Rate Dependent Damage Model for Concrete in Dynamics
Publication: Journal of Engineering Mechanics
Volume 122, Issue 10
Abstract
This paper presents a rate dependent damage model and its implementation in transient dynamics. The rate dependent model is derived from a rate independent damage model simply by changing the expression of the damage evolution equation. The principle of the model follows the format of Perzyna viscoplasticity whereby the definition of the plastic multiplier is modified compared to a standard rate independent plasticity model. The rate dependent model can reproduce very well the major effects of the rate of loading on the response of concrete; that is, an increase of the material strength and a decrease of the softening tangent modulus with increasing strain rate. The wave propagation problem is assessed. We show that the resulting equations of motion are unconditionally hyperbolic. Well-posedness and mesh objectivity are verified numerically on a simple one-dimensional (1D) problem. As an example of implementation in a finite element calculation, the computation of the response of a reinforced concrete beam subjected to an impact is presented.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bazant, Z. P.(1976). “Instability, ductility and size effect in strain softening concrete.”J. Engrg. Mech. Div., ASCE, 102(2), 331–344.
2.
Bazant, Z. P., and Pijaudier-Cabot, G.(1988). “Non local continuum damage, localization instability and convergence.”J. Appl. Mech., 55, 287–293.
3.
Bicanic, N., and Zienckiewicz, O. C.(1983). “Constitutive model for concrete under dynamic loading.”Earthquake Engrg. and Struct. Dyn., 11, 689–711.
4.
Bischoff, P. H., and Perry, S. H.(1991). “Compressive behaviour of concrete at high strain rates.”Mat. and Struct., 24, 425–450.
5.
Bruhwiler, E.(1990). “Fracture of mass concrete under simulated seismic action.”Dam Engrg., 1(3), 153–176.
6.
Carol I., Rizzi, E., and Willam, K. (1994). “Towards a general formulation of elastic degradation and damage based on a loading surface.”Computational modelling of concrete structures, Proc., EURO-C 1994, H. Mang et al., eds., Pineridge press, Swansea, Wales, U.K., 199–208.
7.
De Borst, R., Sluys, L. J., Muhlhaus, H. B., and Pamin, J.(1993). “Fundamental issues in finite element analyses of localization of deformation.”Engrg. Comput., 10, 99–122.
8.
Delgado-Saavedra, H. E. (1985). “A rate dependent model for plain concrete under dynamic multiaxial loads,” PhD thesis, Columbia University, New York, N.Y.
9.
Dubé, J. F., Pijaudier-Cabot, G., La Borderie, C., and Glynn, J. (1994). “Rate dependent damage model for concrete—wave propagation and localization.”Computational Modelling of Concrete Structures, Proc., EURO-C 1994, H. Mang et al., eds., Pineridge press, Swansea, Wales, U.K., 313–322.
10.
Eibl, J., Bischoff, P. H., and Lohrmann, G. (1994). “Failure mechanics of fibre-reinforced concrete and pre-damaged structures; dynamic loading conditions.”Task Rep. BRITE/EURAM P-89-3275, Univ. of Karlsruhe, Karlsruhe, Germany.
11.
Eibl, S. J., and Wunderlich, W. (1994). “Behaviour of reinforced concrete during shock wave loading.”Computational Modelling of Concrete Structures, Proc., EURO-C 1994, H. Mang et al., eds., Pineridge press, Swansea, Wales, U.K., 639–648.
12.
La Borderie, C., Mazars, J., and Pijaudier-Cabot, G. (1993). “Response of plain and reinforced concrete structures under cyclic loading.”ACI STP 134, W. Gerstle and Z. P. Bazant, eds., 147–172.
13.
Ladevèze, P. (1983). “Sur une théorie de l'endommagement anisotrope.”Int. Rep. No. 34, Laboratoire de Mécanique et Technologie, Cachan, France.
14.
Lemaître, J. (1992). A course on damage mechanics . Springer-Verlag New York, Inc., New York, N.Y.
15.
Meyer, C., de Borst, R., Bicanic, N., Filipou, F., and Maekawa, K. “Chaper 6: dynamic loading.”Finite element analysis of reinforced concrete structures II, J. Isenberg, ed., ASCE, New York, N.Y., 314–366.
16.
Needlemann, A.(1987). “Material dependence and mesh sensitivity in localization problems.”Comp. Meth. Appl. Mech. Engrg., 67, 69–86.
17.
Nilsson, L. (1978). “Finite element analysis of impact on concrete structures.”Finite elements in nonlinear mechanics, P. Bergan et al., eds., Tapir, Trondheim, Norway.
18.
Perzyna, P. (1966). Fundamental problems in visco-plasticity; recent advances in applied mechanics . Academic Press, New York, N.Y.
19.
Pijaudier-Cabot, G., and Bazant, Z. P.(1987). “Nonlocal damage theory.”J. Engrg. Mech., ASCE, 113(10), 1512–1533.
20.
Pijaudier-Cabot, G., and Benallal, A.(1993). “Strain localization and bifurcation in a non local continuum.”Int. J. Solids and Struct., 30, 1761–1775.
21.
Sluys, L. J. (1992). “Wave propagation, localisation and dispersion in strain softening solids,” Doctoral dissertation, Delft Univ. of Technology, Delft, The Netherlands.
22.
Sluys, L. J., Bolck, J., and de Borst, R. (1992). “Wave propagation and localisation in viscoplastic media.”Proc., 3rd Int. Conf. on Computational Plasticity, D. R. J. Owen et al., eds., Pineridge press, Swansea, Wales, U.K., 539–550.
23.
Sluys, L. J., and De Borst, R.(1992). “Computational modelling of impact tests on steel fibre reinforced concrete beams.”HERON, 37, 3–15.
24.
Willam, K., Munz, T., Etse, G., and Menétrey, P. (1994). “Failure conditions and localization in concrete.”Computational modelling of concrete structures, Proc., EURO-C 1994, H. Mang et al., eds., Pineridge press, Swansea, Wales, U.K., 263–282.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 122 • Issue 10 • October 1996
Pages: 939 - 947
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Oct 1, 1996
Published in print: Oct 1996
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.