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A coupled elastoplastic damage model for geomaterials. (English) Zbl 1067.74567
Summary: A triaxial constitutive model is developed for elastoplastic behavior of geomaterials, which accounts for tensile damage. The constitutive setting is formulated in the framework of continuum thermodynamics using internal variables. The interaction of elastic damage and plastic flow is examined with the help of very simple constitutive assumptions: (i) a Drucker-Prager yield function is used to define plastic loading of the material in combination with a non-associated flow rule to control inelastic dilatancy; (ii) elastic damage is assumed to be isotropic and is represented by a single scalar variable that evolves under expansive volumetric strain. Thereby, positive volumetric deformations couple the dissipation mechanisms of elastic damage and plastic flow which introduce degradation of the elastic stiffness as well as softening of the strength. The constitutive model is implemented in the finite element program ADINA to determine the response behavior of the combined damage-plasticity model under displacement and mixed control. A number of load histories are examined to illustrate the performance of the material model in axial tension, compression, shear and confined compression. Thereby incipient failure is studied at the material level in the form of non-positive properties of the tangential material tensor of elastoplastic damage and the corresponding localization tensor comparing non-associative with associative plasticity formulations.

74R20 Anelastic fracture and damage
74L10 Soil and rock mechanics
74S05 Finite element methods applied to problems in solid mechanics
Full Text: DOI
[1] ADINA R&D, Theory and Modeling Guide, Volume I: ADINA, Report ARD 01-7, Watertown, MA, 2001
[2] Borja, R.I; Tamagnini, C, Cam-Clay plasticity, part III: extension of the infinitesimal model to include finite strains, Comput. methods appl. mech. engrg., 155, 73-95, (1998) · Zbl 0959.74010
[3] Carol, I; Rizzi, E; Willam, K, On the formulation of anisotropic degradation. I. theory based on a pseudo-logarithmic damage tensor, Int. J. solids struct., 38/4, 491-518, (2001) · Zbl 1006.74007
[4] Carol, I; Rizzi, E; Willam, K, On the formulation of anisotropic degradation. II. generalized pseudo-rankine model for tensile damage, Int. J. solids struct., 38/4, 519-546, (2001) · Zbl 1006.74007
[5] Dafalias, Y.F, Bounding surface plasticity. part I: mathematical foundation and hypoplasticity, J. engrg. mech., ASCE, 112, 966-987, (1986)
[6] Darve, F, Incrementally nonlinear constitutive relationship, (), 213-237
[7] Desai, C, Mechanics of materials and interfaces: the disturbed state concept, (2001), CRC Press Boca Baton, FL
[8] Dragon, A; Mroz, Z, A continuum model for plastic-brittle behaviour of rock and concrete, Int. J. engrg. sci., 17, 121-137, (1979) · Zbl 0391.73092
[9] E. Hansen, K. Willam, I. Carol, A two-surface anisotropic damage/plasticity model for plain concrete, in: R. de Borst, J. Mazars, G. Pijaudier-Cabot, J. van Mier (Eds.), Proceedings of 4th International Conference Fracture Mechanics of Concrete Materials, Framcos-4, Paris, May 28-31, A.A. Balkema, Rotterdam, 2001, pp. 549-556
[10] Kang, H; Willam, K, Localization characteristics of a triaxial concrete model, Asce-jem, 125, 941-950, (1999)
[11] Kolymbas, D, An outline of hypoplasticity, Arch. appl. mech., 61, 143-151, (1991) · Zbl 0734.73023
[12] Lee, J; Fenves, G.L, Plastic-damage model for cyclic loading of concrete structures, J. engrg. mech., ASCE, 124, 892-900, (1998)
[13] Mazars, J; Pijaudier-Cabot, G, Continuum damage theory-application to concrete, J. engrg. mech. ASCE, 115, 345-365, (1989)
[14] Menetrey, Ph; Willam, K, A triaxial failure criterion for concrete and its generalization, ACI struct. J., 92, 311-318, (1995)
[15] Nawrocki, P.A; Mroz, Z, A constitutive model for rock accounting for viscosity and yield stress degradation, Comput. geotech., 25, 247-280, (1999)
[16] Nova, R, Mathematical modelling of natural and engineered geomaterials, Eur. J. mech. A, 135-154, (1992)
[17] Rudnicki, J.W; Rice, J.R, Conditions for the localization of deformation in pressure sensitive dilatant materials, J. mech. phys. solids, 23, 371-394, (1975)
[18] Rudnicki, J.W, Condition for compaction and shear bands in a transversely isotropic material, Int. J. solids struct., 39, 3741-3756, (2002) · Zbl 1087.74545
[19] Shao, J.F; Chiarelli, A.S; Hoteit, N, Modeling of coupled elastoplastic damage in rock materials, Int. J. rock mech. miner. sci., 35, 4-5, (1998), (paper no. 115)
[20] Simo, J.C; Hughes, T.J.R, Computational inelasticity, (1998), Springer-Verlag New York · Zbl 0934.74003
[21] Valanis, K.C; Peters, J.F, Ill-posedness of the initial and boundary value problems in non-associative plasticity, Acta mech., 114, 1-15, (1996) · Zbl 0868.73029
[22] K.J. Willam, Constitutive models for engineering materials, in: Encyclopedia of Physical Science and Technology, third ed., vol. 3, Academic Press, New York, 2002, pp. 603-633, Available from <http://civil.colorado.edu/ willam/matl01.pdf>
[23] Yazdani, S; Schreyer, H.L, An anisotropic damage model with dilatation for concrete, Mech. mater., 7, 231-244, (1988)
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