Anisotropic Damage Model for Concrete
Publication: Journal of Engineering Mechanics
Volume 137, Issue 9
Abstract
In this paper, a damage constitutive model accounting for induced anisotropy and bimodular elastic response is applied to two-dimensional analysis of reinforced concrete structures. Initially, a constitutive model for the concrete is presented, where the material is assumed as an initial elastic isotropic medium presenting anisotropy and bimodular response (distinct elastic responses, whether tension or compression stress states, prevail) induced by damage. Two damage tensors govern the stiffness under prevailing tension or compression stress states. Criteria are then proposed to characterize the dominant states. Finally, the proposed model is used in plane analysis of reinforced concrete beams to show its potential for use and to discuss its limitations.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors wish to thank CNPq (National Council for Scientific and Technological Development) for the financial support.
References
Álvares, M. S. (1993). “On the damage model for the concrete: Formulation, parametric identification and applications with finite element method.” M.S. thesis, Univ. of São Paulo, São Paulo, Brazil.
Bazant, Z. P., and Ozbolt, J. (1990). “Nonlocal microplane model for fracture, damage and size effect in structures.” J. Eng. Mech., 116(11), 2485–2505.
Brancherie, D., and Ibrahimbegovic, A. (2009). “Novel anisotrtopic continuum-discrete damage model capable of representing localized failure of massive structures. Part I: Theoretical formulation and numerical implementation.” Engng. Comput., 26(1/2), 100–127.
Brünig, M. (2004). “An anisotropic continuum damage model: Theory and numerical analyses.” Lat. Am. J. Solids Struct., 1(2), 185–218.
Cauvin, A., and Testa, R. B. (1999). “Damage mechanics: Basic variables in continuum theories.” Int. J. Solids Struct., 36, 747–761.
Comi, C. (2000). “A nonlocal damage model with permanent strains for quasi-brittle materials.” Continuous damage and fracture, A. Benallal, ed., Cachan, France, 221–232.
Curnier, A., He, Q., and Zysset, P. (1995). “Conewise linear elastic materials.” J. Elast., 37(1), 1–38.
Döbert, C., Mahnken, R., and Stein, E. (2000). “Numerical simulation of interface debonding with a combined damage/friction constitutive model.” Comput. Mech., 25(5), 456–467.
Dominguez, N., Brancherie, D., Davenne, L., and Ibrahimbegovic, A. (2005). “Prediction of crack pattern distribution in reinforced concrete by coupling a strong discontinuity model of concrete cracking and a bond-slip of reinforcement model.” Engng. Comput., 22(5/6), 558–582.
Dragon, A., Halm, D., and Désoyer, Th. (2000). “Anisotropic damage in quasi-brittle solids: Modelling, computational issues and applications.” Comput. Methods Appl. Mech. Eng., 183(3–4), 331–352.
Fernandes, G. R., and Venturini, W. S. (2002). “Non-linear boundary element analysis of plates applied on concrete slabs.” Eng. Anal. Boundary Elem., 26(2), 169–181.
Gopalaratnam, V. S., and Shah, S. P. (1985). “Softening response of plain concrete in direct tension.” J. Am. Concr. Inst., 82(3), 310–323.
Hervé, G., Gatuingt, F., and Ibrahimbegovic, A. (2005). “On numerical implementation of a coupled rate dependent damage-plasticity constitutive model for concrete in application to high-rate dynamics.” Engng. Comput., 22(5/6), 583–604.
Ibrahimbegovic, A., Jehel, P., and Davenne, L. (2007). “Coupled damage-plasticity constitutive model and direct stress interpolation.” Comput. Mech., 42, 1–11.
Kachanov, L. M. (1958). “Time of the rupture process of non-linear solid mechanics.” Otd. Tech. Nauk., 8, 28–31.
Kucerova, A., Brancherie, D., Ibrahimbegovic, A., Zeman, J., and Bittnar, Z. (2009). “Novel anisotropic continuum-discrete damage model capable of representing localized failure of massive structures. Part II: Identification from tests under heterogeneous stress field.” Engng. Comput., 26(1/2), 128–144.
Kupfer, H., Hilsdorf, H. K., and Rush, H. (1969). “Behavior of concrete under biaxial stresses.” J. Am. Concr. Inst., 66(8), 656–666.
La Borderie, C. (1991). “Phenomenes unilateraux dans un materiau endommageable: Modelisation et application a l’analyse de structures en beton.” Ph.D. thesis, Univ. of Paris, Paris (in French).
