Paper Titles

Micromechanical Modeling of Damage and Failure in Dual Phase Steels
p.2369

Influence of the Number of Tensile/Compression Cycles on the Fitting of a Mixed Hardening Material Model: Roll Levelling Process Case Study
p.2375

Multi-Scale Modeling of Microstructure Evolution Induced Anisotropy in Metals
p.2388

Test Procedures and Simulation Model Calibration Strategies for Nonlinear Stiffness Behavior of Joints in Large-Scale Structures
p.2400

Numerical Implementation and Finite Element Analysis of Anisotropic Hyperelastic Biomaterials - Influence of Fibers Orientation
p.2414

Numerical Modeling and Digital Image Correlation Strain Measurements of Coated Metal Sheets Submitted to Large Bending Deformation
p.2424

Modelling of Damage in Blanking Processes
p.2432

Influence of Anisotropic Yield Functions on Parameters of Yoshida-Uemori Model
p.2440

Validation of the Computer Simulation Process Applied to the Incremental Forming Process for the Evaluation of Strain Paths
p.2453

HomeKey Engineering MaterialsKey Engineering Materials Vols. 554-557Numerical Implementation and Finite Element...

Numerical Implementation and Finite Element Analysis of Anisotropic Hyperelastic Biomaterials - Influence of Fibers Orientation

Article Preview

Abstract:

Modeling anisotropic behavior of fiber reinforced rubberlike materials is actually of a great interest in many industrials sectors. Indeed, accurately description of the mechanical response and damage of such materials allows the increase of the lifecycle of these materials which generally evolve under several environment conditions. In this paper theoretical study and finite element analysis of anisotropic biomaterials is presented. The mechanical model adopted to achieve this study has been implemented into the finite element code Abaqus using an implicit scheme. This constitutive law has been utilized to perform some numerical simulations. The material parameters of the model have been determined by numerical calibration. One fiber family is considered in this work. Effects of the fiber orientation on the mechanical response and stiffness change of biomaterial is studied. Both the compressible and incompressible states have been taken into account. The results show firstly the capability of the model to reproduce the known results and that optimal fiber orientation can be found.

You might also be interested in these eBooks

The Current State-of-the-Art on Material Forming

Info:

Periodical:

Key Engineering Materials (Volumes 554-557)

Pages:

2414-2423

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.554-557.2414

Citation:

Cite this paper

Online since:

June 2013

Authors:

Rachid Djeridi, Mohand Ould Ouali

Keywords:

Anisotropic Hyperelasticity, Biomaterial, Fiber Reinforced Material, Jacobian Matrix, Numerical Implementation

Export:

RIS, BibTeX

Price:

Permissions:

Request Permissions

[1] R.M. Jones, Mechanics of Composite Materials, McGraw-Hill, Tokyo, 1975.

[2] R.M. Christensen, Mechanics of Composite Materials, Wiley, New York, 1979.

[3] R.F. Gibson, Principles of Composite Material Mechanics, McGraw-Hill, New York, 1994.

[4] Dorfmann, A., Ogden, R.W., A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber. Int. J.Solids Struct. 41(2004), 1855–1878.

DOI: 10.1016/j.ijsolstr.2003.11.014

[5] K.-D. Klee, E. Stein, Discretization in nonlinear continuum mechanics and comparison of some finite element algorithms, in: Proceedings of the Pressure Vessels and Piping Conference, Orlando, 1982.

[6] Rivlin, R.S., Saunders, D.W., Large elastic deformations of isotropic materials. Experiments on the deformation of rubber. Philos. Trans. Roy. Soc. A 243(1951) 251–288.

DOI: 10.1098/rsta.1951.0004

[7] Hart-Smith, L.J., Elasticity parameters for finite deformations of rubber-like materials. J.Appl. Math. Phys. 17(1966) 608–625.

[8] Ogden, R.W., Large deformation isotropic elasticity on the correlation of theory and experiment for incompressible rubber-like solids. Proc. Roy. Soc. Lond. A 326(1972) 565–584.

