A EVI-space-time Galerkin method for dynamics at finite deformation in porous media

Computational Mechanics

Volumn 43, Issue 5, 2009, Pages 585-601

  Chen, Zhiyun ^a   Steeb, Holger ^b   Diebels, Stefan ^a  

^a SAARLAND UNIVERSITY   (Germany)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Discontinuous Galerkin method; Embedded velocity; Finite deformation; Integration method; Porous media; Space time FEM

Indexed keywords

DEFORMATION; INCOMPRESSIBLE FLOW; INTEGRATION; MUSCULOSKELETAL SYSTEM; NUMERICAL METHODS; POROUS MATERIALS; STABILITY;

DISCONTINUOUS GALERKIN METHODS; FINITE DEFORMATIONS; FLUID SATURATED POROUS MATERIALS; INTEGRATION METHOD; LAGRANGIAN DESCRIPTION; SPACE-TIME FEM; TIME-DEPENDENT EQUATIONS; TIME-DISCONTINUOUS GALERKIN METHODS;

GALERKIN METHODS;

EID: 58149487611     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-008-0332-9     Document Type: Article

References (58)

1. K Terzaghi 1923 Die Berechnung der Durchlässigkeitsziffer des Tones aus dem Verlauf der hydromechanischen Spannungserscheinungen, Sitzungsberichte der Akademie der Wissenschaften in Wien Mathematisch-naturwissenschaftliche Klasse 132 125 138
2. MA Biot 1941 General theory of three-dimensional consolidation J Appl Phys 12 155 164
3. MA Biot 1956 Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range J Acoust Soc Am 29 168 178
4. MA Biot 1956 Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range J Acoust Soc Am 29 179 191
5. MA Biot 1962 Mechanics of deformation and acoustic propagation in porous media J Appl Phys 33 1482 1498
6. Truesdell CA, Toupin R (1960) The classical field theories. In: Flügge S (eds) (Herausgeber), Handbuch der Physik III/1. Springer, Berlin
7. RJ Aktin RE Craine 1976 Continuum theories of mixtures: basic theory and historical developement Quart J Mech Appl Math 29 2 209 244
8. RM Bowen 1976 Theory of mixture Continuum Phys III 1 127
9. RM Bowen 1982 Compressible porous media models by use of the theory of mixtures Int J Eng Sci 20 697 735
10. A Bedford DS Drumheller 1973 Recent advances: theories of immiscible and structured mixtures Int J Eng Sci 21 863 960
11. Boer R (2000) Theory of porous media: highlights in the historical development and current state. Springer, Berlin
12. RI Borja E Alarcón 1995 A mathematical framework for finite strain elastoplastic consolidation. Part 1: balance laws, variational formulation and linearization Comp Meth Appl Mech Eng 159 145 171
13. S Diebels W Ehlers 1996 Dynamic analysis of a fully saturated porous medium accounting for geometrical and material non-linearities Int J Numer Meth Eng 39 81 97
14. SH Advani TS Lee JK Lee CS Kim 1993 Hygrothermomechanical evaluation of porous media under finite deformation. Part I-finite element formulations Int J Numer Meth Eng 36 147 160
15. CS Kim TS Lee SH Advani JK Lee 1993 Hygrothermomechanical evaluation of porous media under finite deformation. PartII-model validations and field simulations Int J Numer Meth Eng 36 161 179
16. J Larsson R Larsson 2002 Non-linear analysis of nearly saturated porous media: theoretical and numerical formulation Comp Meth Appl Mech Eng 191 3885 3907
17. C Li R Borja R Regueiro 2004 Dynamics of porous media at finite strain Comp Meth Appl Mech Eng 193 3837 3870
18. Ehlers W (2002) Foundations of multiphasic and porous materials. In: Ehlers W, Bluhm J(eds) Porous media: theory, experiments and numerical applications. Springer, Berlin, pp 3-86
19. Diebels S (2000) Mikropolare Zweiphasenmodelle: Modellierung auf der Basis der Theorie Poröser Medien, Habilitationsschrift, Institut für Mechanik (Bauwesen), Nr. II-4, Universität Stuttgart
20. Ehlers W, Diebels S (1995) Dynamic deformations in the theory of fluid-saturated porous solid materials. In: Parker DF, England AH (eds) Proc. of IUTAM symp.: anisotropy, inhomogeneity and nonlinearity in solid mechanics. Kluwer, Dordrecht, pp 241-246
21. W Ehlers G Eipper 1999 Finite elastic deformations in liquid-saturated and empty porous solids Transport Porous Med 34 179 191
22. Eipper G (1998) Theorie und Numerik finiter elastischer Deformationen in fluidgesättigten porösen Festkörpern, Dissertation, Institut für Mechanik (Bauwesen), Lehrstuhl II, Universität Stuttgart
23. JH Argyris DW Scharpf 1969 Finite elements in space and time Nucl Eng Des 10 456 464
24. I Fried 1969 Finite element analysis of time-dependent phenomena AIAA J 7 1170 1173
25. TJR Hughes GM Hulbert 1988 Space-time finite element methods for elastodynamics: Formulations and error estimates Comp Meth Appl Mech Eng 66 339 363
26. Hulbert G (1989) Space-time finite element methods for second order hyperbolic equations. PhD Thesis, Department of Mechanical Engineering, Stanford University, Stanford
