New descriptions of stress, specific geometry, and strain in three dimensions

Mechanics Research Communications

Volumn 31, Issue 5, 2004, Pages 577-591

  Dean, E T R ^a  

^a Soil Models Limited   (United Kingdom)

Author keywords

Continuum mechanics; Elasto plasticity; Plasticity; Soil; Tensors; Zensors

Indexed keywords

ANISOTROPY; ELASTOPLASTICITY; GRANULAR MATERIALS; GRAPH THEORY; PLASTICITY; SOILS; STRAIN; TENSORS;

COAXIALITY; ISOTROPIC MATERIALS; MATHEMATICAL PROPERTIES; ZENSORS;

CONTINUUM MECHANICS;

EID: 3042812989     PISSN: 00936413     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechrescom.2004.03.001     Document Type: Article

References (37)

1. Al-Tabbaa, A., 1984. Anisotropy of clay. M.Phil. Thesis, Cambridge University.
2. Arthur J.R.F., Menzies T. Inherent anisotropy in a sand. Geotechnique. 27(1):1972;115-128.
3. Arthur J.R.F., Chua K.S., Dunstan T. Induced anisotropy in a sand. Geotechnique. 27(1):1977;13-30.
4. Atkinson J.H. Non-linear soil stiffness in routine design. 40th Rankine Lecture. Geotechnique. 50(5):2000;485-508.
5. Bellotti R., Jamiolkowski M., Lo Presti D.C.F., O'Neill D.A. Anisotropy of small strain stiffness in Ticino Sand. Geotechnique. 46(1):1996;115-131.
6. Bishop A.W., Henkel D.J. The Measurement of Soil Properties in the Triaxial Test. 1962;Edward Arnold Publishers Ltd, London.
7. ′ Geotechnique. 29:1979;469-480.
8. Dean E.T.R. New descriptions of plane strain. Geotechnique. 51(1):2001;15-36. with printing corrections in Erratum, Geotechnique 51(3) 291.
9. Dean, E.T.R., 2002. Zensors in three dimensions. Available from 〈www.soilmodels.co.uk〉.
10. Dean E.T.R. On the idea that many macroscopic elasto-plastic behaviours are determined by properties and interactions at mesoscopic scales. Khan A.S., Kazmi R., Zhou J. Dislocations, Plasticity, and Metal-Forming, Proceedings of International Symposium on Plasticity and its Current Applications. 2003;516-519 NEAT Press, Maryland.
11. Graham J., Crooks J.H.A., Lau S.L.K. Yield envelopes: identification and geotechnical properties. Geotechnique. 38(1):1988;125-134.
12. Gutierrez M., Ishihara K. Non-coaxiality and energy dissipation in granular materials. Soils and Foundations. 40(2):2000;49-60.
13. Il'yushin A.A. On the relation between stresses and small deformations in the mechanics of continuous media. Prikladnaya Matematika I Mekanica. 18:1954;641-666.
14. Kuwano R., Jardine R.J. On the applicability of cross-anisotropic elasticity to granular materials at very small strains. Geotechnique. 52(10):2002;727-749.
15. Kuwano R., Jardine R.J. Discussion: on the applicability of cross-anisotropic elasticity to granular materials at very small strains. Geotechnique. 54(1):2004;75-76.
16. Lambe T.W., Whitman R.V. Soil Mechanics, SI Version. 1979;John Wiley, New York.
17. Lensky V.S. Analysis of plastic behaviour of metals under complex loading. Lee E.H., Symonds P.S. Plasticity, Proceedings of 2nd Symposium on Naval Structural Mechanics. 1960;259-278 Pergamon, Oxford.
18. Lings M.L., Pennington D.S., Nash D.F.T. Anisotropic stiffness parameters and their measurement in a stiff natural clay. Geotechnique. 50(2):2000;109-127.
19. Masad E., Muhunthan B., Chameau J.L. Stress-strain model for clays with anisotropic void ratio distribution. International Journal of Numerical and Analytical Methods in Geomechanics. 22(5):1998;393-416.
20. Masad E., Muhunthan B. Three-dimensional characterization and simulation of anisotropic soil fabric. ASCE Journal of Geotechnical and GeoEnvironmental Engineering. 126(3):2000;199-207.
21. Molenkamp F. Principle of axial shear apparatus. Geotechnique. 48(3):1998;427-432.
22. Muhunthan B., Chameau J.L. Void fabric tensor and ultimate state surface of soils. ASCE Journal of Geotechnical and GeoEnvironmental Engineering. 123(2):1997;173-181.
23. Muir Wood D. Soil Behaviour and Critical State Soil Mechanics. 1990;Cambridge University Press.
24. Noll W. A mathematical theory of the mechanical behaviour of continuous media. Archives for Rational Mechanics and Analysis. 2:1958;197-226.
25. Parry R.H.G. Mohr's Circles, Stress Paths, and Geotechnics. 1995;E&FN Spon.
26. Peric D., Owen D.R.J., Honnor M.E. On work-conjugacy and finite strain elasto-plasticity. Pande G.N., Middleton J. NUMETA 90, Numerical Methods in Engineering: Theory and Applications. 2:1990;718-729 Elsevier, Amsterdam.
27. Pietruszczak S., Krucinski S. Description of clay anisotropy employing the concept of directional porosity. Pietruszczak S., Pande G.N. Proceedings of the 3rd International Conference on Numerical Models in Geomechanics (NUMOG III). 1989;61-70 Elsevier Applied Science, Amsterdam.
28. Saada, A., 1988. A brief revue of constitutive models. In: A. Saada, G. Bianchini (Eds.), Constitutive Equations for Granular Non-Cohesive Soils, Balkema, pp. 7-10.
29. Schofield A.N., Wroth C.P. Critical State Soil Mechanics. 1968;McGraw-Hill, New York.
30. Spencer A.J.M. Continuum Mechanics. 1980;Longmans, London.
31. Stewart I. The bellows conjecture. Scientific American. 279(July):1998;90-92.
32. Ting T.C.T. Anisotropic Elasticity, Theory and Applications. 1996;Oxford University Press.
33. Truesdell C. A First Course in Rational Continuum Mechanics. Vol. 1, General Concepts. 1977;Academic Press, New York.
34. Voight W. Lehrbuch der Kristallphysik. 1910;Leipzig. p. 560.
35. Wood D.M. Explorations of principal stress space with kaolin in a true triaxial apparatus. Geotechnique. 25(4):1975;783-797.
36. Zdravković L., Jardine R.J. The effect on anisotropy of rotating the principal stress axes during consolidation. Geotechnique. 51(1):2001;69-83.
37. Zienkiewicz, O.C., Taylor, R.L., 1994. The Finite Element Method, Basic Formulation and Linear Problems, vol. 1. Fourth Ed., McGraw-Hill, New York.