Initial response of a micro-polar hypoplastic material under plane shearing

Journal of Engineering Mathematics

Volumn 52, Issue 1, 2005, Pages 35-51

  Bauer, Erich ^a  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Granular materials; Hypoplasticity; Interface behavior; Micro polar continuum; Planes hearing

Indexed keywords

BOUNDARY CONDITIONS; DEFORMATION; FUNCTIONS; SHEARING; STRESS ANALYSIS; STRESSES; TENSORS;

MICRO-POLAR BOUNDARY CONDITIONS; MICRO-POLAR HYPOPLASTIC MATERIALS; PLANE SHEARING; STRESS TENSOR;

PLASTIC PRODUCTS;

GRANULAR MEDIUM;

EID: 22844445378     PISSN: 00220833     EISSN: 15732703     Source Type: Journal    
DOI: 10.1007/s10665-004-3949-5     Document Type: Article

References (53)

1. V.K. Garga and J.A. Infante Sedano 2002 Steady state strength of sands in a constant volume ring shear apparatus Geotech. Testing J 25 414-421
2. K.H. Roscoe 1970 The influence of strains in soil mechanics, 10th Rankine Lecture Géotechnique 20 129-170
3. H.B. Mühlhaus and I. Vardoulakis 1987 The thickness of shear bands in granular materials Geotechnique 37 271-283
4. M. Oda 1993 Micro-fabric and couple stress in shear bands of granular materials In: C.C. Thornton (eds.) Powders and Grains, 3 Balkema Rotterdam 161-167
5. J. Desrues R. Chambon M. Mokni and F. Mazerolle 1996 Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography Géotechnique 46 529-546
6. E. Cosserat and F. Cosserat 1909 Théorie des Corps Deformables Herman et fils Paris
7. R.D. Mindlin 1965 Stress functions for a Cosserat continuum Int. J. Solids Struct 1 265-271
8. A.C. Eringen 1976 Polar and nonlocal field theories. Continuum Physics IV Academic Press New York, San Francisco, London 274
9. E.C. Aifantis 1984 On the microstructural original of certain inelastic models J. Engng. Mat. Technol 106 326-334
10. Z.P. Bazant T.B. Belytschko and T.P. Chang 1984 Continuum theory for strain softening ASCE J. Engng. Mech 110 1666-1692
11. H.-B. Mühlhaus 1989 Application of Cosserat theory in numerical solutions of limit load problems Ingenieur Archiv 59 124-137
12. I. Vardoulakis and E.C. Aifantis 1991 A gradient flow theory of plasticity for granular materials Acta Mech 87 197-217
13. D. Kolymbas 1991 An outline of hypoplasticity Arch. Appl. Mech 3 143-151
14. F. Darve 1991 Incrementally non-linear constitutive relationships In: F. Darve (ed.) Geomaterials: Constitutive Equations and Modelling Elsevier Amsterdam 213-237
15. Y.F. Dafalias 1986 Bounding surface plasticity: I. Mathematical foundation and hypoplasticity J. Engng. Mech., ASCE 112 966-987
16. C. Truesdell and W. Noll 1965 The non-linear field theories of mechanics In: S. Flügge (ed.) Encyclopedia of Physics III/c Springer press Heidelberg 1-602
17. D. Kolymbas 1988 A generalized hypoelastic constitutive law. Proc. 11th Int. Conf. Soil Mechanics and Foundation Engineering 5 Balkema Rotterdam 2626
18. W. Wu and E. Bauer 1994 A simple hypoplastic constitutive model for sand Int. J. Num. Anal. Methods Geomech 18 833-862
19. G. Gudehus 1996 A comprehensive constitutive equation for granular materials Soils and Foundations 36 1-12
20. E. Bauer 1996 Calibration of a comprehensive hypoplastic model for granular materials Soils and Foundations 36 13-26
21. P.A. Wolffersdorff von 1996 A hypoplastic relation for granular materials with a predefined limit state surface Mech. Cohesive-Frictional Materials 1 251-271
22. W. Wu and D. Kolymbas 2000 Hypoplasticity then and now In: D. Kolymbas (ed.) Constitutive Modelling of Granular Materials Springer Berlin, Heidelberg, Newyork 57-105
23. C. Tamagnini G. Viggiani and R. Chambon 2000 A review of two different approaches to hypoplasticity In: D. Kolymbas (ed.) Constitutive Modelling of Granular Materials Springer Berlin, Heidelberg, Newyork 107-145
24. E. Bauer and I. Herle 2000 Stationary states in hypoplasticity In: D. Kolymbas (ed.) Constitutive Modelling of Granular Materials Springer Berlin, Heidelberg, Newyork 167-192
25. J. Tejchman and E. Bauer 1996 Numerical simulation of shear band formation with a polar hypoplastic constitutive model Comp. Geotech 19 221-244
26. G. Gudehus 1998 Shear localization in simple grain skeleton with polar effect In: T. Adachi F. Oka and A. Yashima (eds.) Proc. of the 4th Int. Workshop on Localization and Bifurcation Theory for Soils and Rocks Balkema Rotterdam 3-10
27. G. Gudehus 1997 Attractors, percolation thresholds and phase limits of granular soils In: R.P. Behringer and Jenkins J.T. (eds.) Powders and Grains Balkema Rotterdam 169-183
