability of enhanced strain elements in finite elasticity and elastoplasticity de Souza Neto, E. A.; Perić, Djordje; Huang, G. C. Communications in Numerical Methods in Engineering, Vol. 11, Issue 11 https://doi.org/10.1002/cnm.1640111109	journal	November 1995
Two classes of mixed finite element methods Franca, Leopoldo P.; Hughes, Thomas J. R. Computer Methods in Applied Mechanics and Engineering, Vol. 69, Issue 1 https://doi.org/10.1016/0045-7825(88)90168-5	journal	July 1988
A new finite element formulation for computational fluid dynamics: VII. The stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces Hughes, Thomas J. R.; Franca, Leopoldo P. Computer Methods in Applied Mechanics and Engineering, Vol. 65, Issue 1 https://doi.org/10.1016/0045-7825(87)90184-8	journal	November 1987
Stabilized finite element method for viscoplastic flow: formulation and a simple progressive solution strategy Maniatty, Antoinette M.; Liu, Yong; Klaas, Ottmar Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 35-36 https://doi.org/10.1016/S0045-7825(00)00346-7	journal	June 2001
An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics Aguirre, Miquel; Gil, Antonio J.; Bonet, Javier Journal of Computational Physics, Vol. 300 https://doi.org/10.1016/j.jcp.2015.07.029	journal	November 2015
Finite calculus formulation for incompressible solids using linear triangles and tetrahedra Oñate, Eugenio; Rojek, Jerzy; Taylor, Robert L. International Journal for Numerical Methods in Engineering, Vol. 59, Issue 11 https://doi.org/10.1002/nme.922	journal	February 2004
A comparative study of different sets of variables for solving compressible and incompressible flows Hauke, Guillermo; Hughes, Thomas J. R. Computer Methods in Applied Mechanics and Engineering, Vol. 153, Issue 1-2 https://doi.org/10.1016/S0045-7825(97)00043-1	journal	January 1998
A Stabilized Mixed Finite Element Method for Nearly Incompressible Elasticity Masud, Arif; Xia, Kaiming Journal of Applied Mechanics, Vol. 72, Issue 5 https://doi.org/10.1115/1.1985433	journal	January 2005
A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity Gil, Antonio J.; Lee, Chun Hean; Bonet, Javier Computer Methods in Applied Mechanics and Engineering, Vol. 300 https://doi.org/10.1016/j.cma.2015.11.010	journal	March 2016
Polygonal finite elements for finite elasticity: POLYGONAL FINITE ELEMENTS FOR FINITE ELASTICITY Chi, Heng; Talischi, Cameron; Lopez-Pamies, Oscar International Journal for Numerical Methods in Engineering, Vol. 101, Issue 4 https://doi.org/10.1002/nme.4802	journal	November 2014
A mixed three-field FE formulation for stress accurate analysis including the incompressible limit Chiumenti, M.; Cervera, M.; Codina, R. Computer Methods in Applied Mechanics and Engineering, Vol. 283 https://doi.org/10.1016/j.cma.2014.08.004	journal	January 2015
Mixed finite elements for elasticity Arnold, Douglas N.; Winther, Ragnar Numerische Mathematik, Vol. 92, Issue 3 https://doi.org/10.1007/s002110100348	journal	September 2002
An analysis of some mixed-enhanced finite element for plane linear elasticity Auricchio, F.; Beirão da Veiga, L.; Lovadina, C. Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 27-29 https://doi.org/10.1016/j.cma.2004.07.028	journal	July 2005
Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind Nitsche, J. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Vol. 36, Issue 1 https://doi.org/10.1007/BF02995904	journal	July 1971
A 10-node composite tetrahedral finite element for solid mechanics: COMPOSITE TETRAHEDRAL FINITE ELEMENT Ostien, J. T.; Foulk, J. W.; Mota, A. International Journal for Numerical Methods in Engineering, Vol. 107, Issue 13 https://doi.org/10.1002/nme.5218	journal	February 2016
Equivalence of Finite Elements for Nearly Incompressible Elasticity Hughes, T. J. R. Journal of Applied Mechanics, Vol. 44, Issue 1 https://doi.org/10.1115/1.3423994	journal	March 1977
