Three-Dimensional Viscoelastic Model with Nonconstant Coefficients
Publication: Journal of Engineering Mechanics
Volume 127, Issue 8
Abstract
This paper presents a fully 3D viscoelastic model to predict the creep and relaxation behavior of anisotropic materials. This model is based on a phenomenological approach using internal variables and is applicable to nonconstant coefficients. The analytical solution of the set of thermodynamic equations is presented using the reduced time approach in conjunction with modal space. The particular case of isotropic material is presented. In addition, from the general 3D model, the analytical solution in 1D is derived and a connection with the classical rheological model is made. Finally, the model is calibrated and assessed with creep test data for concrete in tension and a parameter sensitivity analysis is performed.
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References
1.
Bazant, Z. P. ( 1975). “Theory of creep and shrinkage in concrete structures: A precis of recent development.” Mechanics today, Vol. 2, Pergamon, New York, 1–93.
2.
Bazant, Z. P. ( 1988). Mathematical modeling of creep and shrinkage of concrete, Wiley, Chichester and New York.
3.
Bazant, Z. P., Hauggard, A. B., and Bawja, S. (1997a). “Microprestress-solidification theory for concrete creep. II: Algorithm and verification.”J. Engrg. Mech., ASCE, 123(11), 1195–1201.
4.
Bazant, Z. P., Hauggard, A. B., Bawja, S., and Ulm, F. J. (1997b). “Microprestress-solidification theory for concrete creep. I: Aging and drying effects.”J. Engrg. Mech., ASCE, 123(11), 1188–1194.
5.
Bazant, Z. P., and Parasannan, S. (1989a). “Solidification theory for concrete creep. I: Formulation.”J. Engrg. Mech., ASCE, 115(8), 1691–1703.
6.
Bazant, Z. P., and Parasannan, S. (1989b). “Solidification theory for concrete creep. II: Verification and application.”J. Engrg. Mech., ASCE, 115(8), 1704–1725.
7.
Biot, M. A. ( 1954). “Theory stress-strain relations in anisotropic viscoelasticity and relaxation phenomena.” J. Appl. Phys., 25(11), 1385–1391.
8.
Bissonnette, B. ( 1996). “Le fluage en traction: Un aspect important de la problématique des réparations minces en béton. PhD thesis, Laval de University, Quebec (in French).
9.
Bissonnette, B., and Pigeon, M. ( 1996). “Tensile creep at early ages of ordinary, silica fume, and fiber reinforcement concrete.” Cement and Concrete Res., 25(5), 1075–1085.
10.
Boudjelal, M. T., Fafard, M., Bissonnette, B., Cloutier, A., Bastien, J., and Pigeon, M. ( 1998). “Durabilité des réparations en béton: Expérimentation et développement d'un modèle numérique prédictif.” Rep. No. GCT-98-30, Civ. Engrg. Dept., Laval University, Quebec (in French).
11.
Byfors, J. ( 1980). “Plain concrete at early ages.” Res. Rep. F3:80, Swedish Cement and Concrete Research Institute, Stockholm.
12.
Coleman, B. D., and Gurtin, M. E. ( 1967). “Thermodynamic of internal variable.” J. Chemical Phys., 47(2), 597–613.
13.
Coussy, O. ( 1995). Mechanics of porous continua, Wiley, New York.
14.
Coussy, O., and Ulm, F. J. ( 1995). “Creep and plasticity due to chemomechanical coupling.” Proc., 4th Int. Conf. Complas IV, Computational plasticity. Fundamentals and applications, Pineridge Press, Swansea, U.K., 925–944.
15.
De Borst, R., and van den Boogaard, A. H. (1994). “Finite element modeling of deformation and cracking in early-age concrete.”J. Engrg. Mech., ASCE, 120(12), 2519–2534.
16.
Granger, L. ( 1996). “Comportement différé du béton dans les enceintes de centrales nucléaires: Analyse et modélisation.” PhD thesis, École Nationale des Ponts et Chaussées, Paris (in French).
17.
Guenot, I. ( 1996). “Contribution l'analyse physique et la modélisation du fluage propre.” Thèse de doctorat de l'École National des Ponts et Chaussées, Paris (in French).
18.
Huet, C., Acker, P., and Baron, J. ( 1982). “Fluage du béton et autres comportements rhéologiques différés.” Connaissance du Béton Hydraulique, R. Sauterey and J. Baron, eds., ENPC Press, Paris, 335–364 (in French).
19.
Lemaitre, J., and Chaboche, J. L. ( 1990). Mechanics of solid materials, Cambridge University Press, London.
20.
Li, Z. X., and Qian, Q. C. ( 1992). “A creep model for concrete with damage in the axial and lateral directions.” Theoretical and Appl. Fracture Mech., 17, 115–120.
21.
Lin, J., and Cloutier, A. ( 1996). “Finite element modeling of the viscoelastic behavior of wood during drying.” Proc., 5th Int. IUFRO Wood Drying Conf., 117–124.
22.
Lubliner, J. ( 1972). “On the thermodynamic foundation of non-linear solid mechanics.” Int. J. Non-Linear Mech., 7, 237–254.
23.
Luhmann, A., and Niemz, P. ( 1993). “Investigations of the failure criterion and mechanosortive creep during wood drying.” Holzforschung und Holzvertung, 45(6), 109–112.
24.
Mauget, B., and Perré, P. ( 1996). “Numerical simulation of drying stresses using a large displacement formulation.” Proc., 5th Int. IUFRO Wood Drying Conf., 59–68.
25.
Morgan, K., Thomas, H. R., and Lewis, R. W. ( 1982). “Numerical modeling of stress reversal in timber drying.” Wood Sci. Technol., 15(2), 139–149.
26.
Neville, A. M., Dilger, W. H., and Brooks, J. J. ( 1983). Creep of plain and structural concrete, Construction Press, London and New York.
27.
Pluvinage, G. ( 1992). “La rupture du bois et de ses composites.” Edition Cepadues, Toulouse, France (in French).
28.
Salin, J. G. ( 1992). “Numerical prediction of checking during timber drying and a new mechano-sorptive creep model.” Holz Roh-Werkst, 50, 195–200.
29.
Schapery, R. A. ( 1964). “Application of thermodynamics to thermomechanical, fracture and birefringement phenomena in viscoelastic media.” J. Appl. Phys., 35(5), 1451–1465.
30.
Schapery, R. A. ( 1968). “On a thermodynamic constitutive theory and its application to various non-linear materials.” Proc., IUTAM Sym. on Irreversible Aspects of Continuum Mech., H. Parkus and L. I. Sedov, eds., Springer, New York, 259–285.
31.
Svensson, S. ( 1996). “Strain and shrinkage force in wood under kiln drying conditions II: Strain, shrinkage and stress measurements under controlled climate conditions.” Hlzforschung, 50, 463–469.
32.
Valanis, K. C. ( 1966). “Thermodynamics of large viscoelastic deformation.” J. Mathematics and Phys., 45(2), 197–212.
33.
Valanis, K. C. ( 1972). Irreversible thermodynamics of continuous media-internal variable theory, Springer, New York.
34.
Wittmann, K. C. ( 1982). “Creep and shrinkage mechanism.” Creep and shrinkage in concrete structures, Z. P. Bazant and F. H. Wittmann, eds., Wiley, New York, 129–161.
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Received: Mar 27, 2000
Published online: Aug 1, 2001
Published in print: Aug 2001
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