Elasticity and permeability of porous fibre-reinforced materials under large deformations

Mechanics of Materials

Volumn 44, Issue , 2012, Pages 58-71

  Federico, Salvatore ^a   Grillo, Alfio ^b  

^a UNIVERSITY OF CALGARY   (Canada)

^b GOETHE UNIVERSITY   (Germany)

Author keywords

Covariant formalism; Fibre reinforced; Large deformations; Non linear elasticity; Permeability; Porous material

Indexed keywords

COVARIANT; COVARIANT FORMALISM; ELASTIC PROPERTIES; ELASTIC STRAIN ENERGY; FIBRE-REINFORCED; FLUID MASS; FLUID PHASIS; GENERAL CURVILINEAR COORDINATES; GENERALISATION; INTEGRAL FORM; LARGE DEFORMATIONS; LARGE STRAINS; NEIGHBOURHOOD; NEW FORMS; NONLINEAR ELASTICITY; PORE FLUIDS; POROUS MATRIXS; POROUS MEDIUM; SATURATION CONSTRAINTS; SOFT BIOLOGICAL TISSUE; STRUCTURE TENSORS; VOLUMETRIC DEFORMATION; VOLUMETRIC FRACTIONS;

COMPACTION; DEFORMATION; ELASTICITY; FIBERS; FLUIDS; MECHANICAL PERMEABILITY; POROUS MATERIALS; TISSUE;

FIBER REINFORCED MATERIALS;

EID: 82755197056     PISSN: 01676636     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechmat.2011.07.010     Document Type: Article

References (68)

