Deformable Porous Media and Composites Manufacturing

A growing number of industrial activities demands advanced materials that satisfy stringent requirements and lower costs. These requirements, which involve a combination of many properties, can often be satisfied by using a composite material, whose constituents act synergically to solve the needs of application. Modelling the behavior of such a heterogeneous material during its production is a very hard task, but it is very useful for the optimization of the manufacturing process itself. This chapter focuses on the deduction of mathematical models of deformable porous media and on their application to composite materials manufacturing as a first step toward the understanding of this complex process.

[1]  Jan-Anders E. Månson,et al.  Prediction of the consolidation of woven fibre-reinforced thermoplastic composites. Part I. Isothermal case , 1998 .

[2]  JD Jan Janssen,et al.  A validation of the quadriphasic mixture theory for intervertebral disc tissue , 1997 .

[3]  Y. Nishida,et al.  Infiltration kinetics of fibrous preforms by aluminum with solidification , 1995 .

[4]  G. S. Beavers,et al.  Flow Through a Deformable Porous Material , 1975 .

[5]  C. Truesdell,et al.  The Classical Field Theories , 1960 .

[6]  M. Reboredo,et al.  Molding by reactive injection of reinforced plastics , 1988 .

[7]  Suresh G. Advani,et al.  Effective average permeability of multi-layer preforms in resin transfer molding , 1996 .

[8]  P. Mallick.  Fiber-reinforced composites : materials, manufacturing, and design , 1989 .

[9]  R. E. Craine,et al.  CONTINUUM THEORIES OF MIXTURES: BASIC THEORY AND HISTORICAL DEVELOPMENT , 1976 .

[10]  P. Saffman.  On the Boundary Condition at the Surface of a Porous Medium , 1971 .

[11]  D. E. Kenyon,et al.  The theory of an incompressible solid-fluid mixture , 1976 .

[12]  George S. Springer,et al.  Heat of Reaction, Degree of Cure, and Viscosity of Hercules 3501-6 Resin , 1982 .

[13]  U. Hornung.  Homogenization and porous media , 1996 .

[14]  J. King,et al.  Mathematical modelling of avascular-tumour growth. , 1997, IMA journal of mathematics applied in medicine and biology.

[15]  R. M. Bowen.  Part I – Theory of Mixtures , 1976 .

[16]  S. Advani,et al.  Experimental investigation and flow visualization of the resin-transfer mold-filling process in a non-planar geometry , 1997 .

[17]  Andrew C. Long,et al.  Processing and mechanical properties of bi-directional preforms for liquid composite moulding , 1995 .

[18]  Reint de Boer,et al.  Highlights in the Historical Development of the Porous Media Theory: Toward a Consistent Macroscopic Theory , 1996 .

[19]  D. E. Kenyon,et al.  A mathematical model of water flux through aortic tissue. , 1979, Bulletin of mathematical biology.

[20]  Constantina Lekakou,et al.  Compressibility and flow permeability of two-dimensional woven reinforcements in the processing of composites , 1996 .

[21]  J. King,et al.  Mathematical modelling of avascular-tumour growth. II: Modelling growth saturation. , 1999, IMA journal of mathematics applied in medicine and biology.

[22]  L A Taber,et al.  A nonliner poroelastic model for the trabecular embryonic heart. , 1994, Journal of biomechanical engineering.

[23]  D. E. Kenyon.  Thermostatics of solid-fluid mixtures , 1976 .

[24]  Chris D. Rudd,et al.  Towards a Manufacturing Technology for High-Volume Production of Composite Components , 1992 .

[25]  J. Nam,et al.  Gas permeation and viscoelastic deformation of prepregs in composite manufacturing processes , 1995 .

[26]  D. Joseph,et al.  ENSEMBLE AVERAGED AND MIXTURE THEORY EQUATIONS FOR INCOMPRESSIBLE FLUID-PARTICLE SUSPENSIONS , 1990 .

[27]  C. Rudd,et al.  Flow and cure phenomena in liquid composite molding , 1994 .

[28]  A. Mikelić,et al.  On the stationary quasi‐Newtonian flow obeying a power‐law , 1995 .

