thermomechanical processes; concrete; constitutive behavior; elastic-plastic material; damage model; fire
Abstract :
[en] This paper aims to develop a multiaxial concrete model for implementation in finite element softwares dedicated to the analysis of structures in fire. The need for proper concrete model remains a challenging task in structural fire engineering because of the complexity of the concrete mechanical behavior characterization and the severe requirements for the material models raised by the development of performance-based design. A fully threedimensional model is developed based on the combination of elastoplasticity and damage theories. The state of damage in concrete, assumed isotropic, is modeled by means of a fourth order damage tensor to capture the unilateral effect. The concrete model comprises a limited number of parameters that can be identified by three simple tests at ambient temperature. At high temperatures, a generic transient creep model is included to take into account explicitly the effect of transient creep strain. The numerical implementation of the concrete model in a finite element software is presented and a series of numerical simulations are conducted for validation. The concrete behavior is accurately captured in a large range of temperature and stress states. A limitation appears when modeling the concrete post-peak behavior in highly confined stress states, due to the coupling assumption between damage and plasticity, but the considered levels of triaxial confinement are unusual stress states in structural concrete.
Disciplines :
Civil engineering
Author, co-author :
Gernay, Thomas ; Université de Liège - ULiège > Département Argenco : Secteur SE > Ingénierie du feu
Millard, Alain; CEA, DEN, DANS, DM2S, SEMT, LM2S, F-91191
Franssen, Jean-Marc ; Université de Liège - ULiège > Département ArGEnCo > Ingénierie du feu
Language :
English
Title :
A multiaxial constitutive model for concrete in the fire situation: Theoretical formulation.
Alternative titles :
[fr] Un modèle constitutif pour le béton en situation d'incendie: Formulation théorique
Publication date :
October 2013
Journal title :
International Journal of Solids and Structures
ISSN :
0020-7683
eISSN :
1879-2146
Publisher :
Pergamon Press (part of Elsevier Science), Oxford, United Kingdom
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
R.K. Abu Al-Rub, and G.Z. Voyiadjis Gradient-enhanced coupled plasticity-anisotropic damage model for concrete fracture: computational aspects and applications International Journal of Damage Mechanics 18 2 2009 115 154
R.K. Abu Al-Rub, and S.M. Kim Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture Engineering Fracture Mechanics 77 10 2010 1577 1603
Anderberg, Y.; Thelandersson, S.; 1976. Stress and deformation characteristics of concrete at high temperatures: 2 experimental investigation and material behavior model. Bulletin 54, Lund Institute of Technology, Sweden.
Annerel, E.; 2010. Assessment of the residual strength of concrete structures after fire exposure. Ph.D. Universiteit Gent.
ASTME - American Society for Testing and Materials, 2007. ASTME119-00 - Standard Methods of Fire Test of Building Construction and Materials. West Conshohocken, PA, USA.
G. Baker, and R. de Borst An anisotropic thermomechanical damage model for concrete at transient elevated temperatures Philosophical Transactions of the Royal Society B 363 2005 2603 2628
I. Carol, E. Rizzi, and K. Willam On the formulation of anisotropic elastic degradation. I. Theory based on a pseudo-logarithmic damage tensor rate International Journal of Solids and Structures 38 2001 491 518
I. Carol, E. Rizzi, and K. Willam On the formulation of anisotropic elastic degradation. II. Generalized pseudo-Rankine model for tensile damage International Journal of Solids and Structures 38 2001 519 546
CAST3M, 2003. Commissariat à l'Energie Atomique. Available at < http://www-cast3m.cea.fr/ >.
CEB-FIB - Comité Euro-International du Béton- Fédération internationale du béton, 1990. CEB-FIB Model code 1990 Bulletin d'information. Lausanne, Switzerland.
J. Cervenka, and V.K. Papanikolaou Three dimensional combined fracture-plastic material model for concrete International Journal of Plasticity 24 2008 2192 2220
Charras, T.; 2010. Personal communication, CEA, France.
U. Cicekli, G.Z. Voyiadjis, and R.K. Abu Al-Rub A plasticity and anisotropic damage model for plain concrete International Journal of Plasticity 23 2007 1874 1900
R. de Borst, and P. Peeters Analysis of concrete structures under thermal loading Computer Methods in Applied Mechanics and Engineering 77 1989 293 310
C. de Sa, and F. Benboudjema Modeling of concrete nonlinear mechanical behavior at high temperatures with different damage-based approaches Materials and Structures 44 2011 1411 1429
R. Desmorat, F. Gatuingt, and F. Ragueneau Nonlocal anisotropic damage model and related computational aspects for quasi-brittle materials Engineering Fracture Mechanics 74 2007 1539 1560
M.S. Dimia, M. Guenfoud, T. Gernay, and J.M. Franssen Collapse of concrete columns during and after the cooling phase of a fire Journal of Fire Protection Engineering 21 4 2011 245 263
C. Ehm, and U. Schneider The high temperature behavior of concrete under biaxial conditions Cement and Concrete Research 15 1985 27 34
European Committee for Standardization, 2004a. CEN Eurocode 2 - Design of concrete structures - Part 1-2: general rules - structural fire design. Brussels.
