Comptes Rendus
An homogenization-based hyperelastic damage model: formulation and application to an EPDM/PP composite
Comptes Rendus. Mécanique, Volume 336 (2008) no. 5, pp. 471-479.

The present Note concerns the formulation, implementation and a first application of a micromechanically based hyperelastic damage model. The approach is based on the second order homogenization method proposed by Lopez-Pamies and Ponte Castañeda (2000) for hyperelastic composites and recently developed by Lopez-Pamies and Ponte Castañeda (2007) in the case of porous elastomers. We first implement the method and proceed to its verification by comparison with Finite Element simulations on a unit cell. Taking advantage of this validation and by using standard thermodynamics arguments, we propose an hyperelastic damage model founded on voids growth phenomena. Finally, we provide an example of validation of the model by comparison with experimental data obtained on an EPDM/PP composite.

La présente Note concerne la formulation, la mise en oeuvre et une application d'un modèle micromécanique d'endommagement dédié aux matériaux hyperélastiques. L'approche suivie repose sur la méthode d'homogénéisation du second ordre proposée par Lopez-Pamies et Ponte Castañeda (2000) pour les composites hyperélastiques et récemment développée par Lopez-Pamies et Ponte Castañeda (2007) dans le cas des élastomères poreux. On met d'abord en oeuvre le modèle dans le cas de milieux poreux et on procède à sa vérification par comparaison à des simulations éléments finis sur une cellule de base. S'appuyant ensuite sur cette validation numérique et utilisant des arguments thermodynamiques standards, on propose un modèle d'endommagement hyperélastique fondé sur des mécanismes de croissance de cavités. Enfin, on fournit un exemple de validation du modèle par comparaison avec des données expérimentales obtenues sur un composite EPDM/PP.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2008.02.001
Keywords: Damage, Hyperelasticity, Porous materials, Micromechanics, Nonlinear homogenization, Numerical verification, Experimental validation
Mot clés : Endommagement, Hyperélasticité, Matériaux poreux, Micromécanique, Homogénéisation non linéaire, Vérification numérique, Validation expérimentale

Vanessa Bouchart 1; Mathias Brieu 1; Djimedo Kondo 1; Moussa Naït-Abdelaziz 1

1 Laboratoire de mécanique de Lille–UMR CNRS 8107, boulevard Paul-Langevin, 59655 Villeneuve d'Acsq cedex, France
@article{CRMECA_2008__336_5_471_0,
     author = {Vanessa Bouchart and Mathias Brieu and Djimedo Kondo and Moussa Na{\"\i}t-Abdelaziz},
     title = {An homogenization-based hyperelastic damage model: formulation and application to an {EPDM/PP} composite},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {471--479},
     publisher = {Elsevier},
     volume = {336},
     number = {5},
     year = {2008},
     doi = {10.1016/j.crme.2008.02.001},
     language = {en},
}
TY  - JOUR
AU  - Vanessa Bouchart
AU  - Mathias Brieu
AU  - Djimedo Kondo
AU  - Moussa Naït-Abdelaziz
TI  - An homogenization-based hyperelastic damage model: formulation and application to an EPDM/PP composite
JO  - Comptes Rendus. Mécanique
PY  - 2008
SP  - 471
EP  - 479
VL  - 336
IS  - 5
PB  - Elsevier
DO  - 10.1016/j.crme.2008.02.001
LA  - en
ID  - CRMECA_2008__336_5_471_0
ER  - 
%0 Journal Article
%A Vanessa Bouchart
%A Mathias Brieu
%A Djimedo Kondo
%A Moussa Naït-Abdelaziz
%T An homogenization-based hyperelastic damage model: formulation and application to an EPDM/PP composite
%J Comptes Rendus. Mécanique
%D 2008
%P 471-479
%V 336
%N 5
%I Elsevier
%R 10.1016/j.crme.2008.02.001
%G en
%F CRMECA_2008__336_5_471_0
Vanessa Bouchart; Mathias Brieu; Djimedo Kondo; Moussa Naït-Abdelaziz. An homogenization-based hyperelastic damage model: formulation and application to an EPDM/PP composite. Comptes Rendus. Mécanique, Volume 336 (2008) no. 5, pp. 471-479. doi : 10.1016/j.crme.2008.02.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.02.001/

