Comptes Rendus
Second-order estimates for the large-deformation response of particle-reinforced rubbers
Comptes Rendus. Mécanique, Volume 331 (2003) no. 1, pp. 1-8.

This paper presents the application of a recently proposed ‘second-order’ homogenization method (J. Mech. Phys. Solids 50 (2002) 737–757) to the estimation of the effective behavior of hyperelastic composites subjected to finite deformations. The main feature of the method is the use of ‘generalized’ secant moduli that depend not only on the phases averages of the fields, but also on the phase covariance tensors. The use of the method is illustrated in the context of particle-, or fiber-reinforced elastomers and estimates analogous to the well-known Hashin–Shtrikman estimates for linear-elastic composites are generated. The new estimates improve on earlier estimates (J. Mech. Phys. Solids 48 (2000) 1389–1411) neglecting the use of fluctuations. In particular, the new estimates, unlike the earlier ones, are capable of recovering the exact incompressibility constraint when the matrix is also taken to be incompressible.

Cet article présente l'application d'une méthode d'homogénéisation récente, dite de deuxième ordre (J. Mech. Phys. Solids 50 (2002) 737–757), afin d'estimer le comportement effectif de matériaux composites hyperélastiques sujets à des grandes déformations. La principale caractéristique de cette méthode est l'utilisation d'un module sécant généralisé par phase qui dépend non seulement des moyennes des champs par phase mais aussi des tenseurs de covariance des fluctuations des phases. L'utilisation de cette procédure est illustrée dans le cas particulier d'élastomères renforcés à particules ou à fibres. Ces nouvelles estimations généralisent celles bien connues de Hashin–Shtrikman obtenues pour des composites élastiques linéaires et améliorent certaines estimations décrites antérieurement (J. Mech. Phys. Solids 48 (2000) 1389–1411) qui, elles, négligeaient l'existence de fluctuations des champs. En particulier, ces nouvelles estimations, contrairement a celles étudiées précédemment, sont capables d'établir la contrainte exacte d'incompressibilité lorsque la matrice est elle aussi supposée incompressible.

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Accepted:
Published online:
DOI: 10.1016/S1631-0721(03)00021-4
Keywords: Computational solid mechanics, Homogenization, Finite deformations, Elastomers
Mot clés : Mécanique des solides numérique, Homogénéisation, Déformations, Matériaux élastomères

Oscar Lopez-Pamies 1; Pedro Ponte Castañeda 1

1 Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA
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Oscar Lopez-Pamies; Pedro Ponte Castañeda. Second-order estimates for the large-deformation response of particle-reinforced rubbers. Comptes Rendus. Mécanique, Volume 331 (2003) no. 1, pp. 1-8. doi : 10.1016/S1631-0721(03)00021-4. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00021-4/

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