[29]  Timothy G. Gutowski,et al.  The Consolidation of Laminate Composites , 1987 .

[30]  Andrew C. Long,et al.  Liquid Moulding Technologies , 1997 .

[31]  Suresh G. Advani,et al.  Numerical and analytical study to estimate the effect of two length scales upon the permeability of a fibrous porous medium , 1995 .

[32]  Grégoire Allaire,et al.  Homogenization of the stokes flow in a connected porous medium , 1989 .

[33]  M. V. Gandhi,et al.  Combined extension and torsion of a swollen cylinder within the context of mixture theory , 1989 .

[34]  Luigi Preziosi,et al.  The theory of deformable porous media and its application to composite materials manufacturing , 1996 .

[35]  E. Sparrow,et al.  Fluid Flow Through a Class of Highly-Deformable Porous Media. Part I: Experiments With Air , 1981 .

[36]  Chris D. Rudd,et al.  Fibre reinforcement for high volume resin transfer moulding (rtm) , 1990 .

[37]  L. Preziosi,et al.  Non-Isothermal Injection Moulding with Resin Cure and Preform Deformability , 2000 .

[38]  Vasilii S Vladimirov.  Equations of mathematical physics , 1971 .

[39]  L. Billi,et al.  Unidirectional infiltration in deformable porous media: Mathematical modeling and self-similar solution , 2000 .

[40]  L. J. Lee,et al.  Mold filling and curing analysis in liquid composite molding , 1993 .

[41]  Van C. Mow,et al.  Mechanics of Animal Joints , 1979 .

[42]  Musa R. Kamal,et al.  Differential scanning calorimetry of epoxy cure: isothermal cure kinetics☆ , 1976 .

[43]  F. Dai,et al.  Diffusion of fluids through transversely isotropic solids , 1990 .

[44]  Hydrodynamic analysis of liquid infiltration of unidirectional fibre arrays by squeeze casting , 1994 .

[45]  E. Liang,et al.  Consolidation of advanced composites having volatile generation , 1995 .

[46]  Suresh G. Advani,et al.  A numerical approach to model non‐isothermal viscous flow through fibrous media with free surfaces , 1994 .

[47]  H. Ene.  Thermal flow , 1996 .

[48]  Graeme J. Pettet,et al.  A new approach to modelling the formation of necrotic regions in tumours , 1998 .

[49]  Musa R. Kamal,et al.  Kinetics and thermal characterization of thermoset cure , 1973 .

[50]  R. Lipton,et al.  VARIATIONAL METHODS, SIZE EFFECTS AND EXTREMAL MICROGEOMETRIES FOR ELASTIC COMPOSITES WITH IMPERFECT INTERFACE , 1995 .

[51]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[52]  Alfio Quarteroni,et al.  Domain Decomposition Methods for Partial Differential Equations , 1999 .

[53]  Kumbakonam R. Rajagopal,et al.  A BOUNDARY VALUE PROBLEM IN GROUNDWATER MOTION ANALYSIS — COMPARISON OF PREDICTIONS BASED ON DARCY’S LAW AND THE CONTINUUM THEORY OF MIXTURES , 1993 .

[54]  Hoon Huh,et al.  A finite element simulation of resin transfer molding based on partial nodal saturation and implicit time integration , 1998 .

[55]  W. Lee,et al.  Numerical simulation of the resin transfer mold filling process using the boundary element method , 1996 .

[56]  D. AMBROSI,et al.  Modeling Injection Molding Processes with Deformable Porous Preforms , 2000, SIAM J. Appl. Math..

[57]  Luigi Preziosi,et al.  Modelling Mathematical Methods and Scientific Computation , 1995 .

[58]  I. Müller.  A thermodynamic theory of mixtures of fluids , 1968 .

[59]  Constantina Lekakou,et al.  Compression and microstructure of fibre plain woven cloths in the processing of polymer composites , 1998 .

[60]  J. Tarbell,et al.  Modeling water flow through arterial tissue. , 1987, Bulletin of mathematical biology.

[61]  Christopher W. Macosko,et al.  Process parameters estimation for structural reaction injection molding and resin transfer molding , 1990 .