A conservative nodal variational multiscale method for Lagrangian shock hydrodynamics Scovazzi, G.; Shadid, J. N.; Love, E. Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 49-52 https://doi.org/10.1016/j.cma.2010.03.027	journal	December 2010
F-bar aided edge-based smoothed finite element method using tetrahedral elements for finite deformation analysisof nearly incompressible solids: F-BARES-FEM-T4 FOR FINITE DEFORMATION NEARLY INCOMPRESSIBLE ANALYSIS Onishi, Y.; Iida, R.; Amaya, K. International Journal for Numerical Methods in Engineering, Vol. 109, Issue 11 https://doi.org/10.1002/nme.5337	journal	August 2016
Mixed linear/linear simplicial elements for incompressible elasticity and plasticity Cervera, M.; Chiumenti, M.; Valverde, Q. Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 49-50 https://doi.org/10.1016/j.cma.2003.07.007	journal	December 2003
On numerically accurate finite element solutions in the fully plastic range Nagtegaal, J. C.; Parks, D. M.; Rice, J. R. Computer Methods in Applied Mechanics and Engineering, Vol. 4, Issue 2 https://doi.org/10.1016/0045-7825(74)90032-2	journal	September 1974
A stabilized nodally integrated tetrahedral Puso, M. A.; Solberg, J. International Journal for Numerical Methods in Engineering, Vol. 67, Issue 6 https://doi.org/10.1002/nme.1651	journal	January 2006
Space-time finite element methods for elastodynamics: Formulations and error estimates Hughes, Thomas J. R.; Hulbert, Gregory M. Computer Methods in Applied Mechanics and Engineering, Vol. 66, Issue 3 https://doi.org/10.1016/0045-7825(88)90006-0	journal	February 1988
A framework for residual-based stabilization of incompressible finite elasticity: Stabilized formulations and <mml:math altimg="si67.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> methods for linear triangles and tetrahedra Masud, Arif; Truster, Timothy J. Computer Methods in Applied Mechanics and Engineering, Vol. 267 https://doi.org/10.1016/j.cma.2013.08.010	journal	December 2013
Triangles and tetrahedra in explicit dynamic codes for solids Zienkiewicz, O. C.; Rojek, J.; Taylor, R. L. International Journal for Numerical Methods in Engineering, Vol. 43, Issue 3 https://doi.org/10.1002/(SICI)1097-0207(19981015)43:3<565::AID-NME454>3.0.CO;2-9	journal	October 1998
A generalized view on Galilean invariance in stabilized compressible flow computations Scovazzi, G.; Love, E. International Journal for Numerical Methods in Fluids, Vol. 64, Issue 10-12 https://doi.org/10.1002/fld.2417	journal	September 2010
A mixed displacement-pressure formulation for numerical analysis of plastic failure Pastor, M.; Quecedo, M.; Zienkiewicz, O. C. Computers & Structures, Vol. 62, Issue 1 https://doi.org/10.1016/S0045-7949(96)00208-8	journal	January 1997
On finite element formulations for nearly incompressible linear elasticity Nakshatrala, K. B.; Masud, A.; Hjelmstad, K. D. Computational Mechanics, Vol. 41, Issue 4 https://doi.org/10.1007/s00466-007-0212-8	journal	August 2007
Stress–Velocity Complete Radiation Boundary Conditions Rabinovich, Daniel; Givoli, Dan; Hagstrom, Thomas Journal of Computational Acoustics, Vol. 21, Issue 03 https://doi.org/10.1142/S0218396X13500033	journal	July 2013
A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics Hughes, T. J. R.; Franca, L. P.; Mallet, M. Computer Methods in Applied Mechanics and Engineering, Vol. 54, Issue 2 https://doi.org/10.1016/0045-7825(86)90127-1	journal	February 1986
Implicit finite incompressible elastodynamics with linear finite elements: A stabilized method in rate form Rossi, S.; Abboud, N.; Scovazzi, G. Computer Methods in Applied Mechanics and Engineering, Vol. 311 https://doi.org/10.1016/j.cma.2016.07.015	journal	November 2016
A class of mixed assumed strain methods and the method of incompatible modes Simo, J. C.; Rifai, M. S. International Journal for Numerical Methods in Engineering, Vol. 29, Issue 8 https://doi.org/10.1002/nme.1620290802	journal	June 1990
A mixed-enhanced strain method Kasper, Eric P.; Taylor, Robert L. Computers & Structures, Vol. 75, Issue 3 https://doi.org/10.1016/S0045-7949(99)00134-0	journal	April 2000
