Formulation and Verification of a Concrete Model with Strong Coupling between Isotropic Damage and Elastoplasticity and Comparison to a Weak Coupling Model
Publication: Journal of Engineering Mechanics
Volume 138, Issue 5
Abstract
In this work, a new concrete model that strongly couples continuum-damage-mechanics to elastoplasticity is presented. The model incorporates a plasticity yield criterion written in terms of the nominal/damaged, rather than effective, stress space. Tensile and compressive behaviors are modeled through the damage-affected-multi-hardening nature of the plasticity yield criterion and the introduction of two (tensile and compressive) plasticity-affected isotropic damage initiation/growth criteria, where plasticity variables are added to the definition of the tensile and compressive growth functions of damage. A nonassociative plastic flow rule is used to control inelastic dilatancy. Specific expressions of the elastic/damage and plastic/damage components of the Helmholtz free energy function are presented. The constitutive equations of the model are consistently derived within a sound framework of irreversible thermodynamics. These free energy expressions are used to define three plasticity and damage interconnected dissipation mechanisms, one plasticity mechanism and two damage mechanisms. The elastic-plastic-damage, elastic-plastic, and elastic-damage tangent operators are also derived. A computational algorithm for the numerical integration of the constitutive equations is proposed on the basis of the doubly passive predictor–plastic-damage corrector approach. The model is implemented in the Finite Element (FE) analysis software ABAQUS through a user defined material subroutine (UMAT). Two- and three-dimensional verification examples are carried out to demonstrate the effectiveness and robustness of the proposed model in producing results that depict experimentally observed concrete behaviors. The results of the proposed model are compared with those of a weak coupling concrete model recently presented by the authors, in which damage was incorporated in the elastic formulation whereas plasticity remained in the effective stress space. The comparison shows the effect of strong-coupling on increasing/accelerating the degradation of concrete when the same material parameters of the weak coupling model are used. The results of the proposed model are also compared with those of well known strong-coupling models available in contemporary literature. To reduce the sensitivity of the nonlinear FE analysis of concrete structures to the refinement of the FE meshes, the damage density parameters are defined to include embedded dimensionless coefficients that are related to concrete’s fracture energies (in tension and compression) and to the geometrical characteristic length provided by ABAQUS software during the analysis. The conclusions drawn from this work clearly indicate the adequacy of the model to describe the different stages of concrete behavior and stiffness and strength degradations attributable to elastoplasticity-affected damage growth. They also show that the model can be further improved and equipped with nonlocal measures to enhance its future performance.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The second author acknowledges the collaboration with Professor Taehyo Park of the Hanyang University, Seoul, Korea, under the World Class University project funded by the National Research Foundation of Korea.
References
Abu Al-Rub, R. K., and Voyiadjis, G. Z. (2003). “On the coupling of anisotropic damage and plasticity models for ductile materials.” Int. J. Solids Struct.IJSOAD, 40(11), 2611–2643.
Abu-Lebdeh, T. M., and Voyiadjis, G. Z. (1993). “Plasticity-damage model for concrete under cyclic multiaxial loading.” J. Eng. Mech.JENMDT, 119(7), 1465–1484.
Bielski, J., Skrzypek, J. J., and Kuna-Ciskal, H. (2006). “Implementation of a model of coupled elastic-plastic unilateral damage material to finite element code.” Int. J. Damage Mech.IDMEEH, 15(1), 5–39.
Cicekli, U., Voyiadjis, G. Z., and Abu Al-Rub, R. K. (2007). “A plasticity and anisotropic damage model for plain concrete.” Int. J. Plast.IJPLER, 23(10–11), 1874–1900.
Chaboche, J. L. (1997). “Thermodynamic formulation of constitutive equations and applications to the viscpliasitity of metals and polymers.” Int. J. Solids Struct.IJSOAD, 34(18), 2239–2254.
Chen, F. W. (1982). “Plasticity in reinforced concrete.” McGraw-Hill, New York.
Coleman, B. D., and Gurtin, M. E. (1967). “Thermodynamics with internal state variables.” J. Chem. Phys.JCPSA6, 47(2), 597–613.
Comi, C., and Perego, U. (2001). “Fracture energy based bi-dissipative damage model for concrete.” Int. J. Solids Struct.IJSOAD, 38(36), 6427–6454.
Contrafatto, L., and Cuomo, M. (2002). “A new thermodynamically consistent continuum model for hardening plasticity coupled with damage.” Int. J. Solids Struct.IJSOAD, 39(25), 6241–6271.
Contrafatto, L., and Cuomo, M. (2006). “A framework of elastic–plastic damaging model for concrete under multiaxial stress states.” Int. J. Plast.IJPLER, 22(12), 2272–2300.