[62]  Stephen Whitaker,et al.  ADVANCES IN THEORY OF FLUID MOTION IN POROUS MEDIA , 1969 .

[63]  Homogenization of the heat equation for a domain with a network of pipes with a well-mixed fluid , 1994 .

[64]  J Parkinson,et al.  The mechanical properties of simulated collagen fibrils. , 1997, Journal of biomechanics.

[65]  Willi Jäger,et al.  On the boundary conditions at the contact interface between a porous medium and a free fluid , 1996 .

[66]  Some thermal problems in flow through a periodic model of porous media , 1981 .

[67]  Jd Jan Janssen,et al.  Finite element analysis of blood flow through biological tissue , 1997 .

[68]  I. Müller.  Rational thermodynamics of mixtures of fluids , 1985 .

[69]  V. Mow,et al.  Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. , 1980, Journal of biomechanical engineering.

[70]  L. Preziosi,et al.  In ltration process in composite materials manufacturing: modeling and qualitative results , 2000 .

[71]  D. Joseph,et al.  Boundary conditions at a naturally permeable wall , 1967, Journal of Fluid Mechanics.

[72]  H. Flower,et al.  Characterization of liquid metal infiltration of a chopped fibre preform aided by external pressure—II. Modelling of liquid metal infiltration process , 1995 .

[73]  Mukesh V. Gandhi,et al.  On boundary conditions for a certain class of problems in mixture theory , 1986 .

[74]  H. Ene.  On the thermodynamic theory of mixtures , 1981 .

[75]  Stephen P. McCarthy,et al.  Compressibility and relaxation of fiber reinforcements during composite processing , 1991 .

[76]  S. Advani,et al.  Permeability model for a woven fabric , 1996 .

[77]  A. Wineman,et al.  UNSTEADY DIFFUSION OF FLUIDS THROUGH SOLIDS UNDERGOING LARGE DEFORMATIONS , 1991 .

[78]  A. Long,et al.  Dynamic core movements during liquid moulding of sandwich structures , 1998 .

[79]  D. S. Drumheller,et al.  Theories of immiscible and structured mixtures , 1983 .

[80]  J. Bear,et al.  Introduction to Modeling of Transport Phenomena in Porous Media , 1990 .

[81]  Enrique Sanchez-Palencia,et al.  On thermal equation for flow in porous media , 1982 .

[82]  J. Cornie,et al.  On the infiltration of metal matrix composites , 1987 .

[83]  L. J. Lee,et al.  Fiber mat deformation in liquid composite molding. I: Experimental analysis , 1993 .

[84]  S. Sideman,et al.  A porous-medium approach for modeling heart mechanics. I. theory , 1986 .

[85]  L. Preziosi,et al.  Modelling matrix injection through elastic porous preforms , 1998 .

[86]  K. Rajagopal,et al.  ON BOUNDARY CONDITIONS IN MIXTURE THEORY , 1995 .

[87]  Peter R. Ciriscioli,et al.  Cure Kinetics and Viscosity of Fiberite 976 Resin , 1987 .

[88]  Wen-Bin Young,et al.  Analysis of resin injection molding in molds with preplaced fiber mats. II: Numerical simulation and experiments of mold filling , 1991 .

[89]  W. Young.  The Effect of Surface Tension on Tow Impregnation of Unidirectional Fibrous Preform in Resin Transfer Molding , 1996 .

[90]  Sanja Marušić.  LOW CONCENTRATION LIMIT FOR A FLUID FLOW THROUGH A FILTER , 1998 .

[91]  Thermal flow in porous media , 1987 .

[92]  Robert Lipton,et al.  Darcy's law for slow viscous flow past a stationary array of bubbles , 1990 .

[93]  W M Lai,et al.  Fluid transport and mechanical properties of articular cartilage: a review. , 1984, Journal of biomechanics.

[94]  L. J. Lee,et al.  Analysis of resin injection molding in molds with preplaced fiber mats. I: Permeability and compressibility measurements , 1991 .

[95]  W M Lai,et al.  Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications. , 1989, Journal of biomechanical engineering.