1. E.S. Almeida, and R.L. Spilker Finite element formulations for hyperelastic transversely isotropic biphasic soft tissues Comput. Meth. Appl. Mech. Eng. 151 1998 513 538 (Pubitemid 128396250)
2. R.M. Aspden, and D.W.L. Hukins Collagen organization in articular cartilage, determined by x-ray diffraction, and its relationship to tissue function Proc. R. Soc. Lond. B 212 1981 299 304 (Pubitemid 11001820)
3. G.A. Ateshian, and J.A. Weiss Anisotropic hydraulic permeability under finite deformation J. Biomech. Eng. 132 2010 111004
4. L. Bennethum, M. Murad, and J. Cushman Macroscale thermodynamics and the chemical potential for swelling porous media Transport Porous Med. 39 2000 187 225 (Pubitemid 30255025)
5. K.L. Billiar, and M.S. Sacks Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp - Part I: Experimental results J. Biomech. 122 2000 23 30 (Pubitemid 30204698)
6. M.A. Biot Theory of finite deformations of porous solids Ind. Univ. Math. J. 21 1972 597 620
7. R.L. Bishop, and S.I. Goldberg Tensor Analysis on Manifolds 1968 Prentice-Hall NJ, USA
8. J. Bonet, and R.D. Wood Nonlinear Continuum Mechanics for Finite Element Analysis Second ed. 2008 Cambridge University Press Cambridge, UK
9. D. Chapelle, J.-F. Gerbeau, J. Sainte-Marie, and I.E. Vignon-Clementel A poroelastic model valid in large strains with applications to perfusion in cardiac modeling Comput. Mech. 46 2010 91 101
10. W. Ehlers, and G. Eipper Finite elastizität bei fluidgesä ttigten hochporösen festkörpern Z. Angew. Math. Mech. 77 1997 S79 S80
11. W. Ehlers, and G. Eipper Finite elastic deformations in liquid-saturated and empty porous solids Transport Porous Med. 34 1999 179 191 (Pubitemid 29384658)
12. A.C. Eringen Mechanics of Continua Robert E 1980 Krieger Publishing Company Huntington, NY, USA
13. S. Federico Volumetric-distortional decomposition of deformation and elasticity tensor Math. Mech. Solids 15 2010 672 690
14. S. Federico, and T.G. Gasser Non-linear elasticity of biological tissues with statistical fibre orientation J. R. Soc. Interface 7 2010 955 966
15. S. Federico, A. Grillo, and W. Herzog A transversely isotropic composite with a statistical distribution of spheroidal inclusions: a geometrical approach to overall properties J. Mech. Phys. Solids 52 2004 2309 2327
16. S. Federico, A. Grillo, S. Imatani, G. Giaquinta, and W. Herzog An energetic approach to the analysis of anisotropic hyperelastic materials Int. J. Eng. Sci. 46 2008 164 181 (Pubitemid 50008516)
17. S. Federico, and W. Herzog On the permeability of fibre-reinforced porous materials Int. J. Solids Struct. 45 2008 2160 2172
18. S. Federico, and W. Herzog Towards an analytical model of soft tissues J. Biomech. 41 2008 3309 3313
19. P.J. Flory Thermodynamic relations for high elastic materials Trans. Faraday Soc. 57 1961 829 838
20. Y.C. Fung Biomechanics: Mechanical Properties of Living Tissue 1981 Springer-Verlag New York, USA
21. T.C. Gasser, R.W. Ogden, and G.A. Holzapfel Hyperelastic modelling of arterial layers with distributed collagen fibre orientations J. R. Soc. Interface 3 2006 15 35 (Pubitemid 46682201)
22. Grillo, A., Federico, S., Wittum, G., 2011. Growth, mass transfer, and remodeling in fiber-reinforced, multi-constituent materials, Int. J. Non-Lin. Mech, in press, doi:10.1016/j.ijnonlinmec.2011.09.026.
23. A. Grillo, S. Federico, G. Wittum, S. Imatani, G. Giaquinta, and M. Mićunović Evolution of a fibre-reinforced growing mixture Nuovo Cimento C 32C 2009 97 119
24. A. Grillo, G. Wittum, G. Giaquinta, and M. Mićunović A multiscale analysis of growth and diffusion dynamics in biological mixtures Int. J. Eng. Sci. 47 2009 261 283
25. A. Grillo, G. Zingali, G. Borrello, S. Federico, W. Herzog, and G. Giaquinta A multiscale description of growth and transport in biological tissues Theor. Appl. Mech. 34 2007 51 87
26. A. Grillo, G. Zingali, G. Borrello, and G. Giaquinta Transport phenomena in living systems and continuum physics Riv. Nuovo Cimento 3 30 2007 485 562
27. Z.Y. Guo, F. Caner, X.Q. Peng, and B. Moran On constitutive modelling of porous neo-hookean composites J. Mech. Phys. Solids 56 2008 2338 2357
28. Z.Y. Guo, X.Q. Peng, and B. Moran A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus J. Mech. Phys. Solids 54 2006 1952 1971 (Pubitemid 43902885)
29. R.H. Hardin, and N.J.A. Sloane McLaren's improved snub cube and other new spherical designs in three dimensions Discrete Comput. Geom. 15 1996 429 441 (Pubitemid 126317256)
30. Hardin, R.H., Sloane, N.J.A., Smith, W.D., 2008. Spherical Codes. http://www.research.att.com/∼njas/packings/.
31. S.M. Hassanizadeh Derivation of basic equations of mass transport in porous media, part ii. generalized Darcy's and Fick's laws Adv. Water Resour. 9 1986 208 222
32. M.H. Holmes, and V.C. Mow The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration J. Biomech. 23 1990 1145 1156
33. G.A. Holzapfel Nonlinear Solid Mechanics A Continuum Approach for Engineering 2000 John Wiley & Sons Chichester, UK
