Abstract
The fundamental macroscopic material property needed to quantify the flow in a fibrous medium viewed as a porous medium is the permeability. Composite processing models require the permeability as input data to predict flow patterns and pressure fields. As permeability reflects both the magnitude and anisotropy of the fluid/fiber resistance, efficient numerical techniques are needed to solve linear and nonlinear homogenization problems online during the flow simulation. In a previous work the expressions of macroscopic permeability were derived in a double-scale porosity medium for both Newtonian and rheo-thinning resins. In the linear case only a microscopic calculation on a representative volume is required, implying as many microscopic calculations as representative microscopic volumes exist in the whole fibrous structure. In the non-linear case, and even when the porous microstructure can be described by a unique representative volume, microscopic calculation must be carried out many times because the microscale resin viscosity depends on the macroscopic velocity, which in turn depends on the permeability that results from a microscopic calculation. Thus, a nonlinear multi-scale problem results. In this paper an original and efficient offline-online procedure is proposed for the efficient solution of nonlinear flow problems in porous media.
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Aghighi S, Ammar A, Metivier C, Normandin M, Chinesta F (2013) Non incremental transient solution of the Rayleigh-Bénard convection model using the PGD. J Non-Newtonian Fluid Mech 200:65–78
Aghighi MS, Ammar A, Metivier C, Chinesta F Parametric solution of the Rayleigh-Bénard convection model by using the PGD: Application to nanofluids. Int J Numer Methods Heat Fluid Flow. In press
Chinesta F, Ammar A, Lamarchand F, Beauchene P, Boust F (2008) Alleviating mesh constraints: Model reduction, parallel time integration and high resolution homogenization. Comput Methods Appl Mech Eng 197:400–413
Chinesta F, Leygue A, Bordeu F, Aguado JV, Cueto E, Gonzalez D, Alfaro I, Ammar A, Huerta A (2013) A. PGD-based computational vademecum for efficient design, optimization and control. Arch Comput Meth Eng 20(1):31–59
Chinesta F, Keunings R, Leygue A (2013) The Proper Generalized Decomposition for Advanced Numerical Simulations. A primer. Springerbriefs, Springer
Chinesta F, Huerta A, Rozza G, Willcox K (2016) Model Order Reduction. In: Erwin Stein, Ren´e de Borst, Tom Hughes (eds) Encyclopedia of Computational Mechanics. Second Edition. John Wiley & Sons, Ltd., New York
Donea J, Huerta A (2003) Finite element methods for flow problems. Wiley
Geers MGD, Kouznetsova VG, Brekelmans WAM (2010) Multi-scale computational homogenization: Trends and challenges. J Comput Appl Math 234(7):2175–2182
Ghnatios Ch, Chinesta F, Binetruy Ch The squeeze flow of composite laminates. Int J Mater Form. In press
Gunes H, Sirisup S, Em Karniadakis G (2006) Gappy data: To Krig or not to Krig? J Comput Phys 212:358– 382
Lamari H, Ammar A, Cartraud P, Legrain G, Jacquemin F, Chinesta F (2010) Routes for efficient computational homogenization of non-linear materials using the proper generalized decomposition. Arch Comput Meth Eng 17(4):373– 391
Lopez E, Abisset-Chavanne E, Lebel F, Upadhyay R, Comas-Cardona S, Binetruy C, Chinesta F Advanced thermal simulation of processes involving materials exhibiting fine-scale microstructures. Int J Mater Form. In press
Lopez E, Abisset-Chavanne E, Comas-Cardona S, Binetruy et C, Chinesta F Flow modeling of linear and nonlinear fluids in two and three scale fibrous fabrics. In press
Nguyen VP, Stroeuen M, Sluys LJ (2011) Multiscale continous and discontinous modeling of heterogeneous materials: a review on recent developments. J Multiscale Model 03: 229
Ponte Castañeda P., Suquet P (1998) Nonlinear composites. Adv Appl Mech 34:171–302
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Lopez, E., Leygue, A., Abisset-Chavanne, E. et al. Flow modeling of linear and nonlinear fluids in two scale fibrous fabrics. Int J Mater Form 10, 317–328 (2017). https://doi.org/10.1007/s12289-015-1280-5
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DOI: https://doi.org/10.1007/s12289-015-1280-5