Labadi, Y., and Hannachi, N. E. (1997). “Finite element analysis of anisotropic damage mechanics problems.” Proc., Conf. on Computational Plasticity: Fundamentals and Applications, D. R. J. Owen and E. Hinton, eds., CIMNE, Barcelona, 1102–1107.
Lemaitre, J. (1996). A course on damage mechanics, Springer Verlag, Berlin.
Lemaitre, J., and Chaboche, J. L. (1990). Mechanics of solid materials, Cambridge University Press, Cambridge, UK.
Lemaitre, J., Desmorat, R., and Sauzay, M. (2000). “Anisotropic damage law of evolution.” Eur. J. Mech. A. Solids, 19(2), 187–208.
Mazars, J. (1986). “A description of micro and macroscale damage of concrete structures.” Eng. Fract. Mech., 25, 729–737.
Mazars, J., Berthaud, Y., and Ramtani, S. (1990). “The unilateral behaviour of damaged concrete.” Eng. Fract. Mech., 35(4–5), 629–635.
Murakami, S., and Kamiya, K. (1997). “Constitutive and damage evolution equations of elastic-brittle materials based on irreversible thermodynamics.” Int. J. Mech. Sci., 39(4), 473–486.
Ortiz, M. (1985). “A constitutive theory for the inelastic behavior of concrete.” Mech. Mater., 4(1), 67–93.
Perego, M. (1989). “Damage of brittle materials: Constitutive models, analysis by finite element method and applications.” Ph.D. thesis, Politecnico de Milano, Milan, Italy.
Pichler, B., and Dormieux, L. (2009). “Instability during cohesive zone growth.” Eng. Fract. Mech., 76(11), 1729–1749.
Pietruszczak, S., and Mroz, Z. (2001). “On failure criteria for anisotropic cohesive-frictional materials.” Int. J. Numer. Anal. Methods Geomech., 25(5), 509–524.
Pituba, J. J. C. (2003). “On the formulation of damage model for the concrete.” Ph.D. thesis, Univ. of São Paulo, São Paulo, Brazil.
Pituba, J. J. C. (2006). “On the formulation of damage constitutive models for bimodular anistropic media.” Proc., III European Conf. on Computational Mechanics, C. A. M. Soares, et al., eds., Springer, Netherlands.
Pituba, J. J. C. (2007). “An anisotropic model of damage and unilateral effect for brittle materials.” Proc., XX Int. Conf. on Computer, Information and Systems Science and Engineering, World Academy of Science, Engineering and Technology (WASET), Barcelona, Spain.
Pituba, J. J. C. (2010). “Evaluation of an anisotropic damage model taking into account the effects of resistance loss due to shear.” Proc., XXXI CILAMCE—Iberian Latin-American Congress on Computational Methods Applied in Engineering, E. N. Dvorkin, M. B. Goldschmit, and M. A. Sorti, eds., Argentine Association of Computational Mechanics (AMCA), Buenos Aires, Argentina.
Proença, S. P. B., and Pituba, J. J. C. (2003). “A damage constitutive model accounting for induced anisotropy and bimodular elastic response.” Lat. Am. J. Solids Struct., 1, 101–117.
Rabotnov, Y. N. (1969). Creep problems in structural members, North-Holland, Amsterdam, Netherlands.
Van Mier, G. M. (1997). Fracture process of concrete, CRC, Zurich, Switzerland.
Welemane, H., and Cormery, F. (2002). “Some remarks on the damage unilateral effect modeling for microcracked materials.” Int. J. Damage Mech., 11(1), 65–86.
Willam, K., Stankowski, T., and Sture, S. (1988). “Theory and basic concepts for modelling concrete behaviour.” Contribution to the 26th CEB Plenary Session, Dubrovnik, Croatia.
Zhu, Q., Kondo, D., Shao, J., and Pensee, V. (2008). “Micromechanical modelling of anisotropic damage in brittle rocks and application.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 45(4), 467–477.
Zhu, Q., Kondo, D., and Shao, J. (2009). “Homogenization-based analysis of anisotropic damage in brittle materials with unilateral effect and interactions between microcracks.” Int. J. Numer. Anal. Methods Geomech., 33(6), 749–772.
Information & Authors
Information
Published In
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Dec 30, 2009
Accepted: Mar 9, 2011
Published online: Mar 10, 2011
Published in print: Sep 1, 2011
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.