Faria, R., Oliver, J., and Cervera, M. (1998). “A strain-based plastic viscous-damage model for massive concrete structures.” Int. J. Solids Struct.IJSOAD, 35(14), 1533–1558.
Feenstra, P. H., and Borst, R. D. (1996). “A composite plasticity model for concrete.” Int. J. Solids Struct.IJSOAD, 33(5), 707–730.
Fichant, S., La Borderie, C., and Pijaudier-Cabot, G. (1999). “Isotropic and anisotropic descriptions of damage in concrete structures.” Mech. Cohes.-Frict. Mater.MCFMFA, 4(4), 339–359.
Gatuingt, F., and Pijaudier-Cabot, G. (2002). “Coupled gurson plasticity and damage model for concrete structures in dynamics.” 15th ASCE Engineering Mechanics Conference, Columbia Univ., New York.
Gopalaratnam, V. S., and Shah, S. P. (1985). “Softening response of plain concrete in direct tension.” J. Am. Concr. Inst.JACIAX, 82(3), 311–323.
Hayakawa, K., and Murakami, S. (1997). “Thermodunamical modeling of elastic-plastic damage and experimental validation of damage potential.” Int. J. Damage Mech.IDMEEH, 6(4), 333–362.
Hansen, N. R., and Schreyer, H. L. (1994). “A thermodynamically consistent framework for theories of elastoplasticity coupled with damage.” Int. J. Solids Struct.IJSOAD, 31(3), 359–389.
Jason, L., Huerta, A., Pijaudier-Cabot, G., and Ghavamian, S. (2006). “An elastic plastic damage formulation for concrete: Application to elementary tests and comparison with an isotropic damage model.” Comput. Methods Appl. Mech. Eng.CMMECC, 195(52), 7077–7092.
Jefferson, A. D. (2003). “Craft—A plastic damage contact model for concrete. I. Model theory and thermodynamic considerations.” Int. J. Solids Struct.IJSOAD, 40(22), 5973–5999.
Ju, J. W. (1989). “On energy-based coupled elasto-plastic damage theories: Constitutive modeling and computational aspects.” Int. J. Solids Struct.IJSOAD, 25(7), 803–833.
Júnior, F. S., and Venturini, W. S. (2007). “Damage modelling of reinforced concrete beams.” Adv. Eng. Softw.AESODT, 38(8–9), 538–546.
Kachanov, L. M. (1958). “On the creep fracture time.” Izv. Akad. Nauk USSR Otd. Tech 8, 26–31 (in Russian).
Karsan, I. D., and Jirsa, J. O. (1969). “Behaviour of concrete under compressive loadings.” J. Struct. Div.JSDEAG, 95(12), 2535–2563.
Kotsovos, M. D., and Newman, J. B. (1977). “Behavior of concrete under multiaxial stress.” J. Am. Concr. Inst.JACIAX, 74(9), 443–444.
Labadi, Y., and Hannachi, N. E. (2005). “Numerical simulation of brittle damage in concrete.” Strength Mater.SMTLB5, 37(3)268–281.
Lammer, H., and Tsakmakis, C. (2000). “Discussion of coupled elastoplasticity and damage constitutive equations for small and finite deformations.” Int. J. Plast.IJPLER, 16(5), 495–523.
Lee, J., and Fenves, G. L. (1998). “A plastic-damage model for cyclic loading of concrete structures.” J. Eng. Mech.JENMDT, 124(8), 892–900.
Lee, J., and Fenves, G. L. (2000). “A return-mapping algorithm for plastic-damage models: 3-D and plane stress formulation.” Int. J. Numer. Methods Eng.IJNMBH, 50(2), 487–506.
Lemaitre, J. (1985). “A continuous damage mechanics model for ductile fracture.” J. Eng. Mater. Technol.JMAEEV, 107(1), 83–89.
Lemaitre, J., and Chaboche, J. L. (1998). “Mechanics of solid materials.” 2nd Ed., Cambridge University Press, Cambridge, U.K.
Lubliner, J., Oliver, J., Oller, S., and Onate, E. (1989) “A plastic-damage model for concrete.” Int. J. Solids Struct.IJSOAD, 25(3), 299–326.
Luccioni, B., Oller, S., and Danesi, R. (1996). “Coupled plastic-damaged model.” Comput. Methods Appl. Mech. Eng.CMMECC, 129(1–2), 81–89.
Mazars, J. (1984). “Application de la mécanique de l’endommagement au comportement non linéaire et a la rupture du béton de structure.” Thèse de Doctorat d’ Etat, L.M.T., Université Paris (in French).
Mazars, J., and Pijaudier-Cabot, G. (1989). “Continuum damage theory—Application to concrete.” J. Eng. Mech.JENMDT, 115(2), 345–365.
