Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T05:32:41.614Z Has data issue: false hasContentIssue false
  • English
  • Français

Macroscopic behavior of a reinforced elastomer:micromechanical modelling and validation

Published online by Cambridge University Press:  17 August 2007

Vanessa Bouchart ,
Mathias Brieu ,
Djimedo Kondo  and
Moussa Naït Abdelaziz
Vanessa Bouchart
Affiliation:
Laboratoire de Mécanique de Lille, Boulevard Paul Langevin, 59655 Villeneuve d'Ascq, France
Mathias Brieu
Affiliation:
Laboratoire de Mécanique de Lille, Boulevard Paul Langevin, 59655 Villeneuve d'Ascq, France
Djimedo Kondo
Affiliation:
Laboratoire de Mécanique de Lille, Boulevard Paul Langevin, 59655 Villeneuve d'Ascq, France
Moussa Naït Abdelaziz
Affiliation:
Laboratoire de Mécanique de Lille, Boulevard Paul Langevin, 59655 Villeneuve d'Ascq, France
Get access

Abstract

In the present study, we propose an evaluation of a non-linear homogenization model applied to hyperelastic composites having random microstructure. This modelling approach consists in a 3D implementation of the secondorder method introduced by Ponte Castañeda & Tiberio [1]. We first recall the basic principles of this method. Then, we investigate a composite made up of an hyperelastic matrix reinforced by spherical deformable or rigid particles.Computational issues of the micromechanical model are discussed and some obtained results allowto demonstrate the reinforcement effect of the particles. In order to provide a rigorous evaluation of the methodology, finite elements computations, on an unit cell, are performed and compared to the predictions of the model. Finally, a confrontation with experimental results is provided.

Keywords

Non-linear homogenizationhyperelasticitysecond order methodelastomersfinite deformationsHomogénéisation non-linéairehyperélasticitéméthode du second ordreélastomèresgrandes déformations
Type
Research Article
Information
Mechanics & Industry , Volume 8 , Issue 3: Congrès Mécanique de Grenoble , May 2007 , pp. 199 - 205
Copyright
© AFM, EDP Sciences, 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ponte Castañeda, P., Tiberio, E., A second order homogenization method in finite elasticity and applications to black-filled elastomers, J. Mech. Phys. Solids 48 (2000) 1389–1411 CrossRef
Brieu, M., Devries, F., Homogénéisation de composites élastomères, Méthode et algorithme, Comptes Rendus de l'Académie des Sciences, Series IIB, Mechanics-Physics-Chemistry-Astronomy 326 (1998) 379–384
Lahellec, N., Mazerolle, F., Michel, J.C., Second order estimate of the macroscopic behavior of periodic hyperelastic composites: theory and experimental validation, J. Mech. Phys. Solids 52 (2004) 27–49 CrossRef
Ponte Castañeda, P., Exact second order estimates for the effective mechanical properties of non-linear composite materials, J. Mech. Phys. Solids 44 (1996) 827–862 CrossRef
Lopez-Pamies, O., Ponte Castañeda, P., On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations, II- Application to cylindrical fibers, J. Mech. Phys. Solids 54 (2006) 831–863 CrossRef
Hill, R., Convexity conditions and existence theorems in non-linear elasticity, Arch. Rat. Mech. Anal. 63 (1972) 337–403
Levin, V.M., Thermek expansion coefficients of heterogeneous materials, Mekh. Tverd. Tela 2 (1967) 83–94
W.H. Press, et al., Numerical recipes in Fortran, The art of scientific computing, 2nd Edition, Cambridge University Press, 1992
R.W. Ogden, Non linear elastic deformations, Dover Publications Inc., New York, 1984
Doghri, I., Ouaar, A., Homogenization of two-phase elasto-plastic composite materials and structures study of tangent operators, cyclic plasticity and numerical algorithms, Inter. J. Solids and Structures 40 (2003) 1681–1712 CrossRef
Lambert-Diani, J., New, C. Rey phenomenological behavior laws for rubbers and thermoplastics elastomers, Eur. J. Mech., A, Solids 18 (1999) 1027–1043 CrossRef
R.P. Brown, Physical testing of Polymer, 3rd Edition, Chapman and Hall, 1984