Full 3D finite element Cosserat formulation with application in layered structures

Applied Mathematical Modelling

Volumn 33, Issue 8, 2009, Pages 3450-3464

  Riahi, Azadeh ^a   Curran, John H ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Characteristic length; Cosserat theory; Discrete element method; Finite element; Layered plate; Micropolar theory

Indexed keywords

CHARACTERISTIC LENGTH; COSSERAT THEORY; DISCRETE ELEMENT METHOD; FINITE ELEMENT; LAYERED PLATE; MICROPOLAR THEORY;

CONTINUUM MECHANICS; ELASTICITY; PLATES (STRUCTURAL COMPONENTS); THREE DIMENSIONAL;

FINITE ELEMENT METHOD;

EID: 64249137828     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2008.11.022     Document Type: Article

References (41)

1. Cosserat E., and Cosserat F. Théorie des Corps Déformables (1909), Hermann, Paris
2. Mindlin R.D. Second gradient of strain and surface-tension in linear elasticity. Int. J. Solids Struct. 1 4 (1965) 417-438
3. Kroner E. Mechanics of generalized continua. Proceeding of IUTAM Symposium on Generalized Cosserat Continuum and Continuous Theory of Dislocations with Applications (1967), Springer-Verlag, Berlin
4. Shaefer H. Das Cosserat-kontinuum ZAMM. J. Appl. Math. Mech./Z. Angew. Math. Mech. 47 (1967) 485-498
5. Dyszlewicz J. Micropolar Theory of Elasticity (2004), Springer
6. de Borst R., and Mühlhaus H.B. Gradient-dependent plasticity - formulation and algorithmic aspects. Int. J. Numer. Meth. Eng. 35 3 (1992) 521-539
7. de Borst R. A generalization of J2-flow theory for polar continua. Comput. Meth. Appl. Mech. Eng. 103 3 (1993) 347-362
8. Mühlhaus H.B., and Vardoulakis I. The thickness of shear bands in granular materials. Geotechnique 37 3 (1987) 271-283
9. Ehlers W., Ramm E., Diebels S., and D'Addetta G.A. From particle ensembles to Cosserat continua: homogenization of contact forces towards stresses and couple stresses. Int. J. Solids Struct. 40 (2003) 6681-6702
10. Pasternack E., and Mühlhaus H.B. Generalised homogenisation procedures for granular materials. J. Eng. Math. 52 (2005) 199-229
11. Khoei A.R., Gharehbaghi S.A., Tabarraie A.R., Riahi A., and estimation E. adaptivity and data transfer in enriched plasticity continua to analysis of shear band localization. Appl. Math. Model. 31 6 (2007) 983-1000
12. Froiio F., Tomassetti G., and Vardoulakis I. Mechanics of granular materials: The discrete and the continuum descriptions juxtaposed. Int. J. Solids Struct. 43 (2006) 7684-7720
13. Arslan H., and Sture S. Evaluation of a physical length scale for granular materials. Comp. Mater. Sci. 42 (2008) 525-530
14. Mühlhaus H.B. Continuum Models for Layered and Blocky Materials, Comprehensive Rock Mechanics (1993), Pergamon Press, Oxford
15. Mühlhaus H.B. A Relative Gradient Method for Laminated Materials, Continuum Models for Materials with Microstructure (1995), Wiley, Toronto
16. Adhikary D.P., Dyskin A.V., and Jewell R.J. Numerical modelling of the flexural deformation of foliated rock slopes. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33 6 (1996) 595-606
17. Adhikary D.P., and Dyskin A.V. A Cosserat continuum for layered materials. Comput. Geotech. 20 1 (1997) 15-45
18. Adhikary D.P., and Dyskin A.V. A continuum model of layered rock masses with non-associative joint plasticity. Int. J. Numer. Anal. Method Geomech. 22 4 (1998) 245-261
19. Adhikary D.P., Mühlhaus H.B., and Dyskin A.V. Modeling the large deformations in stratified media; the Cosserat continuum approach. Mech. Cohesive-Frictional Mater. 4 3 (1999) 195-213
20. Adhikary D.P., and Guo H. An orthotropic Cosserat elasto-plastic model for layered rocks. Rock Mech. Rock Eng. 35 3 (2002) 161-170
21. Adhikary D.P., and Dyskin A.V. Modelling of progressive and instantaneous failures of foliated rock slopes. Rock Mech. Rock Eng. 40 4 (2007) 349-362
22. Dai C., Mühlhaus H.B., Meek J., and Duncan Fama M. Modeling of blocky rock masses using the Cosserat method. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33 4 (1996) 425-432
23. Sulem J., and Mühlhaus H.B. A continuum model for periodic two-dimensional block structures. Mech. Cohesive-Frictional Mater. 2 (1997) 31-46
24. Sulem J., and Cerrolaza M. Finite element analysis of the indentation test on rocks with microstructure. Comput. Geotechn. 29 (2002) 95-117
25. Naghdi P.M. The theory of plates and shells. In: Flügges S. (Ed). Handbuch der Physics vol. 2 (1972), Springer-Verlag, Berlin
26. Rubin M.B. Cosserat Theories: Shells, Rods, and Points (2000), Kluwer Academic Publishers, Boston
27. Rubin M.B. Numerical solution of axisymmetric nonlinear elastic problems including shells using the theory of a Cosserat point. Comp. Mech. 36 (2005) 266-288
28. Liu D., Cao D.Q., Rosing R., Wang C.H.T., and Richardson A. Finite element formulation of slender structures with shear deformation based on the Cosserat theory. Int. J. Solids Struct. 44 (2007) 7785-7802
29. Malcolm D.J., and Glockner P.G. Nonlinear sandwich shell and Cosserat surface theory. J. Eng. Mech. Div. 98 5 (1972) 1183-1203
30. Malcolm D.J., and Glockner P.G. Variational principles for idealized sandwich shells. Int. J. Engng. Sci. 14 (1976) 661-671
31. A Note on Nonlinear Compatibility Equations for Sandwich Shells and Cosserat Surfaces.
32. Steinmann P. A micropolar theory of finite deformation and finite rotation multiplicative elasto-plasticity. Int. J. Solids Struct. 31 8 (1994) 1063-1084
33. Truesdell C., and Toupin R. The classical field theories. Handbuch der Physik 3 1 (1960) 226-793
34. Szilard R. Theories and Applications of Plate Analysis: Classical, Numerical, and Engineering Methods (2004), John Wiley, New York
35. Sharma K.G., and Pande G.N. Stability of rock masses reinforced by passive, fully-grouted rock bolts. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 25 5 (1988) 273-285
36. A. Riahi, Ph.D. thesis, University of Toronto, Toronto, 2008.
37. V Zvolinski N., and Shkhinek K.N. Continuum model for a laminar elastic medium. Solid Mech. 19 1 (1984) 1-9
38. Cundall P.A., and Strack O.D.L. A discrete model for granular assemblies. Geotechnique 29 1 (1979) 47-65
39. 2, Two-dimensional finite element slope stability analysis, Version 6.0, Toronto, 2005.
40. Timoshenko S., and Goodier J.N. Theory of elasticity. third ed. (1970), McGraw-Hill, New York
41. Itasca Inc., 3DEC, Three-dimensional Distinct Universal Code, Version 4, Minneapolis, 2003.