DOI: 10.1098/rspa.1972.0026

[9] Lambert-Diani, J., Rey, C., New phenomenological behaviour laws for rubbers and thermoplastic elastomers. Eur. J. Mech. A/ Solids 18(1999) 1027–1043.

DOI: 10.1016/s0997-7538(99)00147-3

[10] Boyce, M.C., Arruda, E.M., Constitutive models for rubber elasticity: a review. Rubber Chem. Technol. 73(2000) 504–523.

DOI: 10.5254/1.3547602

[11] C.Truesdell, W.Noll, The nonlinear field theories, in: S. Flugge (Ed.), Handbuch der Physik, Band III/3, Springer, Berlin, 1965.

[12] E.S. Suhubi, Thermoelastic solids, in: A.C. Eringen (Ed.), Continuum Physics II, Academic Press, New York.

[13] A.I. Lurie, Nonlinear theory of elasticity, in: J.D. Achenbach et al. (Eds.), North-Holland Series in Applied Mathematics and Mechanics, North-Holland, Amsterdam, 1990.

DOI: 10.1016/b978-0-444-87439-9.50001-2

[14] A.J.M. Spencer, Continuum theory of the mechanics of fibre-reinforced composites, CISM Courses and Lectures, No. 282,Springer, Wien, 1984.

[15] J. Schroder, Theoretische und algorithmische Konzeptezur phanomenologischen Beschreibung anisotropen Materialverhaltens, Dissertation, Universitat Hannover, 1996.

[16] J.A. Weiss, N.M. Bradley, S. Govindjee, Finite element implementation of incompressible, transversely isotropic hyperelasticity, Computer Methods in Applied Mechanics and Engineering 135 (1996) 107-128.

DOI: 10.1016/0045-7825(96)01035-3

[17] Holzapfel G.A., Gasser T., A viscoelastic model for fibre-reinforced composites at finite strains: continuum basis, computational aspects and applications. Comput. Meth. Appl. Mech. Eng. 190(2001) 4379–4403.

DOI: 10.1016/s0045-7825(00)00323-6

[18] Puso M.A., Weiss J., Finite element implementation of anisotropic quasilinear viscoelasticity. ASME J. Biomech. Eng. 120(1998) 162–170.

[19] Johnson G., Livesay, G., Woo, S., Rajagopal, K., A single integral finite strain viscoelastic model of ligaments and tendons. ASME J. Biomech. Eng. 118(1996) 221–226.

DOI: 10.1115/1.2795963

[20] Humphrey J., Mechanics of the arterial wall: review and directions. Crit. Rev. Biomed. Eng.23(1995)1–162.

DOI: 10.1615/critrevbiomedeng.v23.i1-2.10

[21] Pinsky P., Datye V., A microstructurally-based finite element model of the incised human cornea.J.Biomech.10(1991)907–922.

DOI: 10.1016/0021-9290(91)90169-n

[22] Hayes W.C., Mockros L.F., Viscoelastic constitutive relations for human articular cartilage. J. Appl. Physiol. 18(1971) 562–568.

[23] Pickett A.K., Johnson A.F., Numerical simulation of the forming process in long fibre reinforced thermoplastics, Composite Mat.Thech., V(1996) 233-242

[24] Kyriacou S.K., Schwab C., Humphrey J.D., Finite element analysis of nonlinear orthotropic hyperelastic membranes, Comput.Mech., 18(1996) 269-278

DOI: 10.1007/bf00364142

[25] J. Diana, M. Brieu, P. Gilormini, Observation and modelling of the anisotropic visco-hyperelastic behavior of a rubberlike material, Int. J. Solids Struct. 43 (2006) 3044–3056.

DOI: 10.1016/j.ijsolstr.2005.06.045

[26] A.E. Green, Large Elastic Deformations (Clarendon Press, Oxford, UK, 1970).