A priori estimates for mixed finite element methods for the wave equation Cowsat, Lawrence C.; Dupont, Todd F.; Wheeler, Mary F. Computer Methods in Applied Mechanics and Engineering, Vol. 82, Issue 1-3 https://doi.org/10.1016/0045-7825(90)90165-I	journal	September 1990
Nonconforming Mixed Elements for Elasticity Arnold, Douglas N.; Winther, Ragnar Mathematical Models and Methods in Applied Sciences, Vol. 13, Issue 03 https://doi.org/10.1142/S0218202503002507	journal	March 2003
A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations Shakib, Farzin; Hughes, Thomas J. R.; Johan, Zdeněk Computer Methods in Applied Mechanics and Engineering, Vol. 89, Issue 1-3 https://doi.org/10.1016/0045-7825(91)90041-4	journal	August 1991
A new finite element formulation for computational fluid dynamics: V. Circumventing the babuška-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations Hughes, Thomas J. R.; Franca, Leopoldo P.; Balestra, Marc Computer Methods in Applied Mechanics and Engineering, Vol. 59, Issue 1 https://doi.org/10.1016/0045-7825(86)90025-3	journal	November 1986
Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes Dohrmann, C. R.; Heinstein, M. W.; Jung, J. International Journal for Numerical Methods in Engineering, Vol. 47, Issue 9 https://doi.org/10.1002/(SICI)1097-0207(20000330)47:9<1549::AID-NME842>3.0.CO;2-K	journal	March 2000
A unified approach to compressible and incompressible flows Hauke, G.; Hughes, T. J. R. Computer Methods in Applied Mechanics and Engineering, Vol. 113, Issue 3-4 https://doi.org/10.1016/0045-7825(94)90055-8	journal	March 1994
A stabilized formulation for incompressible plasticity using linear triangles and tetrahedra Chiumenti, M.; Valverde, Q.; Agelet de Saracibar, C. International Journal of Plasticity, Vol. 20, Issue 8-9 https://doi.org/10.1016/j.ijplas.2003.11.009	journal	August 2004
Mixed Methods for Elastodynamics with Weak Symmetry Arnold, Douglas N.; Lee, Jeonghun J. SIAM Journal on Numerical Analysis, Vol. 52, Issue 6 https://doi.org/10.1137/13095032X	journal	January 2014
Stabilized shock hydrodynamics: I. A Lagrangian method Scovazzi, G.; Christon, M. A.; Hughes, T. J. R. Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 4-6 https://doi.org/10.1016/j.cma.2006.08.008	journal	January 2007
On a tensor cross product based formulation of large strain solid mechanics Bonet, Javier; Gil, Antonio J.; Ortigosa, Rogelio International Journal of Solids and Structures, Vol. 84 https://doi.org/10.1016/j.ijsolstr.2015.12.030	journal	May 2016
A mixed-enhanced formulation tetrahedral finite elements Taylor, Robert L. International Journal for Numerical Methods in Engineering, Vol. 47, Issue 1-3 https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<205::AID-NME768>3.0.CO;2-J	journal	January 2000
A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations Chiumenti, M.; Valverde, Q.; Agelet de Saracibar, C. Computer Methods in Applied Mechanics and Engineering, Vol. 191, Issue 46 https://doi.org/10.1016/S0045-7825(02)00443-7	journal	November 2002
A Nitsche method for wave propagation problems in time domain Song, T.; Scovazzi, G. Computer Methods in Applied Mechanics and Engineering, Vol. 293 https://doi.org/10.1016/j.cma.2015.05.001	journal	August 2015
Triangular composite finite elements Guo, Yong; Ortiz, Michael; Belytschko, Ted International Journal for Numerical Methods in Engineering, Vol. 47, Issue 1-3 https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<287::AID-NME772>3.0.CO;2-M	journal	January 2000
A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications Bonet, J.; Burton, A. J. Communications in Numerical Methods in Engineering, Vol. 14, Issue 5 https://doi.org/10.1002/(SICI)1099-0887(199805)14:5<437::AID-CNM162>3.0.CO;2-W	journal	May 1998
Galilean invariance and stabilized methods for compressible flows: GALILEAN INVARIANCE AND STABILIZED METHODS FOR COMPRESSIBLE FLOWS Scovazzi, G. International Journal for Numerical Methods in Fluids, Vol. 54, Issue 6-8 https://doi.org/10.1002/fld.1423	journal	February 2007
