### 3D simulation of transversely isotropic laminated composites in RTM using poromechanics

#### Abstract

In the present paper we are trying to establish a 3D simulation framework for Resin Transfer Molding for a laminated preform using the already developed porous media theory for composite materials process simulation purposes. The aim here is to implement the process phenomena, such as coupling of sub-processes that are happening simultaneously, in a full 3D description of the problem. For this purpose, an 8-node solid shell element is employed to be able to handle complex 3D stress-strain states. The development is exemplified considering RTM process where the main focus of the modeling will be on the flow advancement into fiber preform and flow front capturing. To this end, the theory of two-phase porous media is used along with assuming hyper-elastic material response for the fiber bed to formulate the problem. A finite element formulation and implementation of the two-phase problem is developed, and the results are presented accordingly.

#### Keywords

#### Full Text:

PDF#### References

C.S. Desai, Finite Element Methods for Flow in Porous Media, Finite Element in Fluids, vol. 1, John Wiley and Sons (1975) pp. 157182

Y. Song, W. Chui, J. Glimm, B. Lindquist, F. Tangerman, Application of front tracking to the simulation of resin transfer method, Comput. Math. Appl., 33 (9) (1997), pp. 4760

M.K. Kang, W. Lee, A flow-front refinement for the numerical simulation of the resin transfer molding process, Compos. Sci. Technol., 59 (1999), pp.16631674

A. Hammami, B.R. Gebart, Analysis of the vacuum infusion moulding processes Polym. Compos., 21 (1) (2000), pp. 2840

S. Soukane, F. Trochu, Application of the level set method to the simulation of resin transfer molding, Compos. Sci. Technol., 66 (2006), pp. 10671080

Celle, P., Drapier, S., Bergheau, J., 2008a. Numerical modelling of liquid infusion into fibrous media undergoing compaction. Eur. J. Mech. A Solids 27, pp. 647661

Celle, P., Drapier, S., Bergheau, J., 2008b. Numerical aspects of fluid infusion inside a compressible porous medium undergoing large strains. Eur. J. Comput. Mech. 17, pp. 819827.

K.M. Pillai, C.L. Tucker, F.N. Phelan, Numerical simulation of injection/compression liquid composite moulding. Part 2: preform compression, Compos. Part A, 32 (2001), pp. 207220

M. Li, C.L. Tucker, Modelling and simulation of two-dimensional consolidation for thermoset matrix composites, Compos. Part A, 33 (2002), pp. 877892

R. Larsson, M. Wysocki, S. Toll, Process modeling of composites using two-phase porous media theory, Eur. J. Mech. A/Solids, 23 (2004), pp. 1536

Larsson R, Rouhi M S, Wysocki M, Free surface flow and preform deformation in composites manufacturing based on porous media theory, European Journal of Mechanics - A/Solids, Volume 31, Issue 1, JanuaryFebruary 2012, Pages 1-12.

M.S. Rouhi, M. Wysocki, R. Larsson, Modeling of coupled dual-scale flow-deformation processes in composites manufacturing, Composites Part A: Applied Science and Manufacturing, Volume 46, March 2013, Pages 108-116.

M.S. Rouhi, M. Wysocki, R. Larsson, Experimental assessment of coupled dual-scale flow-deformation processes in composites manufacturing, Journal of Composites Part A: Applied Science and Manufacturing, 46(2015)215223.

M.S. Rouhi, R. Larsson, M. Wysocki, Holistic modeling of composites manufacturing using poromechanics, Journal of Advanced Mnaufatcuring: Polymer and Composites Science, DOI:10.1080/20550340.2016.1141457

M.S. Rouhi, Infusion modelling using two phase porous media theory, Chalmers University of Technology, 2009:42, Master Thesis report

Solid Elements, Chapter 8, Advanced Finite Element Methods for Solids, Plates and Shells (AFEM) (ASEN 6367) - Spring 2013 Department of Aerospace Engineering Sciences University of Colorado at Boulder

S. Klinkel, F. Gruttmann and W. Wagner, A robust non-linear solid shell element based on a mixed variational formulation, Comput. Methods Appl. Mech. Engrg. 195 (2006) 179201

Buchter, N., Ramm, E., Roehl, D., Three-dimensional extension of nonlinear shell formulation based on the enhanced assumed strain concept, Int. J. Num. Meth. Eng., 1994, 37, 2551-2568

M. F. Ausserer and S. W. Lee, An eighteen node solid element for thin shell analysis, Int. J. Numer. Meth. Engrg., 26, 13451364, 1988.

D. J. Haas and S.W. Lee,Anine-node assumed-strain finite element for composite plates and shells, Computers and Structures, 26, 445452, 1987.

H. C. Park, C. Cho and S. W. Lee, An efficient assumed strain element model with six dof per node for geometrically nonlinear shells, Int. J. Numer. Meth. Engrg., 38, 4101-4122, 1995.

K. Y. Sze and A. Ghali, A hexahedral element for plates, shells and beam by selective scaling, Int. J. Numer. Meth. Engrg., 36, 15191540, 1993.

