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Beyond failure in granular materials. (English) Zbl 0893.73047

The interrelations among different constitutive models of granular materials are discussed with special reference to failure and stability. For the hyperplastic constitutive equation, the accessible stress states and the stable stress states are found to be enclosed by a bound surface and a stability surface in the stress space, respectively. Theoretical findings about the bound surface and the stability surface are verified qualitatively by presenting results of triaxial tests on dry sand.

MSC:

74R99 Fracture and damage
74A20 Theory of constitutive functions in solid mechanics
74-05 Experimental work for problems pertaining to mechanics of deformable solids
Full Text: DOI

References:

[1] ’A Constitutive Theory for Soils and other Granular Materials, ’ Habilitation in German, Karlsruhe University, (1988).
[2] Wu, Mech. Mater. 9 pp 245– (1990) · doi:10.1016/0167-6636(90)90006-2
[3] Kolymbas, Ing. Arch. 61 pp 143– (1991)
[4] Wu, Int. J. Eng. Sci. 29 pp 195– (1991) · Zbl 0762.73017 · doi:10.1016/0020-7225(91)90016-V
[5] ’Hypoplasticity as a mathematical model for mechanical behaviour of granular materials, ’ Dissertation, Karlsruhe University, (1992), (in German).
[6] and , ’A hypoplastic constitutive model for barotropy and pyknotropy of granular materials, ’ in Proc. Int. Workshop Modern Approaches in Plasticity, Elsevier, Amsterdam, (1993), pp. 225-258. · doi:10.1016/B978-0-444-89970-5.50016-9
[7] Wu, Int. j. nutner. anal, methods geomech. 18 pp 833– (1994) · Zbl 0818.73057 · doi:10.1002/nag.1610181203
[8] Kolymbas, Int. j. numer. anal, methods geomech. 19 pp 415– (1995) · Zbl 0829.73057 · doi:10.1002/nag.1610190604
[9] Bauer, Powder Technol. 85 pp 1– (1995) · doi:10.1016/0032-5910(95)02999-I
[10] Wu, Mech. Cohesive-Frictional Mater. 1 pp 145– (1996) · doi:10.1002/(SICI)1099-1484(199604)1:2<145::AID-CFM8>3.0.CO;2-9
[11] Wu, Mech. Mater. 23 pp 45– (1996) · doi:10.1016/0167-6636(96)00006-3
[12] Tejchman, Comput. Geotech. 18 pp 71– (1996) · doi:10.1016/0266-352X(95)00018-6
[13] and , ’The nonlinear field theories of mechanics, ’ in (ed.) Encyclopedia of Physics, III/1, Springer, Berlin, (1965).
[14] Hill, J. Mech. Phys. Solids 7 pp 209– (1959) · Zbl 0086.17301 · doi:10.1016/0022-5096(59)90007-9
[15] Truesdell, J. Appl. Phys. 27 pp 441– (1956) · doi:10.1063/1.1722399
[16] ’Comportment elasto-plastique des milieux granularien, ’ Foundation of Plasticity, Noordoff, Leiden, 1973, pp. 33-49.
[17] Romano, Arch. Mech. 20 pp 1011– (1974)
[18] Davis, Int. j. numer. anal, methods geomech. 2 pp 255– (1978) · Zbl 0377.73114 · doi:10.1002/nag.1610020306
[19] Bazant, Int. J. solids Struct. 14 pp 691– (1978) · Zbl 0387.73028 · doi:10.1016/0020-7683(78)90029-X
[20] ’A comparison of some constitutive laws for soils under radially symmetric loading and unloading, ’ in Proc. 3rd Int. Conf. Numer. Methods Geomech., Balkema, Holland, 1979, pp. 1309-1323.
[21] Royis, Eur. J. Mech. (A/Solids) 8 pp 385– (1989)
[22] Tokuoka, J. Ration. Mech. Anal. 42 pp 239– (1971)
[23] ’Hypoplasticity vs. elastoplasticity, selected topics, ’ in Proc. Int. Workshop Modern Approaches in Plasticity, Elsevier, Amsterdam, 1993, pp. 277-307.
[24] and , ’A mathematical theory of plasticity based on the concept of slip, ’ NACA TN 1871, (1949).
[25] Sawczuk, ZAMP 19 pp 770– (1968) · Zbl 0177.54404 · doi:10.1007/BF01591007
[26] Goldscheider, Mech. Resear. Comm. 3 pp 463– (1976) · doi:10.1016/0093-6413(76)90037-9
[27] Wu, Int. j. numer. methods eng. 30 pp 491– (1990) · Zbl 0716.73029 · doi:10.1002/nme.1620300308
[28] Chambon, Int. j. numer. anal, methods geomech. 18 pp 253– (1994) · Zbl 0809.73049 · doi:10.1002/nag.1610180404
[29] Wu, ASTM Geotech. Testing J. 14 pp 276– (1991) · doi:10.1520/GTJ10572J
[30] Hill, J. Mech. Phy. Solids 16 pp 229– (1968) · Zbl 0162.28702 · doi:10.1016/0022-5096(68)90031-8
[31] Hill, J. Mech. Phy. Solids 16 pp 315– (1968) · Zbl 0167.54302 · doi:10.1016/0022-5096(68)90018-5
[32] Bazant, J. eng. mech. div. ASCE 114 pp 2013– (1988) · doi:10.1061/(ASCE)0733-9399(1988)114:12(2013)
[33] Valanis, J.appl. mech., ASME 52 pp 649– (1985) · Zbl 0577.73008 · doi:10.1115/1.3169115
[34] Petryk, J Mech. Phys. Solids 40 pp 1227– (1992) · Zbl 0763.73028 · doi:10.1016/0022-5096(92)90014-S
[35] ’Controllability of the incremental response of soil specimen subjected to arbitrary loading programmes, ’ private communication, (1995).
[36] Lade, J. eng. Mech. Div ASCE 113 pp 1302– (1987) · doi:10.1061/(ASCE)0733-9399(1987)113:9(1302)
[37] Chu, Geotechnique 44 pp 65– (1994) · doi:10.1680/geot.1994.44.1.65
[38] ’A five constant model unifying well established concepts, ’ Proc. Int. Workshop on Constitutive Relations for Soils, Balkema, Holland, 1982, pp. 175-197.
[39] Drucker, J. eng. mech. div. ASCE 114 pp 1842– (1988)
[40] ’Aspects of invariance in solid mechanics, ’ in (ed.), Advances in Applied Mechanics 8, Academic Press, New York, 1978, pp. 1-75. · Zbl 0475.73026
[41] Truesdell, J. Ration. Mech. Anal 4 pp 83– (1955)
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