A gradient flow theory of plasticity for granular materials

I. Vardoulakis1,2, Elias C. Aifantis3,4
1Department of Civil and Mineral Engineering, University of Minnesota, USA
2Department of Engineering Science, National Technical University of Athens, Greece
3Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, USA
4Division of Physics and Mechanics, School of Technology, Aristotle University of Thessaloniki, Greece

Tóm tắt

Từ khóa


Tài liệu tham khảo

Aifantis, E. C.: On the microstructural origin of certain inelastic models. Transactions of ASME. J. Mat. Engng. Tech.106, 326?330 (1984).

Aifantis, E. C.: The physics of plastic deformation. Int. J. Plasticity3, 211?247 (1987).

Triantaphyllidis, N., Aifantis, E. C.: A gradient approach to localization of deformation-I. Hyperelastic materials. J. Elasticity16, 225?238 (1986).

Zbib, H., Aifantis, E. C.: On the localization and post-localization of plastic deformation. Part I. On the initiation of shear-bands; Part II. On the evolution and thickness of shear bands; Part III. On the structure and velocity of Portevin-Le Chatelier bands. Res. Mechanica23, 261?277, 279?292, 293?305 (Special Issue on Material Instabilities, Aifantis, E. C. et al. eds.) 1988.

Aifantis, E. C.: On the problem of dislocation patterning and persistent slip bands. In: Non-linear phenomena in materials science (also in: Solid state phenomena, vols. 3 and 4), (Kubin, L., Martin, G., eds.) pp. 397?406. Trans. Tech. Publ. 1988.

Zbib, H., Aifantis, E. C.: Instabilities in metals and geomaterials: a gradient approach. In: PACAM Congress of Applied Mechanics, (Steele, C. R., Bevilacqua, eds.) pp. 532?535, Brazil: PUC-Rio 1989.

Mühlhaus, H.-B., Aifantis, E. C.: The influence of microstructure-induced gradients on the localization of deformation in viscoplastic materials. Acta Mechanica (in press).

Vardoulakis, I., Aifantis, E. C.: Gradient dependent dilatancy and its implications in shear banding. Ingenieur Archiv59, 197?208 (1989).

Raniecki, B., Bruhns, O. T.: Bounds to bifurcation stresses in solids with non-associated plastic flow law of finite strain. J. Mech. Phys. Sol.29, 153?172 (1981)

Vardoulakis, I., Graf, B.: Calibration of constitutive models for granular materials using data from biaxial experiments. Gèotechnique35, 299?317 (1985).

Mühlhaus, H.-B., Aifantis, E. C.: A variational principle for gradient plasticity. Int. J. Solids Struct. (in press).

Mindlin, R. C.: Microstructure in linear elasticity. Arch. Rat. Mech.10, 51?78 (1964).

Aifantis, E. C.: On the mechanics of modulated structures. In: Modulated structure materials. NATO ASI Series 83. (Tsakalakos, T., ed.) pp. 357?385. Martinus-Nijhoff 1984.

Bazant, Z. P.: The impricate continuum and its variational derivation. J. Engng. Mech.110, 1693?1712 (1984).

Pijaudier-Cabot, G., Bazant, Z., Tabbara, M.: Comparison of various models for strain softening. Eng. Comput.5, 141?150 (1988).

Vardoulakis, I.: Shear-banding and liquefaction in granular materials on the basis of a Cosserat continuum theory. Ingenieur Archiv59, 106?113 (1989).

Vardoulakis, I.: Theoretical and experimental bounds for shear-band bifurcation strain in biaxial tests on dry sand. Res. Mechanica23, 239?259 (Special Issue on Material Instabilities, Aifantis, E. C. et al. eds.) 1988.

Mühlhaus, H.-B., Vardoulakis, I.: The thickness of shear bands in granular materials. Gèotechnique37, 271?283 (1987).

Mandel, J.: Propagation des surfaces de discontinuite dans un milieu elastoplastique. In: Stress waves in anelastic solids, pp. 331?341. Berlin: Springer 1964.

Vardoulakis, I.: Shear band inclination and shear modulus of sand in biaxial tests. Int. J. Num. Anal. Meth. Geomech.4, 103?119 (1980).

Rice, J. R.: On the stability of dilatant hardening of saturated rock masses. J. Geoph. Res.80, 1531?1536 (1975).

Vardoulakis, I.: Stability and bifurcation of undrained, plane rectilinear deformations on water-saturated granular soils. Int. J. Num. Anal. Meth. Geomech.9, 339?414 (1985).

Han, C., Vardoulakis, I.: Plane-strain compression experiments on water-saturated finegrained sand. Gèotechnique (in press).

Zbib, H. M., Aifantis, E. C.: A gradient-dependent flow theory of plasticity: application to metal and soil instabilities. Appl. Mech. Rev.42, 295?304 (1989).

Kuttler, K., Aifantis, E. C.: Existence, uniqueness, and long-time behavior of materials with non-monotone equations of state and higher order gradients. Quart. J. Appl. Math.48, 473?489 (1990).