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Second-order estimates for the large-deformation response of particle-reinforced rubbersEstimations homogénéisées pour le comportement mécanique des caoutchoucs renforcés en grandes déformations
Authors:Oscar Lopez-Pamies  Pedro Ponte Castañeda
Institution:Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA
Abstract: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. To cite this article: O. Lopez-Pamies, P. Ponte Castañeda, C. R. Mecanique 331 (2003).
Keywords:Computational solid mechanics  Homogenization  Finite deformations  Elastomers  Mécanique des solides numérique  Homogénéisation  Déformations  Matériaux élastomères
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