[96]  Bernhard A. Schrefler,et al.  The Finite Element Method in the Deformation and Consolidation of Porous Media , 1987 .

[97]  A. Wineman,et al.  The diffusion of a fluid through a highly elastic spherical membrane , 1983 .

[98]  Bernhard A. Schrefler,et al.  Coupled heat, water and gas flow in deformable porous media , 1995 .

[99]  Eugene H. Wissler,et al.  Viscoelastic Effects in the Flow of Non-Newtonian Fluids through a Porous Medium , 1971 .

[100]  Chris D. Rudd,et al.  Effects of process variables on cycle time during resin transfer moulding for high volume manufacture , 1990 .

[101]  Charles Nicholson,et al.  Diffusion from an injected volume of a substance in brain tissue with arbitrary volume fraction and tortuosity , 1985, Brain Research.

[102]  R. E. Craine,et al.  Continuum Theories of Mixtures: Applications , 1976 .

[103]  B. Seedhom,et al.  Articular cartilage deformation under physiological cyclic loading--apparatus and measurement technique. , 1997, Journal of biomechanics.

[104]  Jeannine Saint Jean Paulin,et al.  HOMOGENIZATION AND TWO-SCALE CONVERGENCE FOR A STOKES OR NAVIER-STOKES FLOW IN AN ELASTIC THIN POROUS MEDIUM , 1996 .

[105]  L. J. Lee,et al.  Fiber mat deformation in liquid composite molding. II: Modeling , 1993 .

[106]  L. J. Lee,et al.  Non-isothermal Mold Filling and Curing Simulation in Thin Cavities with Preplaced Fiber Mats , 1991 .

[107]  James Glimm,et al.  Case Study from Industry: Process Modeling in Resin Transfer Molding as a Method to Enhance Product Quality , 1997, SIAM Rev..

[108]  A. Long,et al.  In‐plane permeability determination for simulation of liquid composite molding of complex shapes , 1996 .

[109]  L. J. Lee,et al.  Mold filling analysis in resin transfer molding , 1996 .

[110]  M. V. Gandhi,et al.  Some nonlinear diffusion problems within the context of the theory of interacting continua , 1987 .

[111]  Jacques-Louis Lions,et al.  Some Methods in the Mathematical Analysis of Systems and Their Control , 1981 .

[112]  Walter Herzog,et al.  An improved solution for the contact of two biphasic cartilage layers , 1997 .

[113]  D. Purslow,et al.  Autoclave moulding of carbon fibre-reinforced epoxies , 1986 .

[114]  K. Rajagopal,et al.  Unsteady diffusion of fluids through a non-linearly elastic cylindrical annulus , 1993 .

[115]  T. Clyne,et al.  The squeeze infiltration process for fabrication of metal-matrix composites , 1987 .

[116]  R. M. Bowen,et al.  Incompressible porous media models by use of the theory of mixtures , 1980 .

[117]  J. Summerscales,et al.  Microstructural image analysis applied to fibre composite materials: a review , 1993 .

[118]  S. Torquato.  Thermal Conductivity of Disordered Heterogeneous Media from the Microstructure , 1987 .

[119]  F. Trochu,et al.  Modeling the edge effect in liquid composites molding , 1998 .

[120]  Jacques Baranger,et al.  STATIONARY SOLUTIONS TO A QUASI-NEWTONIAN FLOW WITH VISCOUS HEATING , 1995 .

[121]  S. Advani,et al.  The consolidation of commingled thermoplastic fabrics , 1991 .

[122]  Suresh G. Advani,et al.  Modelling and simulation of resin transfer moulding (RTM)—gate control, venting and dry spot prediction , 1996 .

[123]  G Jayaraman,et al.  Water transport in the arterial wall--a theoretical study. , 1983, Journal of biomechanics.

[124]  R. M. Bowen,et al.  A Theory of constrained mixtures with multiple temperatures , 1979 .

[125]  Suresh G. Advani,et al.  The interaction between micro- and macro-scopic flow in RTM preforms , 1994 .

[126]  Andreas Mortensen,et al.  Forced unidirectional infiltration of deformable porous media , 1996, Journal of Fluid Mechanics.