European Committee for Standardization, 2004. CEN Eurocode 4 - Design of composite steel and concrete structures - Part 1-2: general rules - structural fire design. Brussels.
P.H. Feenstra, and R. de Borst A composite plasticity model for concrete International Journal of Solids and Structures 33 1996 707 730
Franssen, J.-M.; 1993. Thermal elongation of concrete during heating up to 700 C and cooling; stress-strain relationship of Tempcore steel after heating up to 650 C and cooling. Univ. Liege, Liege, Belgium.
J.-M. Franssen SAFIR: a thermal/structural program for modeling structures under fire Engineering Journal - AISC 42 3 2005 143 158
D. Gawin, F. Pesavento, and B.A. Schrefler Modelling of deformations of high strength concrete at elevated temperatures Materials and Structures: Concrete Science and Engineering 37 2004 218 236
Gernay, T.; Franssen, J.-M.; 2010. Consideration of transient creep in the Eurocode constitutive model for concrete in the fire situation. In: Proceedings of the 6th International Conference on Structures in Fire, SiF'10, East Lansing, MI, 2010, pp. 784-791.
Gernay, T.; Dimia, M.S.; 2011. Structural behavior of concrete columns under natural fires including cooling down phase. In: Barros, H.; Faria, R.; Pina, C.; Ferreira, C. (Eds.), Proceedings of the International Conference on Recent Advances in Nonlinear Models - Structural Concrete Applications, Coimbra, Portugal 24-25 Nov. 2011, RAGRAF, pp. 637-656.
T. Gernay, and J.-M. Franssen A formulation of the Eurocode 2 concrete model at elevated temperature that includes an explicit term for transient creep Fire Safety Journal 51 2012 1 9
T. Gernay Effect of transient creep strain model on the behavior of concrete columns subjected to heating and cooling Fire Technology 48 2 2012 313 329
Gernay, T.; 2012. A constitutive model for concrete in the fire situation including transient creep and cooling down phases. Ph. D. University of Liege, pp. 269.
V.S. Gopalaratnam, and S.P. Shah Softening response of plain concrete in direct tension ACI Journal Proceedings 82 3 1985 310 323
P. Grassl, K. Lundgren, and K. Gylltoft Concrete in compression: a plasticity theory with a novel hardening law International Journal of Solids and Structures 39 2002 5205 5223
P. Grassl, and M. Jirasek Damage-plastic model for concrete failure International Journal of Solids and Structures 43 2006 7166 7196
Heinfling, G.; 1998. Contribution à la modélisation numérique du comportement du béton et des structures en béton armé sous sollicitations thermo-mécaniques à hautes températures. Ph. D. Thesis, INSA Lyon.
A. Hillerborg, M. Modeer, and P.E. Petersson Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements Cement and Concrete Research 6 6 1976 773 782
Imran, I.; 1994. Applications of nonassociated plasticity in modeling the mechanical response of concrete. Ph. D. thesis, University of Toronto.
ISO - International Standards Office, 1975. ISO834 - Fire resistance tests - elements of building construction. Geneva, ISO.
J. Ju On energy-based coupled elasto-plastic damage theories: constitutive modeling and computational aspects International Journal of Solids and Structures 25 1989 803 833
J. Ju Isotropic and anisotropic damage variables in continuum damage mechanics Journal of Engineering Mechanics ASCE 116 12 1990 2764 2770
I.D. Karsan, and J.O. Jirsa Behavior of concrete under compressive loadings Journal of Structural Division ASCE 95 12 1969 2535 2563
A. Khennane, and G. Baker Thermoplasticity model for concrete under transient temperature and biaxial stress Proceedings of the Royal Society of London 439 1992 59 80
V.K.R. Kodur Performance-based fire resistance design of concrete-filled steel columns Journal of Constructional Steel Research Institute 51 1999 21 36
W.T. Koiter Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface Quarterly of Applied Mathematics 11 1953 350 354
W. Krätzig, and R. Pölling An elasto-plastic damage model for reinforced concrete with minimum number of material parameters Computers and Structures 82 15-16 2004 1201 1215
H.B. Kupfer, H.K. Hilsdorf, and H. Rüsch Behavior of concrete under biaxial stresses Journal of the American Concrete Institute 66 1969 656 666
H.B. Kupfer, and K.H. Gerstle Behavior of concrete under biaxial stresses Journal of the Engineering Mechanics Division ASCE 99 1973 853 866
J. Lee, and G.L. Fenves Plastic-damage model for cyclic loading of concrete structures Journal of Engineering Mechanics ASCE 124 8 1998 892 900
L. Li, and J. Purkiss Stress-strain constitutive equations of concrete material at elevated temperatures Fire Safety Journal 40 2005 669 686
T. Li, and R. Crouch A C2 plasticity model for structural concrete Computers and Structures 88 23-24 2010 1322 1332
Y.H. Li, and J.M. Franssen Test results and model for the residual compressive strength of concrete after a fire Journal of Structural Fire Engineering 2 1 2011 29 44
J. Lubliner, J. Oliver, S. Oller, and E. Onate A plastic-damage model for concrete International Journal of Solids and Structures 25 3 1989 299 326
B.M. Luccioni, M.I. Figueroa, and R.F. Danesi Thermo-mechanic model for concrete exposed to elevated temperatures Engineering Structures 25 6 2003 729 742
Maréchal, J.C.; 1970. Variations in the modulus of elasticity and poisson's ratio with temperature. In: ACI Int. Seminar on CNR, Berlin.