[27] A.J.M. Spencer, Continuum Theory of the Mechanics of Fibre-Reinforced Composites (Springer-Verlag, New York, 1984).

[28] J. Schröder, P. Neff, D. Balzani, A variational approach for materially stable anisotropic hyperelasticity, Int. J. Solids Struct. 42 (2005) 4352–4371.

DOI: 10.1016/j.ijsolstr.2004.11.021

[29] Y.C. Fung, K. Fronek, P. Patitucci, Pseudoelasticity of arteries and the choice of its mathematical expression, Am. J. Physiol. 237 (1979)H620–H631.

DOI: 10.1152/ajpheart.1979.237.5.h620

[30] G.A. Holzapfel, T.C. Gasser, R.W. Ogden, A new constitutive framework for arterial wall mechanics and a comparative study of material models, J. Elasticity 61 (2000) 1–48.

DOI: 10.1007/0-306-48389-0_1

[31] T.C. Gasser, R.W. Ogden, G.A. Holzapfel, Hyperelastic modelling of arterial layers with distributed collagen fibre orientations, J. R. Soc.Interface 3 (2006) 15–35.

DOI: 10.1098/rsif.2005.0073

[32] J.A. Weiss, B.N. Maker, S. Govindjee, Finite element implementation of incompressible, transversely isotropic hyperelasticity, Comp. Meth. Appl. Mech. Engng. 135 (1996) 107–128.

DOI: 10.1016/0045-7825(96)01035-3

[33] J.D. Humphrey, R.K. Strumph and F.C.P. Yin, Determination of a constitutive relation for passive myocardium, I. A new functional form, ASME J. Biomech. Engrg. 112 (1990) 333-339.

DOI: 10.1115/1.2891193

[34] J.D. Humphrey and F.C.P. Yin, On constitutive relations and finite deformations of passive cardiac tissue: I. A pseudostrain-energy approach, ASME J. Biomech. Engrg. 109 (1987) 298-304.

DOI: 10.1115/1.3138684

[35] M. Kaliske A formulation of elasticity and viscoelasticity for fibre reinforced material at small and finite strains Comput. Methods Appl. Mech. Engrg. 185 (2000) 225-243

DOI: 10.1016/s0045-7825(99)00261-3

[36] T.C. Doyle, J.L. Ericksen, Nonlinear elasticity, in: Advances in Applied Mechanics IV, Academic Press, New York, 1956.

[37] Itskov M., and Aksel N., A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function. International Journal of Solids and Structures,41(2004)3833-3848.

DOI: 10.1016/j.ijsolstr.2004.02.027

[38] J.C. Simo, T.J.R. Hughes, Computational Inelasticity, Interdisciplinary Applied Mathematics 7, Springer, New York, 1998.

[39] Weiss J., Maker B., Govindjee S., Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput. Meth. Appl. Mech. Eng. 135(1996) 107–128.

DOI: 10.1016/0045-7825(96)01035-3

[40] M.Timmel, M.Kaliske, S.Kolling Phenomenological and Micromechanical Modelling of Anisotropic effects in hyperelastic Materials, procedings of the 6th LS-DYNA Forum, Franctanhal Germany (2007) D-II, 1-24

[41] Gasser, T. C., G. A. Holzapfel, and R.W. Ogden,"Hyperelastic Modelling of Arterial Layers with Distributed Collagen Fibre Orientations," Journal of the Royal Society Interface,3(2006)15–35.

DOI: 10.1098/rsif.2005.0073

[42] Holzapfel G. A., T. C. Gasser, and R. W. Ogden, "A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models," Journal of Elasticity, 61(2000)1–48.

DOI: 10.1007/0-306-48389-0_1

[43] Holzapfel G.A., Gasser T., Stadler M., A structural model for the viscoelastic behaviour of arterial walls: continuum formulation and finite element analysis. Eur. J. Mech. A/Solids 21(2002) 441–463

DOI: 10.1016/s0997-7538(01)01206-2