27. GM Hulbert GM Hughes 1990 Space-time finite element methods for second-order hyperbolic equations Comp Meth Appl Mech Eng 84 327 348
28. C Johnson 1990 Adaptive finite element methods for diffusion and convection problems Comp Meth Appl Mech Eng 82 301 322
29. Reed WH, Hill TR: Triangular mesh methods for the neutron transport equation, Los Alamos Scientific Laboratory Report LA-UR-73-479
30. B Cockburn CW Shu 1989 TVB Runge-Kutta local projection discontinuous Galerkin finite element methods for conservation laws. II: General framework Math Comp 52 411 435
31. B Cockburn SY Lin CW Shu 1989 TVB Runge-Kutta local projection discontinuous Galerkin finite element methods for conservation laws III: one dimensional systems J Comp Phys 84 90 113
32. B Cockburn S Hou CW Shu 1990 TVB Runge-Kutta local projection discontinuous Galerkin finite element methods for conservation laws. IV: The multidimensional case Math Comp 54 545 581
33. Z Chen H Steeb S Diebels 2006 A time-discontinuous Galerkin method for the dynamical analysis of porous media Int J Numer Anal Meth Geomech 30 1113 1134
34. Z Chen H Steeb S Diebels 2008 A new hybrid velocity integration method applied to elastic wave propagation Int J Numer Meth Eng 74 1 56 79
35. Chen Z, Steeb H, Diebels S: Dynamic analysis of porous materials: numerical modeling with a space-time FEM. In: Proc Appl Math Mech
36. Ehlers W, Bluhm J (eds) (2002) Porous media. Springer, Berlin
37. Boer R (2000) Theory of porous media. Springer, Berlin
38. RM Bowen 1980 Incompressible porous media models by use of the theory of mixtures Int J Eng Sci 18 1129 1148
39. de Boer R, Ehlers W (1986) Theorie der Mehrkomponentenkontinua mit Anwendung auf bodenmechanische Probleme. In: Forschungsberichte aus dem Fachbereich Bauwesen, vol 40, Universität-GH-Essen
40. Marsden JE, Hughes TJR (1983) Mathematical foundations of elasticity. Dover Publications Inc., New York
41. Terzaghi K (1943) Theoretical soil mechanics. Wiley, New York
42. B Markert 2007 A constitutive approach to 3-d nonlinear fluid flow through finite deformable porous continua, with application to a high-porosity polyurethane foam Transport Porous Med 70 3 427 450
43. Ellsiepen P (1999) Zeit- und Ortsadaptive Verfahren angewandt auf Mehrphasenprobleme poröser Medien, PhD-thesis, Institute of Applied Mechanics (CE), Chair II, University of Stuttgart
44. S Breuer 1999 Quasi-static and dynamic behavior of saturated porous media with incompressible constituents Transport Porous Med 34 285 303
45. A Masud TJR Hughes 1997 A space-time Galerkin/least-squares finite element formulation of the navier-stokes equations for moving domain problems Comp Meth Appl Mech Eng 146 91 126
46. B Cockburn 2003 Discontinuous Galerkin methods Z Angew Math Mech 11 731 754
47. Zienkiewicz OC (1984) Coupled problems and their numerical solution. In: Lewis RW, Bettess P, Hinton E(eds) Numerical methods in coupled systems. Wiley, New York, pp 35-68
48. Wriggers P (1988) Konsistente Lineariserung in der Kontinuumsmechanik und ihre Anwendung auf die Finite-Element-Methode, Bericht Nr. F88/4 (1999) Institut für Baustatik und Numerische Mechanik, Univerität Honnover
49. Eriksson K, Estep D, Hansbo P, Johnson C (1996) Computational differential equations. Cambridge University Press, Cambridge
50. C Gresho RL Lee 1979 Don't suppress the wiggles-they're telling you something, Finite Element Methods in Convection dominated Flows ASME AME 34 27 61
51. Wall WA (1999) Fluid-Struktur-Interaktion mit stabilisierten Finiten Elementen, Bericht Nr. 31 (1999) Institut für Baustatik der Universität Stuttgart
52. Steeb H, Cirak F, Ramm E (2000) On local error estimators for non-self-adjoint boundary value problems. Z Angew Math Mech 507-508
53. AN Brooks TJR Hughes 1982 Streamline upwind/petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Comp Meth Appl Mech Eng 32 199 259
54. TJR Hughes LP Franca M Hulbert 1989 A new finite element formulation for computational fluid dynamics: Viii. the Galerkin/Least-squares method for advective-diffusive equations Comp Meth Appl Mech Eng 73 173 189
55. LP Franca SL Frey TJR Hughes 1992 Stabilized finite element methods: I. application to the advective-diffusive model Comp Meth Appl Mech Eng 95 253 276
56. JR Cash 1979 Diagonally implicit Runge-Kutta formulae with error estimates J Inst Maths Appl 24 293 301
57. P Bogacki LF Shampine 1989 A 3(2) pair of Runge-Kutta formulas Appl Math Lett 2 321 325
58. Gibson LJ, Ashby LJ (1997) A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations for moving domain problems. Cambridge University Press, Cambridge