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Coupled plastic-damaged model. (English) Zbl 0860.73047
Summary: A constitutive model that couples plasticity and damage is presented. The model is thermodynamically consistent and comes from a generalization of classical plasticity theory and isotropic damage theory of Kachanov. Coupling between plasticity and damage is achieved through a simultaneous solution of the plastic and damage problems. After a description of the model, a numerical algorithm for the integration of the resulting constitutive equations is presented. An Euler backward type algorithm is particularly suitable to solve plain stress nonlinear problems with a 2D finite element program. The consistent stiffnes matrix is also derived. The paper is completed with some examples that show that the model accurately reproduces the behaviour of elastic-plastic-damaged materials.

74R99 Fracture and damage
74C99 Plastic materials, materials of stress-rate and internal-variable type
74S05 Finite element methods applied to problems in solid mechanics
Full Text: DOI
[1] Oller, S., Un modelo de ‘daño continuo’ para materiales friccionales, ()
[2] Lubliner, J.; Oliver, J.; Oller, S.; Oñate, E., A plastic damage model for concrete, Int. J. solids struct., 25, 3, 299-326, (1989)
[3] Ju, J.W., On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects, Int. J. solids struct., 25, 7, 803-833, (1989) · Zbl 0715.73055
[4] Voyiadjis, G.Z.; Kattan, P.I., A plasticity-damage theory for large deformation of solids—I. theoretical formulation, Int. J. engrg. sci., 30, 9, 1089-1108, (1992) · Zbl 0756.73038
[5] Kachanov, L.M., Time of the reputre process under creep conditions, IVZ akad nauk-S.S.R.-otd tech nauk, 8, 26-31, (1958)
[6] Edlund, U.; Klarbring, A., A coupled elastic-plastic damage model for rubber-modified epoxy adhesives, Int. J. solids struct., 30, 19, 2693-2708, (1993) · Zbl 0800.73328
[7] Luccioni, B.M., Formulación de un modelo constitutive para materiales ortótropos, ()
[8] Green, A.; Naghdi, P., A general theory for an elastic-plastic continuum, Arch. rational mech. anal., 18, 19-281, (1964) · Zbl 0133.17701
[9] Lubliner, J., Plasticity theory, (1990), MacMillan New York · Zbl 0745.73006
[10] Oller, S.; Oliver, J.; Cervera, M.; Oñate, J., Simulacíon de procesos de localización en mecánica de sólidos, mediante un modelo plástico, (), 423-431
[11] Malvern, L.E., Introduction to the mechanics of continuous medium, (1969), Prentice Hall Englewood Cliffs, NJ · Zbl 0181.53303
[12] Lubliner, J., On the thermodynamic foundations of non-linear mechanics, Int. J. non linear mech., 7, 237-254, (1972) · Zbl 0265.73005
[13] Oliver, J., A consistent characteristic length for smeared cracking models, Int. J. numer. methods engrg., 28, 461-474, (1989) · Zbl 0676.73066
[14] Ortiz, M.; Popov, E.P., Accuracy and stability of integration algorithms for elastoplastic constitutive relations, Int. J. numer. methods engrg., 21, 1561-1576, (1985) · Zbl 0585.73057
[15] Ortiz, M.; Simo, J.C., An analysis of a new class of integration algorithm for elasto-plastic constitutive relations, Int. J. numer. methods engrg., 83, 353-366, (1986) · Zbl 0585.73058
[16] J.C. Simo and T.J.R. Hughes, Elastoplasticity and viscoplasticity. Computational Aspects (Springer-Verlag, Berlin) 97-137, in press
[17] Crisfield, M.A., Non-linear finite element analysis of solids and structures, (1991), John Wiley & Sons Lts England · Zbl 0809.73005
[18] Simo, J.C.; Taylor, R.L., Consistent tangent operators for rate independent elastoplasticity, Comput. methods appl. mech. engrg., 48, 101-118, (1985) · Zbl 0535.73025
[19] Mitchell, G.P.; Owen, D.R.J., Numerical solutions for elasto-plastic problems, Engrg. comput., 5, 274-284, (1988)
[20] Kupfer, H.; Hidsford, H.; Rusch, H., Behaviour of concrete under biaxial stresses, J. aci, 66, 8, 656-666, (1969)
[21] Sinha, B.P.; Gerstle, K.H.; Tulin, L.G., Stress-strain relations for concrete under cyclic loading, J. aci, 62, 2, 195-210, (1964)
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