A macroscopic description of the quasi-static behavior of granular materials based on the theory of porous media

Granular Matter

Volumn 2, Issue 3, 2000, Pages 143-152

  Diebels, Stefan ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034378055     PISSN: 14345021     EISSN: 14347636     Source Type: Journal    
DOI: 10.1007/s100359900034     Document Type: Article

References (41)

1. C. Truesdell, Sulle basi della termomeccanica. Rend. Lincei (8), 22:33-38, 158-166, 1957
2. C. Truesdell & R. A. Toupin. The classical field theories. In S. Flügge, editor, Handbuch der Physik III/1, pages 226-793. Springer-Verlag, Berlin 1960
3. R. M. Bowen, Incompressible porous media models by use of the theory of mixtures. Int. J. Engng. Sci., 18:1129-1148, 1980
4. R. M. Bowen, Compressible porous media models by use of the theory of mixtures. Int. J. Engng. Sci., 20:697-735, 1982
5. R. de Boer & W. Ehlers, Theorie der Mehrkomponentenkontinua mit Anwendung auf bodenmechanische Probleme, Teil I. Forschungsberichte aus dem Fachbereich Bauwesen 40, Universität-GH-Essen, 1986
6. W. Ehlers, Poröse Medien - Ein kontinumsmechanisches Modell auf der Basis der Mischungstheorie. Forschungsberichte aus dem Fachbereich Bauwesen 45, Universtität-GH-Essen, 1989
7. W. Ehlers, Constitutive equations for granular materials in geomechanical context. In K. Hutter, editor, Continuum mechanics in environmental sciences and geophysics, CISM Courses and Lectures No. 337, pages 313-402. Springer-Verlag, Wien, 1993
8. E. Cosserat & F. Cosserat, Théorie des corps déformable. A. Hermann et Fils, Paris, 1909
9. A. C. Eringen & C. B. Kafadar, Polar field theories. In A. C. Eringen, editor, Continuum Physics, Vol IV - Polar and nonlocal field theories, pages 1-73. Academic Press, New York, 1976
10. D. Besdo, Inelastic behaviour of plane frictionless block-systems described as Cosserat media. Arch. Mech., 37:603-619, 1985
11. B. Zastrau, Zur Berechnung orientierter Kontinua -Entwicklung einer Direktortheorie und Anwendung der Methode der Finiten Elemente. Fortschrittberichte der VDI-Zeitschriften, Reihe 4 (Bauingenieurwesen) Nr. 60, VDI-Verlag, Düsseldorf, 1981
12. R. de Borst, Simulation of strain localization: A reappraisal of the Cosserat continuum. Eng. Comp., 8:317-332, 1991
13. W. Ehlers & W. Volk, On theoretical and numerical methods in the theory of porous media based on polar and non-polar solid materials. Int. J. Solids Struct., 35:4597-4617, 1998
14. P. Steinmann, A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity. Int. J. Solids Struct., 31:1063-1084, 1994
15. S. Diebels & W. Ehlers, On basic equations of multiphase micropolar materials. Technische Mechanik, 16:77-88, 1996
16. R. de Boer, Vektor-und Tensorrechnung für Ingenieure. Springer-Verlag, Berlin, 1982
17. S. Diebels, Constitutive modelling of micropolar porous media. In J.-F. Thimus et al., editors, Poromechanics - A Tribute to Maurice A. Biot, pages 71-76. A. A. Balkema, Rotterdam, 1998
18. S. Diebels, A micropolar theory of porous media: Constitutive modelling. Transport in Porous Media, 34:193-208, 1999
19. C. Truesdell, Thermodynamics of diffusion. In C. Truesdell, editor, Rational Thermodynamics (2nd ed.), pages 219-236. Springer-Verlag, New York, 1984
20. A. C. Eringen, Simple microfluids. Int. J. Engng. Sci., 2:205-217, 1964