P. Betch and E. Stein, An assumed strain approach avoiding artificial thickness straining for a nonlinear 4-node shell element, Comp. Meths. Appl. Mech. Engrg., 11, 899909, 1997.

M. Bischoff and E. Ramm, Shear deformable shell elements for large strains and rotations, Int. J. Numer. Meth. Engrg., 40, 445452, 1997.

R. Hauptmann and K. Schweizerhof, A systematic development of solid-shell element formulations for linear and nonlinear analysis employing only displacement degrees of freedom, Int. J. Numer. Meth. Engrg., 42, 4969, 1988.

Parish, A continuum-based shell theory for nonlinear application, Int. J. Numer. Meth. Engrg., 38, 18551883, 1995.

J. C. Simo and M. S. Rifai, A class of mixed assumed strain methods and the method of incompatible modes, Int. J. Numer. Meth. Engrg., 29, 15951638, 1990.

R. H. MacNeal, Toward a defect free four-noded membrane element, Finite Elem. Anal. Des., 5, 3137, 1989.

R. H. MacNeal anf R. L. Harder, A proposed standard set of problems to test finite element accuracy, Finite Elem. Anal. Des., 1, 320, 1985.

T. H. H. Pian, Finite elements based on consistently assumed stresses and displacements, Finite Elem. Anal. Des., 1, 131140, 1985.

K. Y. Sze, S. Yi and M. H. Tay, An explicit hybrid-stabilized eighteen node solid element for thin shell analysis, Int. J. Numer. Meth. Engrg., 40, 18391856, 1997.

K. Y. Sze, D. Zhu, An quadratic assumed natural strain curved triangular shell element, Comp. Meths. Appl. Mech. Engrg., 174, 5771, 1999.

A Solid Shell Element, Chapter 32, Advanced Finite Element Methods (ASEN6367) - Spring 2013 Department of Aerospace Engineering Sciences University of Colorado at Boulder

K. C. Park and G. M. Stanley, A curved C0 shell element based on assumed natural coordinate strains, J. Appl. Mech., 53, 278290, 1986.

K.J. Bathe and E. N. Dvorkin, A formulation of general shell elements the use of mixed interpolation of tensorial components, Int. J. Numer. Meth. Engrg., 22, 697-722, 1986.

etsch, P., Stein, E., An assumed strain approach avoiding artifcial thickness straining for a nonlinear 4-node shell element, Comm. Num. Meth. Eng., 1995, 11, 899-909

Eberlein, R., Wriggers, P., Finite element formulations of 5- and 6-parameter shell theories accounting for finite plastic strains, in 'Computational Plasticity, Fundamentals and Applications', Owen, D.R.J. and Onate, E. and Hinton, E. (Eds.), CIMNE, Barcelona, 1997, 1898-1903

Bischoff, M., Ramm, E., Shear deformable shell elements for large strains and rotations, Int. J. Num. Meth. Eng., 1997, 40, 4427-4449

Maarten Labordus, Permeability Measurements: In plane and through the thickness, Center of Lightweight Structures TUD-TNO, Kluverwegl, Delft, The netherlands.

R. Loendersloot, R. Akkerman, Through-Thickness Permeability Measurements of Fibre Reinforcements, University of Twente, Twente Institute of Mechanics, The Netherlands.

Lundstrom TS. Permeability of non-crimp stitched fabrics. Compos A 2000; 31: 13451353.

Xueliang Xiao, Andreas Endruweit, Xuesen Zeng, Jinlian Hu, Andrew Long, Through-thickness permeability study of orthogonal and angle-interlock woven fabrics, J Mater Sci (2015) 50:12571266, DOI:10.1007/s10853-014-8683-4

Endruweit A, Long AC. Analysis of compressibility and permeability of selected 3D woven reinforcements. J Compos Mater 2010; 44: 28332862

Belov EB, Lomov SV, Verpoest I, et al. Modelling of permeability of textile reinforcements: lattice Boltzmann method. Compos Sci Technol 2004; 64:10691080.

Verleye B, Lomov SV, Long A, et al. Permeability prediction for the meso-macro coupling in the simulation of the impregnation stage of resin transfer moulding. Compos A 2010; 41: 2935.

ZUO-RONG CHEN AND LIN YE, Permeability Predictions for Woven Fabric Preforms, Journal of Composite Materials June 1, 2010 44: 1569-1586

Gebart B R, 'Permeability of unidirectional reinforcements for RTM', Journal of Composite Materials, 26 (1992), p. 1100-1133.

S. Bickerton. Modeling and control of flow during impregnation of heterogeneous porous media, with application to composite mold filling processes. PhD thesis, University of Delaware, Newark, DE, 1999.

DOI: http://dx.doi.org/10.18063/msacm.v3i1.926

(

**40**Abstract Views,

**22**PDF Downloads)

### Refbacks

- There are currently no refbacks.

Copyright (c) 2018 Mohammad Sadegh Rouhi 1, Maciej Wysocki 2

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.