A Priori Estimates for Mixed Finite Element Approximations of Second-Order Hyperbolic Equations with Absorbing Boundary Conditions Cowsar, Lawrence C.; Dupont, Todd F.; Wheeler, Mary F. SIAM Journal on Numerical Analysis, Vol. 33, Issue 2 https://doi.org/10.1137/0733026	journal	April 1996
A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multidimensional advective-diffusive systems Hughes, Thomas J. R.; Franca, Leopoldo P.; Mallet, Michel Computer Methods in Applied Mechanics and Engineering, Vol. 63, Issue 1 https://doi.org/10.1016/0045-7825(87)90125-3	journal	July 1987
Stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications Bonet, J.; Marriott, H.; Hassan, O. International Journal for Numerical Methods in Engineering, Vol. 50, Issue 1 https://doi.org/10.1002/1097-0207(20010110)50:1<119::AID-NME24>3.0.CO;2-C	journal	January 2000
A hybridizable discontinuous Galerkin formulation for non-linear elasticity Kabaria, Hardik; Lew, Adrian J.; Cockburn, Bernardo Computer Methods in Applied Mechanics and Engineering, Vol. 283 https://doi.org/10.1016/j.cma.2014.08.012	journal	January 2015
A vertex centred Finite Volume Jameson–Schmidt–Turkel (JST) algorithm for a mixed conservation formulation in solid dynamics Aguirre, Miquel; Gil, Antonio J.; Bonet, Javier Journal of Computational Physics, Vol. 259 https://doi.org/10.1016/j.jcp.2013.12.012	journal	February 2014
Discontinuous Galerkin finite element methods for second order hyperbolic problems Johnson, Claes Computer Methods in Applied Mechanics and Engineering, Vol. 107, Issue 1-2 https://doi.org/10.1016/0045-7825(93)90170-3	journal	August 1993
A mixed-enhanced strain method Kasper, Eric P.; L. Taylor, Robert Computers & Structures, Vol. 75, Issue 3 https://doi.org/10.1016/S0045-7949(99)00135-2	journal	April 2000
A higher-order Godunov method for modeling finite deformation in elastic-plastic solids Trangenstein, John A.; Colella, Phillip Communications on Pure and Applied Mathematics, Vol. 44, Issue 1 https://doi.org/10.1002/cpa.3160440103	journal	January 1991
P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method Virieux, Jean GEOPHYSICS, Vol. 51, Issue 4 https://doi.org/10.1190/1.1442147	journal	April 1986
F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking Neto, E. A. de Souza; Pires, F. M. Andrade; Owen, D. R. J. International Journal for Numerical Methods in Engineering, Vol. 62, Issue 3 https://doi.org/10.1002/nme.1187	journal	January 2005
Development of a stabilised Petrov–Galerkin formulation for conservation laws in Lagrangian fast solid dynamics Lee, Chun Hean; Gil, Antonio J.; Bonet, Javier Computer Methods in Applied Mechanics and Engineering, Vol. 268 https://doi.org/10.1016/j.cma.2013.09.004	journal	January 2014
On mixed finite element methods for linear elastodynamics Makridakis, Ch. G. Numerische Mathematik, Vol. 61, Issue 1 https://doi.org/10.1007/BF01385506	journal	December 1992
Generalization of selective integration procedures to anisotropic and nonlinear media Hughes, Thomas J. R. International Journal for Numerical Methods in Engineering, Vol. 15, Issue 9 https://doi.org/10.1002/nme.1620150914	journal	September 1980
Higher order stabilized finite element method for hyperelastic finite deformation Maniatty, Antoinette M.; Liu, Yong; Klaas, Ottmar Computer Methods in Applied Mechanics and Engineering, Vol. 191, Issue 13-14 https://doi.org/10.1016/S0045-7825(01)00335-8	journal	January 2002
A computational framework for polyconvex large strain elasticity Bonet, Javier; Gil, Antonio J.; Ortigosa, Rogelio Computer Methods in Applied Mechanics and Engineering, Vol. 283 https://doi.org/10.1016/j.cma.2014.10.002	journal	January 2015
A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equations Hughes, Thomas J. R.; Franca, Leopoldo P.; Hulbert, Gregory M. Computer Methods in Applied Mechanics and Engineering, Vol. 73, Issue 2 https://doi.org/10.1016/0045-7825(89)90111-4	journal	May 1989
