Isogeometric Analysis of a Multiphase Porous Media Model for Concrete
Publication: Journal of Engineering Mechanics
Volume 144, Issue 2
Abstract
This paper presents isogeometric analysis of a hygro-thermo-chemo-mechanical concrete model at early age and beyond. Balance equations are introduced at the microscale and averaged to obtain balance equations at the macroscale. Constitutive laws are then applied directly at the macroscale. The final balance equations are mass, momentum, and energy based. These are written as a function of five primary variables in two dimensions: gas pressure, capillary pressure, temperature, and displacements. The standard finite-element shape functions are replaced by non-uniform rational B-splines that are used in isogeometric analysis. These basis functions possess a higher degree of continuity and can be used to construct an exact geometry when compared with their finite-element counterparts. Also, local mesh refinement at the mesh boundary is achieved easily with isogeometric basis functions. These properties make the isogeometric basis functions very suitable for describing the many transient processes that occur, especially in concrete at an early age. Isogeometric basis functions are implemented directly into an existing finite-element model. The accuracy of the isogeometric concept is compared and validated against the finite-element-based approach. The examples show that the isogeometric model is more accurate than the finite-element model on a per-degree-of-freedom basis.
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References
Baroghel-Bouny, V., Mainguy, M., Lassabatere, T., and Coussy, O. (1999). “Characterization and identification of equilibrium and transfer moisture properties for ordinary and high-performance cementitious materials.” Cem. Concr. Res., 29(8), 1225–1238.
Bazilevs, Y., et al. (2010). “Isogeometric analysis using t-splines.” Comput. Methods Appl. Mech. Eng., 199(5), 229–263.
Cervera, M., Oliver, J., and Prato, T. (1999). “Thermo-chemo-mechanical model for concrete. II: Damage and creep.” J. Eng. Mech., 1028–1039.
Collier, N., Pardo, D., Dalcin, L., Paszynski, M., and Calo, V. M. (2012). “The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers.” Comput. Methods Appl. Mech. Eng., 213–216, 353–361.
Cottrell, J. A., Hughes, T. J. R., and Bazilevs, Y. (2009). Isogeometric analysis: Toward integration of CAD and FEA, Wiley, New York.
Cox, M. G. (1972). “The numerical evaluation of b-splines.” IMA J. Appl. Math., 10(2), 134–149.
De Boor, C. (1972). “On calculating with b-splines.” J. Approximation Theory, 6(1), 50–62.
Gawin, D., Pesavento, F., and Schrefler, B. A. (2004). “Modelling of deformations of high strength concrete at elevated temperatures.” Mater. Struct., 37(4), 218–236.
Gawin, D., Pesavento, F., and Schrefler, B. A. (2006a). “Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. I: Hydration and hygro-thermal phenomena.” Int. J. Numer. Methods Eng., 67(3), 299–331.
Gawin, D., Pesavento, F., and Schrefler, B. A. (2006b). “Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. II: Shrinkage and creep of concrete.” Int. J. Numer. Methods Eng., 67(3), 332–363.
Gawin, D., Pesavento, F., and Schrefler, B. A. (2006c). “Towards prediction of the thermal spalling risk through a multi-phase porous media model of concrete.” Comput. Methods Appl. Mech. Eng., 195(41), 5707–5729.
Gawin, D., Pesavento, F., and Schrefler, B. A. (2007). “Modelling creep and shrinkage of concrete by means of effective stresses.” Mater. Struct., 40(6), 579–591.
Gawin, D., Pesavento, F., and Schrefler, B. A. (2003). “Modelling of hygro-thermal behaviour of concrete at high temperature with thermo-chemical and mechanical material degradation.” Comput. Methods Appl. Mech. Eng., 192(13), 1731–1771.
Gawin, D., Pesavento, F., and Schrefler, B. A. (2009). “Modeling deterioration of cementitious materials exposed to calcium leaching in non-isothermal conditions.” Comput. Methods Appl. Mech. Eng., 198(37), 3051–3083.
Gens, A., and Olivella, S. (2001). “THM phenomena in saturated and unsaturated porous media: Fundamentals and formulation.” Revue française de génie civil, 5(6), 693–717.
Gray, W. G., and Miller, C. T. (2005). “Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems. 1: Motivation and overview.” Advan. Water Resour., 28(2), 161–180.