Menzel, A., Ekh, M., Runesson, K., and Steinmann, P. (2005). “A framework for multiplicative elastoplasticity with kinematic hardening coupled to anisotropic damage.” Int. J. Plast.IJPLER, 21(3), 397–434.
Nechnech, W., Meftah, F., and Reynouard, J. M. (2002). “An elasto-plastic damage model for plain concrete subjected to high temperatures.” J. of Eng. Struct., 24(5), 597–611.
Oliver, J., Cervera, M., Oller, S., and Lubliner, J. (1990). “Isotropic damage models and smeared crack analysis of concrete.” Proc., SCI-C 2nd Int. Conf. Computer Aided Analysis and Design of Concrete Structures, Pineridge, 3195–3220.
Salari, M. R., Saeb, S., Willam, K. J., Patchet, S. J., and Carrasco, R. C. (2004). “A coupled elastoplastic damage model for geomaterials.” Comput. Methods Appl. Mech. Eng.CMMECC, 193(27–29), 2625–2643.
Saritas, A., and Filippou, F. C. (2009). “Numerical integration of a class of 3d plastic-damage concrete models condensation of 3d stress-strain relations for use in beam finite elements.” Eng. Struct., 31(10), 2327–2336.ENSTDF
Shao, J. F., Jia, Y., Kondo, D., and Chiarelli, A. S. (2006). “A coupled elastoplastic damage model for semi-brittle materials and extension to unsaturated conditions.” Mech. Mater.MSMSD3, 38(3), 218–232.
Shen, X., Yang, L., and Zhu, F. (2004). “A Plasticity-based damage model for concrete.” Adv. Struct. Eng., 7(5), 461–467.
Simo, J., and Hughes, T. (1998). Computational inelasticity. Springer-Verlag, New York.
Steinmann, P., Miehe, C., and Stein, E. (1994). “Comparison of different finite deformation inelastic damage models within multiplicative elastoplasticity for ductile materials.” Comput. Mech., 13(6), 458–474.
Tao, X., and Phillips, D. V. (2005). “A simplified isotropic damage model for concrete under bi-axial stress states.” Cem. Concr. Compos.CCOCEG, 27(6), 716–726.
Taqieddin, Z. N. (2008). “Elasto-plastic and damage modeling of reinforced concrete.” Ph.D. thesis, Louisiana State University, Baton Rouge, LA.
Taqieddin, Z. N., and Voyiadjis, G. Z. (2009). “Elastic plastic and damage model for concrete materials: Part II: Implementation and application to concrete and reinforced concrete.” Int. J. Struct. Changes Solids—Mech. App.IJSOAD, 1(1), 187–209.
Voyiadjis, G. Z., and Abu-Lebdeh, T. M. (1993). “Damage model for concrete using bounding surface concept.” J. Eng. Mech.JENMDT, 119(9), 1865–1885.
Voyiadjis, G. Z., and Kattan, P. I. (1999). Advances in damage mechanics: Metals and metal-matrix composites, Elsevier, Oxford, U.K.
Voyiadjis, G. Z., and Kattan, P. I. (2006). Advances in damage mechanics: Metals and metal matrix composites, with an introduction to fabric tensors. 2nd Ed., Elsevier, Oxford, U.K.
Voyiadjis, G. Z., and Taqieddin, Z. N. (2009). “Elastic plastic and damage model for concrete materials: Part I—Theoretical formulation.” Int. J. Struct. Changes Solids—Mech. App., 1(1), 31–59.
Voyiadjis, G. Z., Taqieddin, Z. N., and Kattan, P. I. (2008a). “Anisotropic damage-plasticity model for concrete.” Int. J. Plast.IJPLER, 24(10), 1946–1965.
Voyiadjis, G. Z., Taqieddin, Z. N., and Kattan, P. I. (2008b). “Theoretical formulation of a coupled elastic-plastic anisotropic damage model for concrete using the strain energy equivalence concept.” Int. J. Damage Mech.IDMEEH, 18(7), 603–638.
Willam, K., Rhee, I., and Xi, Y. (2005). “Thermal degradation of heterogeneous concrete materials.” J. Mater. Civil Eng.JMCEE7, 17(3), 276–285.
Wu, J. Y., Li, J., and Faria, R. (2006). “An energy release rate-based plastic-damage model for concrete.” Int. J. Solids Struct.IJSOAD, 43(3–4), 583–612.
Yazdani, S., and Schreyer, H. L. (1990). “Combined plasticity and damage mechanics model for plain concrete.” J. Eng. Mech.JENMDT, 116(7), 1435–1450.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 5 • May 2012
Pages: 530 - 541
Copyright
© 2012. American Society of Civil Engineers.
History
Received: May 27, 2011
Accepted: Oct 4, 2011
Published online: Oct 6, 2011
Published in print: May 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.