[1] R.W. Ogden; D.G. Roxburgh A pseudo-elastic model for the Mullins effect in filled rubber, Proc. R. Soc. Lond. A, Volume 455 (1999), pp. 2861-2878

[2] S. Govindjee; J.C. Simo A micro-mechanically based continuum damage model for carbon black-filled rubbers incorporating Mullins effect, J. Mech. Phys. Solids, Volume 39 (1991) no. 1, pp. 87-112

[3] J. Li; D. Mayau; V. Lagarrigue A constitutive model dealing with damage due to cavity growth and the Mullins effect in rubber-like materials under triaxial loading, J. Mech. Phys. Solids, Volume 56 (2008) no. 3, pp. 953-973

[4] M. Brieu; F. Devries Micro-mechanical approach and algorithm for the study of damage appearance in elastomer composites, Compos. Struc., Volume 46 (1999) no. 4, pp. 309-319

[5] P. Ponte Castañeda Exact second order estimates for the effective mechanical properties of non linear composite materials, J. Mech. Phys. Solids, Volume 44 (1996), pp. 827-862

[6] P. Ponte Castañeda; E. Tiberio A second order homogenization method in finite elasticity and applications to black-filled elastomers, J. Mech. Phys. Solids, Volume 48 (2000), pp. 1389-1411

[7] N. Lahellec; F. Mazerolle; J.C. Michel Second order estimate of the macroscopic behavior of periodic hyperelastic composites: theory and experimental validation, J. Mech. Phys. Solids, Volume 52 (2004), pp. 27-49

[8] O. Lopez-Pamies; P. Ponte Castañeda Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: I Analysis, J. Mech. Phys. Solids, Volume 55 (2007), pp. 1677-1701

[9] V. Bouchart; M. Brieu; D. Kondo; M. Naït-Abdelaziz Macroscopic behavior of a reinforced elastomer: micromechanical modelling and validation, Mécanique & Industries, Volume 8 (2007), pp. 199-205

[10] R. Hill Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal., Volume 63 (1972), pp. 337-403

[11] P. Ponte-Castañeda; P. Suquet Nonlinear composites, Adv. Appl. Mech., Volume 34 (1998), pp. 171-302

[12] V.M. Levin Thermek expansion coefficients of heterogeneous materials, Mekh. Tverd. Tela, Volume 2 (1967), pp. 83-94

[13] Z. Hashin; S. Shtrikman On some variational principles in anisotropic and homogeneous elasticity, J. Mech. Phys. Solids, Volume 10 (1962), pp. 335-342

[14] W.H. Press et al. Numerical Recipes in Fortran, The Art of Scientific Computing, Cambridge University Press, 1992

[15] J. Llorca; J. Segurado Three-dimensional multiparticle cell simulations of deformation and damage in sphere-reinforced composites, Mater. Sci. Eng. A, Volume 365 (2004), pp. 267-274

[16] J. Lambert-Diani; C. Rey New phenomenological behavior laws for rubbers and thermoplastics elastomers, Eur. J. Mech A Solids, Volume 18 (1999), pp. 1027-1043

[17] M. Brieu, 1999. Homogénéisation et endommagement des composites élastomères par techniques de calcul parallèle. Thèse de doctorat, École normale supérieure de Cachan

[18] V. Bouchart, 2007. Etude expérimentale et modélisation micromécanique du comportement et de l'endommagement des élastomères renforcés. Thèse de doctorat, Université des Sciences et Technologies de Lille

Cited by Sources:

Comments - Policy