Gray, W. G., Schrefler, B. A., and Pesavento, F. (2009). “The solid phase stress tensor in porous media mechanics and the Hill-Mandel condition.” J. Mech. Phys. Solids, 57(3), 539–554.
Hassanizadeh, M., and Gray, W. G. (1979a). “General conservation equations for multi-phase systems. I: Averaging procedure.” Adv. Water Resour., 2, 131–144.
Hassanizadeh, M., and Gray, W. G. (1979b). “General conservation equations for multi-phase systems. II: Mass, momenta, energy, and entropy equations.” Adv. Water Resour., 2, 191–203.
Hassanizadeh, M., and Gray, W. G. (1980). “General conservation equations for multi-phase systems. III: Constitutive theory for porous media flow.” Adv. Water Resour., 3(1), 25–40.
Hughes, T. J. R., Cottrell, J. A., and Bazilevs, Y. (2005). “Isogeometric analysis: CAD, finite elements, nurbs, exact geometry and mesh refinement.” Comput. Methods Appl. Mech. Eng., 194(39), 4135–4195.
Irzal, F., Remmers, J. J. C., Verhoosel, C. V., and Borst, R. (2013). “Isogeometric finite element analysis of poroelasticity.” Int. J. Numer. Anal. Methods Geomech., 37(12), 1891–1907.
Kaasschieter, E. F., Frijns, A. J. H., and Huyghe, J. M. (2003). “Mixed finite element modelling of cartilaginous tissues.” Math. Comput. Simul, 61(3), 549–560.
Kiendl, J., Bletzinger, K. U., Linhard, J., and Wüchner, R. (2009). “Isogeometric shell analysis with Kirchhoff-love elements.” Comput. Methods Appl. Mech. Eng., 198(49), 3902–3914.
Lewis, R. W., and Schrefler, B. A. (1987). The finite element method in the deformation and consolidation of porous media, Wiley, New York.
Nguyen, M. N., Bui, T. Q., Yu, T., and Hirose, S. (2014). “Isogeometric analysis for unsaturated flow problems.” Comput. Geotech., 62, 257–267.
Pesavento, F. (2000). “Non-linear modeling of concrete as multiphase porous material in high temperature conditions.” Ph.D. thesis, Univ. of Padova, Padova, Italy.
Pesavento, F., Gawin, D., and Schrefler, B. A. (2008). “Modeling cementitious materials as multiphase porous media: Theoretical framework and applications.” Acta Mech., 201(1), 313–339.
Pesavento, F., Schrefler, B. A., and Sciumè, G. (2017). “Multiphase flow in deforming porous media: A review.” Arch. Comput. Methods Eng., 24(2), 423–448.
Pesavento, F., Gawin, D., Wyrzykowski, M., Schrefler, B. A., and Simoni, L. (2012). “Modeling alkali-silica reaction in non-isothermal, partially saturated cement based materials.” Comput. Methods Appl. Mech. Eng., 225, 95–115.
Schrefler, B. A. (2002). “Mechanics and thermodynamics of saturated/unsaturated porous materials and quantitative solutions.” Appl. Mech. Rev., 55(4), 351–388.
Sciumè, G., Benboudjema, F., De Sa, C., Pesavento, F., Berthaud, Y., and Schrefler, B. A. (2013). “A multiphysics model for concrete at early age applied to repairs problems.” Eng. Struct., 57, 374–387.
Ulm, F.-J., and Coussy, O. (1995). “Modeling of thermochemomechanical couplings of concrete at early ages.” J. Eng. Mech., 121(7), 785–794.
Van Genuchten, M. T. (1980). “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J., 44(5), 892–898.
Verhoosel, C. V., Scott, M. A., Hughes, T. J. R., and De Borst, R. (2011). “An isogeometric analysis approach to gradient damage models.” Int. J. Numer. Methods Eng., 86(1), 115–134.
Zienkiewicz, O. C., and Taylor, R. L. (2000). The finite element method: Solid mechanics, Vol. 2, Butterworth-Heinemann, Oxford, U.K.
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©2017 American Society of Civil Engineers.
History
Received: Sep 6, 2016
Accepted: Jun 28, 2017
Published online: Nov 30, 2017
Published in print: Feb 1, 2018
Discussion open until: Apr 30, 2018
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