21. I-S. Liu, Method of Lagrange multipliers for exploitation of the entropy principle. Arch. Rat. Mech. Anal., 46:131-148, 1972
22. I-S. Liu & I. Müller, Thermodynamics of mixture of fluids. In C. Truesdell, editor, Rational Thermodynamcis (2nd ed.), pages 264-285. Springer-Verlag, New York, 1984
23. B. D. Coleman & W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rat. Mech. Anal., 13:167-178, 1963
24. W. Ehlers, On thermodynamics of elasto-plastic porous media. Arch. Mech., 41:73-93, 1989
25. B. Svendsen & K. Hutter, On the thermodynamics of a mixture of isotropic materials with constraints. Int. J. Engng. Sci., 33:2021-2054, 1995
26. W. Ehlers, P. Ellsiepen, P. Blome, D. Mahnkopf, & B. Markert, Theoretische und numerische Studien zur Lösung von Rand-und Anfangswertproblemen in der Theorie Poröser Medien, Bericht aus dem Institut für Mechanik (Bauwesen) Nr. 99-II-1. Universtität Stuttgart, 1999. Abschlußbericht zum gleichnamigen DFG-Projekt
27. K. Hutter, K. Jöhnk, & B. Svendsen, On interfacial transition conditions in two phase gravity flow. ZAMP, 45:746-762, 1994
28. T. Wu, K. Hutter, & B. Svendsen, On shear flow of a saturated ice-sediment mixture with thermodynamical equilibrium pressure and momentum exchange. Proc. R. Soc. Lond., A 454:71-88, 1998
29. J. P. Boehler, Representations for isotropic and anisotropic non-polynomial tensor functions. In J. P. Boehler, editor, Applications of tensor functions in solid mechanics, CISM Courses and Lectures No. 292, pages 31-53. Springer-Verlag, Wien, 1987
30. J. C. Simo & R. L. Taylor, Penalty function formulations for incompressible nonlinear elastostatics. Comp. Methods Appl. Mech. Engng., 35:107-118, 1982
31. R. de Borst, Numerical modelling of bifurcation and localization in cohesive-frictional materials. Pageoph., 137:368-390, 1991
32. L. Šuklje, Rheological Aspects of Soil Mechanics. Wiley-Interscience, London, 1969
33. W. Ehlers & G. Eipper, Finite elastic deformations in liquid-saturated and empty porous solids. Transport in Porous Media, 34:179-191, 1998
34. W. Ehlers, Compressible and hybrid two-phase models in porous media theories. In Y. C. Angel, editor, Anisotropy and Inhomogeneity in Elasticity and Plasticity, AMD-vol. 158, pages 25-38. ASME, 1993
35. P. Ellsiepen (Hrsg.) PANDAS - Benutzer-und Referenzhandbuch, Bericht aus dem Institut für Mechanik (Bauwesen) Nr. 97-II-9. Universität Stuttgart, 1997
36. S. Diebels & W. Ehlers. Dynamic analysis of a fully saturated porous medium accounting for geometrical and material nonlinearities. Int. J. Numer. Meth. Eng., 39:81-97, 1996
37. S. Diebels, P. Ellsiepen, & W. Ehlers, A two-phase model for viscoplastic geomaterials. In D. Besdo and R. Bogacz, editors, Dynamics of Continua, pages 103-112. Shaker Verlag, Aachen, 1998
38. S. Diebels, P. Ellsiepen, & W. Ehlers, Error-controlled Runge-Kutta time integration of a viscoplastic hybrid two-phase model. Technische Mechanik, 16:19-27, 1999
39. W. Ehlers & G. Eipper, The simple tension problem at large volumetric strains computed from hyperelastic material laws. Acta Mech., accepted, 1998
40. R. S. Lakes, Experimental microelasticity of two porous solids. Int. J. Solids Struct., 22:55-63, 1986
41. R. S. Lakes, Experimental methods for study of Cosserat elastic solids and other generalized elastic continua. In H.-B. Mühlhaus, editor, Continuum Models for Materials with Microstructure, pages 1-25. John Wiley and Sons, 1995