×

zbMATH — the first resource for mathematics

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.

MSC:
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
PDF BibTeX XML Cite
Full Text: DOI
References:
[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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.