Stabilized finite element method for viscoplastic flow: formulation with state variable evolution Maniatty, Antoinette M.; Liu, Yong International Journal for Numerical Methods in Engineering, Vol. 56, Issue 2 https://doi.org/10.1002/nme.554	journal	January 2002
Mixed finite element methods for linear elasticity with weakly imposed symmetry Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar Mathematics of Computation, Vol. 76, Issue 260 https://doi.org/10.1090/S0025-5718-07-01998-9	journal	October 2007
A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach: A DYNAMIC VMS APPROACH FOR TRANSIENT NEARLY INCOMPRESSIBLE ELASTICITY Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi International Journal for Numerical Methods in Engineering, Vol. 106, Issue 10 https://doi.org/10.1002/nme.5138	journal	November 2015
A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems Hughes, Thomas J. R.; Mallet, Michel Computer Methods in Applied Mechanics and Engineering, Vol. 58, Issue 3 https://doi.org/10.1016/0045-7825(86)90153-2	journal	November 1986
CBS-based stabilization in explicit solid dynamics Rojek, Jerzy; Oñate, Eugenio; Taylor, Robert L. International Journal for Numerical Methods in Engineering, Vol. 66, Issue 10 https://doi.org/10.1002/nme.1689	journal	June 2006
A discourse on Galilean invariance, SUPG stabilization, and the variational multiscale framework Scovazzi, G. Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 4-6 https://doi.org/10.1016/j.cma.2006.08.012	journal	January 2007
A stabilized mixed finite element method for finite elasticity. Klaas, Ottmar; Maniatty, Antoinette; Shephard, Mark S. Computer Methods in Applied Mechanics and Engineering, Vol. 180, Issue 1-2 https://doi.org/10.1016/S0045-7825(99)00059-6	journal	November 1999
Stabilized finite element formulation for elastic–plastic finite deformations Ramesh, Binoj; Maniatty, Antoinette M. Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 6-8 https://doi.org/10.1016/j.cma.2004.06.025	journal	February 2005
Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity Cervera, M.; Chiumenti, M.; Benedetti, L. Computer Methods in Applied Mechanics and Engineering, Vol. 285 https://doi.org/10.1016/j.cma.2014.11.040	journal	March 2015
Error-bounds for finite element method Babuška, Ivo Numerische Mathematik, Vol. 16, Issue 4 https://doi.org/10.1007/BF02165003	journal	January 1971
Lagrangian shock hydrodynamics on tetrahedral meshes: A stable and accurate variational multiscale approach Scovazzi, G. Journal of Computational Physics, Vol. 231, Issue 24 https://doi.org/10.1016/j.jcp.2012.06.033	journal	October 2012
A uniform nodal strain tetrahedron with isochoric stabilization Gee, M. W.; Dohrmann, C. R.; Key, S. W. International Journal for Numerical Methods in Engineering, Vol. 78, Issue 4 https://doi.org/10.1002/nme.2493	journal	April 2009
A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity Bonet, Javier; Gil, Antonio J.; Lee, Chun Hean Computer Methods in Applied Mechanics and Engineering, Vol. 283 https://doi.org/10.1016/j.cma.2014.09.024	journal	January 2015
On the enhancement of low-order mixed finite element methods for the large deformation analysis of diffusion in solids: On the enhancement of low-order mixed finite element methods for the large deformation analysis of diffusion in solids Krischok, Andreas; Linder, Christian International Journal for Numerical Methods in Engineering, Vol. 106, Issue 4 https://doi.org/10.1002/nme.5120	journal	October 2015
A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics Gil, Antonio J.; Lee, Chun Hean; Bonet, Javier Computer Methods in Applied Mechanics and Engineering, Vol. 276 https://doi.org/10.1016/j.cma.2014.04.006	journal	July 2014
The Double Absorbing Boundary method for a class of anisotropic elastic media Rabinovich, Daniel; Givoli, Dan; Bielak, Jacobo Computer Methods in Applied Mechanics and Engineering, Vol. 315 https://doi.org/10.1016/j.cma.2016.10.035	journal	March 2017