28. J. Tejchman 1997 Modelling of shear localisation and autogeneous dynamic effects in granular bodies Veröffentlichungen des Institutes für Bodenmechanik und Felsmechanik der Universität Fridericiaca in Karlsruhe 140 353pp
29. E. Bauer and W. Huang 1999 Numerical study of polar effects in shear zones In: G.N. Pande S. Pietruszczak and H.F. Schweigers (eds.) Proc. of the 7th Int. Symp. on Num. Models in Geomechanics Balkema Rotterdam 133-138
30. J. Tejchman and G. Gudehus 2001 Shearing of a narrow granular layer with polar quantities Int. J. Num. Meth. Geomech 25 1-28
31. W. Huang K. Nübel and E. Bauer 2002 Polar extension of a hypoplastic model for granular materials with shear localization Mech. Materials 34 563-576
32. J. Tejchman and I. Herle 1999 A "class A" prediction of the bearing capacity of plane strain footings on sand Soils and Foundations 39 47-60
33. K. Nübel and R. Cudmani 2000 Examples of finite element calculations with the hypoplastic law D. Kolymbas Constitutive Modelling of Granular Materials Springer Berlin, Heidelberg, Newyork 523-538
34. E. Bauer W. Huang 2001 Numerical investigation of strain localization in a hypoplstic Cosserat material under shearing In: C.S. Desai T. Kundu S. Harpalani D. Contractor and J. Kemeny (eds.) Proc. of the 10th Int. Conf. on Computer Methods and Advances in Geomechanics Balkema Rotterdam 525-528
35. G. Gudehus and K. Nübel 2004 Evolution of shear bands in sand Géotechnique 54 187-201
36. J. Hill 2000 Some symmetrical cavity problems for a hypoplstic granular material Q. J. Mech. Appl. Math 53 111-135
37. E. Bauer and W. Huang 2001 Evolution of polar quantities in a granular Cosserat material under shearing In: H.-B. Mühlhaus A.V. Dyskin and E. Pasternak (eds.) Proc. 5th Int. Workshop on Bifurcation and Localization Theory in Geomechanics Balkema Rotterdam 227-238
38. W. Huang 2000 Hypoplastic Modelling of Shear Localisation in Granular Materials. Dissertation Graz University of Technology Austria 107pp
39. W. Wu and A. Niemunis 1996 Failure criterion, flow rule and dissipation function derived from hypoplasticity Mech. Cohesive-Frictional Materials 1 145-163
40. W. Wu and E. Bauer 1993 A hypoplastic model for barotropy and pyknotropy of granular soils In: D. Kolymbas (ed.) Proc. of the Int. Workshop on Modern Approaches to Plasticity Elsevier Amsterdam 225-245
41. W. Wu E. Bauer and D. Kolymbas 1996 Hypoplastic constitutive model with critical state for granular materials Mech. Materials 23 45-69
42. W. Wu E. Bauer A. Niemunis and I. Herle 1993 Visco-hypoplastic models for cohesive soils In: D. Kolymbas (ed.) Proc. of the Int. Workshop on Modern Approaches to Plasticity Elsevier Amsterdam 365-383
43. Gudehus G. 2004. Hypoplastic shear localisation in psammoids and peloids. 2nd Int. Symposium on Continuous and Discontinuous Modelling of Cohesive Frictional Materials, Publication in print.
44. W. Wu 1998 Rational approach to anisotropy of sand Int. J. Num Anal. Methods in Geomech 24 921-940
45. E. Bauer W. Wu and W. Huang 2003 Influence of initially transverse isotropy on shear banding in granular materials In: J.F. Labuz and A. Arescher (eds.) Proc. of the Int. Workshop on Bifurcation and Instabilities in Geomechanics Balkema Rotterdam 161-172
46. E. Bauer and W. Wu 1994 Extension of Hypoplastic Constitutive Model with Respect to Cohesive Powders In: H.J. Siriwardane and M.M. Zadan (eds.) Proc. of the Eighth Intern. Conf. on Computer Methods and Advances in Geomechanics Balkema Rotterdam 531-536
47. A. Niemunis and I. Herle 1997 Hypoplastic model for cohesionless soils with elastic strain range Mech. Cohesive-Frictional Materials 2 279-299
48. A.E. Green and P.M. Naghdi 1965 A general Theory of an elastic-plastic continuum Arch. Rat. Mech. Anal 18 251-281
49. W. Huang and E. Bauer 2003 Numerical investigations of shear localization in a micro-polar hypoplastic material Int. J. Num. Anal. Meth. Geomech 27 325-352
50. Matsuoka H., Nakai T. 1977. Stress-strain relationship of soil based on the 'SMP'. Proc. of Speciality Session 9, IX Int. Conf. Soil Mech. Found. Eng., Tokyo pp. 153-162.
51. E. Bauer 2000 Conditions for embedding Casagrande's critical states into hypoplasticity Mech Cohesive-Frictional Materials 5 125-148
52. W. Huang E. Bauer and S. Sloan 2003 Behaviour of interfacial layer along granular soil-structure interfaces Struct. Engng. Mech 15 315-329
53. G. Gudehus 2001 Forced and spontaneous polarisation in shear zones In: H.-B. Mühlhaus A.V. Dyskin and E. Pasternak (eds.) Proc. 5th Int. Workshop on bifurcation and Localization Theory in Geomechanics Balkema Rotterdam 45-51