M. Matallah, and C. La Borderie Inelasticity-damage-based model for numerical modeling of concrete cracking Engineering Fracture Mechanics 76 2009 1087 1108
Mazars, J.; 1984. Application de la mécanique de l'endommagement au comportement non linéaire et à la rupture du béton de structure. Ph. D. thesis, Université Paris VI.
B.J. Meacham, and R.P.L. Custer Performance-based fire safety engineering: an introduction of basic concepts Journal of Constructional Steel Research Institute 7 1992 35 54
G. Meschke, R. Lackner, and H. Mang An anisotropic elastoplastic-damage model for plain concrete International Journal for Numerical Methods in Engineering 42 4 1998 703 727
W. Nechnech, F. Meftah, and J.M. Reynouard An elasto-plastic damage model for plain concrete subjected to high temperatures Engineering Structures 24 2002 597 611
E. Onate, S. Oller, J. Oliver, and J. Lubliner A constitutive model for cracking of concrete based on the incremental theory of plasticity Engineering Computations: International Journal for Computer-Aided Engineering 5 4 1993 309 319
M. Ortiz A constitutive theory for the inelastic behavior of concrete Mechanics of Materials 4 1985 67 93
C. Poinard, Y. Malecot, and L. Daudeville Damage of concrete in a very high stress state: experimental investigation Materials and Structures 43 2010 15 29
E. Pramono, and K.J. Willam Implicit integration of composite yield surfaces with corners Engineering Computation 7 1989 186 197
Ramtani, S.; 1990. Contribution à la modélisation du comportement multiaxial du béton endommagé avec description du caractère unilatéral. Ph. D. thesis, Université de Paris VI E.N.S. de Cachan.
B. Richard, F. Ragueneau, C. Cremona, and L. Adelaide Isotropic continuum damage mechanics for concrete under cyclic loading: stiffness recovery, inelastic strains and frictional sliding Engineering Fracture Mechanics 77 2010 1203 1223
Rots, J.G.; 1988. Computational modelling of concrete fracture. Ph. D. thesis, Delft University of Technology.
A. Saritas, and F.C. Filippou Numerical integration of a class of 3d plastic-damage concrete models condensation of 3d stress-strain relations for use in beam finite elements Engineering Structures 31 10 2009 2327 2336
U. Schneider Properties of Materials at High Temperatures: Concrete 1985 RILEM Kassel, Germany
U. Schneider Concrete at high temperatures - a general review Fire Safety Journal 13 1988 55 68
J.C. Simo, and T.J.R. Hughes Computational Inelasticity 1998 Springer New York
Z. Taqieddin, G.Z. Voyiadjis, F. ASCE, and A.H. Almasri Formulation and verification of a concrete model with strong coupling between isotropic damage and elastoplasticity and comparison to a weak coupling model Journal of Engineering Mechanics ASCE 138 2012 530 541
S. Thelandersson Modelling of combined thermal and mechanical action in concrete ASCE Journal of Engineering Mechanics 113 1987 893 906
Vonk, R.A.; 1992. Softening of concrete loaded in compression. Ph. D. thesis, Eindhoven University of Technology.
G.Z. Voyiadjis, Z. Taqieddin, and P. Kattan Anisotropic damage-plasticity model for concrete International Journal of Plasticity 24 10 2008 1946 1965
G.Z. Voyiadjis, Z. Taqieddin, and P. Kattan Theoretical formulation of a coupled elastic-plastic anisotropic damage model for concrete using the strain energy equivalence concept International Journal of Damage Mechanics 18 7 2009 603 638
Willam, K.J.; Warnke, E.P.; 1974. Constitutive model for the triaxial behavior of concrete. In: Seminar on Concrete Structures Subjected to Triaxial Stresses. Int. Assoc. of Bridge and Struct. Eng. Conf.; Bergamo, Italy.
J.Y. Wu, J. Li, and R. Faria An energy release rate-based plastic-damage model for concrete International Journal of Solids and Structures 43 2006 583 612
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