Simple stabilizing matrices for the computation of compressible flows in primitive variables Hauke, Guillermo Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 51-52 https://doi.org/10.1016/S0045-7825(01)00267-5	journal	October 2001
Mixed finite element methods — Reduced and selective integration techniques: A unification of concepts Malkus, David S.; Hughes, Thomas J. R. Computer Methods in Applied Mechanics and Engineering, Vol. 15, Issue 1 https://doi.org/10.1016/0045-7825(78)90005-1	journal	July 1978
Numerical algorithms for strong discontinuities in elastic—plastic solids Trangenstein, John A.; Pember, Richard B. Journal of Computational Physics, Vol. 103, Issue 1 https://doi.org/10.1016/0021-9991(92)90326-T	journal	November 1992
A new finite element formulation for computational fluid dynamics: IX. Fourier analysis of space-time Galerkin/least-squares algorithms Shakib, Farzin; Hughes, Thomas J. R. Computer Methods in Applied Mechanics and Engineering, Vol. 87, Issue 1 https://doi.org/10.1016/0045-7825(91)90145-V	journal	May 1991
A new framework for large strain electromechanics based on convex multi-variable strain energies: Variational formulation and material characterisation Gil, Antonio J.; Ortigosa, Rogelio Computer Methods in Applied Mechanics and Engineering, Vol. 302 https://doi.org/10.1016/j.cma.2015.11.036	journal	April 2016
An iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics Li, Xikui; Han, Xianhong; Pastor, M. Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 35-36 https://doi.org/10.1016/S0045-7825(03)00378-5	journal	August 2003
Mixed stabilized finite element methods in nonlinear solid mechanics Cervera, M.; Chiumenti, M.; Codina, R. Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 37-40 https://doi.org/10.1016/j.cma.2010.04.005	journal	August 2010
Mixed stabilized finite element methods in nonlinear solid mechanics Cervera, M.; Chiumenti, M.; Codina, R. Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 37-40 https://doi.org/10.1016/j.cma.2010.04.006	journal	August 2010
A new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems Mira, P.; Pastor, M.; Li, T. Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 37-38 https://doi.org/10.1016/S0045-7825(03)00416-X	journal	September 2003
A new framework for large strain electromechanics based on convex multi-variable strain energies: Finite Element discretisation and computational implementation Ortigosa, Rogelio; Gil, Antonio J. Computer Methods in Applied Mechanics and Engineering, Vol. 302 https://doi.org/10.1016/j.cma.2015.12.007	journal	April 2016
A second-order Godunov algorithm for two-dimensional solid mechanics Trangenstein, John A. Computational Mechanics, Vol. 13, Issue 5 https://doi.org/10.1007/BF00512588	journal	September 1994
A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems Hughes, Thomas J. R.; Mallet, Michel Computer Methods in Applied Mechanics and Engineering, Vol. 58, Issue 3 https://doi.org/10.1016/0045-7825(86)90152-0	journal	November 1986
Stabilized finite elements with equal order of interpolation for soil dynamics problems Pastor, M.; Zienkiewicz, O. C.; Li, T. Archives of Computational Methods in Engineering, Vol. 6, Issue 1 https://doi.org/10.1007/BF02828328	journal	March 1999
A new finite element formulation for computational fluid dynamics: II. Beyond SUPG Hughes, Thomas J. R.; Mallet, Michel; Akira, Mizukami Computer Methods in Applied Mechanics and Engineering, Vol. 54, Issue 3 https://doi.org/10.1016/0045-7825(86)90110-6	journal	March 1986
A continuous space-time finite element method for the wave equation French, Donald; Peterson, Todd Mathematics of Computation, Vol. 65, Issue 214 https://doi.org/10.1090/S0025-5718-96-00685-0	journal	January 1996
Numerical solution of the acoustic wave equation using Raviart–Thomas elements Jenkins, Eleanor W. Journal of Computational and Applied Mathematics, Vol. 206, Issue 1 https://doi.org/10.1016/j.cam.2006.08.003	journal	September 2007