34. G.A. Holzapfel, T.C. Gasser, and R.W. Ogden A new constitutive framework for arterial wall mechanics and a comparative study of material models J. Elast. 61 2000 1 48 (Pubitemid 32732278)
35. C. Hurschler, B. Loitz-Ramage, and R. Vanderby Jr. A structurally based stress-stretch relationship for tendon and ligament J. Biomech. Eng. 119 1997 392 399 (Pubitemid 27516435)
36. A.N. Kolmogorov, and S.V. Fomin Elements of the Theory of Functions and Functional Analysis 1999 Dover
37. L.D. Landau, and E.M. Lifshitz Electrodynamics of Continuous Media 1960 Pergamon Press Oxford, UK
38. Y. Lanir Constitutive equations for fibrous connective tissues J. Biomech. 16 1983 1 12 (Pubitemid 13125809)
39. B. Loret, and F.M.F. Simoes A framework for deformation, generalized diffusion and growth in multi-species multi-phase biological tissues Eur. J. Mech. A/Solids 24 2005 757 781 (Pubitemid 41353730)
40. J.E. Marsden, and T.J.R. Hughes Mathematical Foundations of Elasticity 1994 Dover New York, USA
41. R. McLaughlin A study of the differential scheme for composite materials Int. J. Eng. Sci. 15 1977 237 244
42. J. Merodio On constitutive equations for fiber-reinforced nonlinearly viscoelastic solids Mech. Res. Commun. 33 2006 764 770 (Pubitemid 44037765)
43. J. Merodio, and R.W. Ogden Material instabilities in fiber-reinforced nonlinearly elastic solids under plane deformation Arch. Mech. 54 2002 525 552 (Pubitemid 36270120)
44. C. Miehe Aspects of the formulation and finite element implementation of large strain isotropic elasticity Int. J. Numer. Meth. Eng. 37 1994 1981 2004
45. J. Mollenhauer, M. Aurich, C. Muehleman, G. Khelashvilli, and T.C. Irving X-ray diffraction of the molecular substructure of human articular cartilage Conn. Tiss. Res. 44 2003 201 207 (Pubitemid 38035552)
46. L.W. Morland A simple constitutive theory for a fluid-saturated porous solid J. Geophys. Res. 77 1972 890 900
47. A.N. Norris A differential scheme for the effective moduli of composites Mech. Mat. 4 1985 1 16 (Pubitemid 15561666)
48. R.W. Ogden Nearly isochoric elastic deformations: Application to rubberlike solids J. Mech. Phys. Solids 26 1978 37 57 (Pubitemid 8611350)
49. T. Olsson, and A. Klarbring Residual stresses in soft tissue as a consequence of growth and remodeling: application to an arterial geometry Eur. J. Mech. A/Solids 27 2008 959 974
50. S. Podzniakov, and C.-F. Tsang A self-consistent approach for calculating the effective hydraulic conductivity of a binary, heterogeneous medium Water Resour. Res. 40 2004 1 13, W0510
51. Y.P. Qiu, and G.J. Weng On the application of Mori-Tanaka's theory involving transversely isotropic spheroidal inclusions Int. J. Eng. Sci. 28 1990 1121 1137
52. S. Quiligotti On bulk growth mechanics of solid-fluid mixtures Theor. Appl. Mech. 28/29 2002 277 288
53. S. Quiligotti, G.A. Maugin, and F. Dell'Isola An eshelbian approach to the nonlinear mechanics of contrained solid-fluid mixtures Acta Mech. 160 2003 45 60
54. T.M. Quinn, P. Dierickx, and A.J. Grodzinsky Glycosaminoglycan network geometry may contribute to anisotropic hydraulic permeability in cartilage under compression J. Biomech. 34 2001 1483 1490 (Pubitemid 32970763)
55. M.S. Sacks Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues J. Biomech. Eng. 125 2003 280 287 (Pubitemid 36506143)
56. C. Sansour On the physical assumptions underlying the volumetric-isochoric split and the case of anisotropy Eur. J. Mech. A/Solids 27 2008 28 39 (Pubitemid 350181482)
57. G. Sciarra, G. Maugin, and K. Hutter A variational approach to a microstructured theory of solid-fluid mixtures Archive Appl. Mech. 73 2003 199 224
58. J.C. Simo, R.L. Taylor, and K.S. Pister Variational and projection methods for the volume constraint in finite deformation elasto-plasticity Comput. Meth. Appl. Mech. Eng. 51 1985 177 208
59. Simulia (Ed.), 2010. ABAQUS/Standard User's Manual, Version 6.10. Simulia, Inc., Providence, RI, USA.
60. K. Terzaghi Theoretical Soil Mechanics 1943 Wiley New York, USA
61. L.J. Walpole Elastic behavior of composite materials: Theoretical foundations Adv. Appl. Mech. 21 1981 169 242 (Pubitemid 12465509)
62. L.J. Walpole Fourth-rank tensors of the thirty-two crystal classes: Multiplication tables Proc. R. Soc. Lond. A 391 1984 149 179
63. J.A. Weiss, and J.C. Gardiner Computational modeling of ligament mechanics Crit. Rev. Biomed. Eng. 29 2001 303 371 (Pubitemid 33070575)
64. A.A. White, and M.M. Panjabi Clinical Biomechanics of the Spine 1978 Lippincott Philadelphia, USA
65. K. Wilmański On thermodynamics of nonlinear poroelastic materials J. Elast. 71 2003 247 261
66. W. Wilson, J.M. Huyghe, and C.C. van Donkelaar Depth-dependent compressive equilibrium properties of articular cartilage explained by its composition Biomech. Model. Mechanobiol. 6 2007 43 53 (Pubitemid 44893159)
67. J.Z. Wu, and W. Herzog Finite element simulation of location- and time-dependent mechanical behavior of chondrocytes in unconfined compression tests Ann. Biomed. Eng. 28 2000 318 330
68. R.W. Zimmermann Elastic moduli of a solid containing spherical inclusions Mech. Mat. 12 1991 17 24