Tetrahedral composite finite elements Thoutireddy, P.; Molinari, J. F.; Repetto, E. A. International Journal for Numerical Methods in Engineering, Vol. 53, Issue 6 https://doi.org/10.1002/nme.337	journal	January 2001
Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics Lafontaine, N. M.; Rossi, R.; Cervera, M. Computational Mechanics, Vol. 55, Issue 3 https://doi.org/10.1007/s00466-015-1121-x	journal	January 2015
Design of simple low order finite elements for large strain analysis of nearly incompressible solids de Souza Neto, E. A.; Perić, D.; Dutko, M. International Journal of Solids and Structures, Vol. 33, Issue 20-22 https://doi.org/10.1016/0020-7683(95)00259-6	journal	August 1996
An assessment of the average nodal volume formulation for the analysis of nearly incompressible solids under finite strains Andrade Pires, F. M.; de Souza Neto, E. A.; de la Cuesta Padilla, J. L. Communications in Numerical Methods in Engineering, Vol. 20, Issue 7 https://doi.org/10.1002/cnm.697	journal	April 2004
Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity: Motivation, formulation, and numerical examples Eyck, Alex Ten; Celiker, Fatih; Lew, Adrian Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 45-48 https://doi.org/10.1016/j.cma.2008.02.020	journal	August 2008
Discontinuous Galerkin methods for non-linear elasticity Ten Eyck, A.; Lew, A. International Journal for Numerical Methods in Engineering, Vol. 67, Issue 9 https://doi.org/10.1002/nme.1667	journal	January 2006
Development of a cell centred upwind finite volume algorithm for a new conservation law formulation in structural dynamics Lee, Chun Hean; Gil, Antonio J.; Bonet, Javier Computers & Structures, Vol. 118 https://doi.org/10.1016/j.compstruc.2012.12.008	journal	March 2013
Approximation des problèmes aux limites non homogènes pour des opérateurs non linéaires Aubin, Jean-Pierre Journal of Mathematical Analysis and Applications, Vol. 30, Issue 3 https://doi.org/10.1016/0022-247X(70)90139-3	journal	June 1970
On stability and convergence of projection methods based on pressure Poisson equation Guermond, J. -L.; Quartapelle, L. International Journal for Numerical Methods in Fluids, Vol. 26, Issue 9 https://doi.org/10.1002/(SICI)1097-0363(19980515)26:9<1039::AID-FLD675>3.0.CO;2-U	journal	May 1998
Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity: Analytical estimates Eyck, Alex Ten; Celiker, Fatih; Lew, Adrian Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 33-40 https://doi.org/10.1016/j.cma.2008.02.022	journal	June 2008
A stabilized finite element formulation for finite deformation elastoplasticity in geomechanics Xia, Kaiming; Masud, Arif Computers and Geotechnics, Vol. 36, Issue 3 https://doi.org/10.1016/j.compgeo.2008.05.001	journal	April 2009

Similar Records

An efficient time-domain perfectly matched layers formulation for elastodynamics on spherical domains

Journal Article · Tue Jul 15 00:00:00 EDT 2014 · International Journal for Numerical Methods in Engineering · OSTI ID:1538113

Sagiyama, K.; Govindjee, S.; Persson, P. -O.

Nonlinear elastodynamic behavior of intact and fractured rock under in-situ stress and saturation conditions

Journal Article · Sun May 16 00:00:00 EDT 2021 · Journal of the Mechanics and Physics of Solids · OSTI ID:1538113

Manogharan, Prabhakaran; Wood, Clay; Marone, Chris; +3 more

A weighted Shifted Boundary Method for free surface flow problems

Journal Article · Fri Sep 10 00:00:00 EDT 2021 · Journal of Computational Physics · OSTI ID:1538113

Colomés, Oriol; Main, Alex; Nouveau, Léo; +1 more

Related Subjects

42 ENGINEERING
weak boundary conditions
wave equation
nodal stress or nodal strain
elastodynamics
stabilized methods
variational multiscale analysis

Title: A velocity/stress mixed stabilized nodal finite element for elastodynamics: Analysis and computations with strongly and weakly enforced boundary conditions

Citation Formats

References (107)

Similar Records

Related Subjects