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Hyperelastic homogenized law for reinforced elastomer at finite strain with edge effects

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Summary

This paper investigates the static microstructural effects of periodic hyperelastic composites at finite strain. In the region far enough from the boundaries, the classic two-scale asymptotic homogenization process is used with the assumption of near incompressiblity of the elastomer. An application of this approach is given using periodically stratified composites. This homogenized evolution law is determined on a prescribed macroscopic deformation gradient. An iterative Newton-Raphson's scheme is used in solving this problem. The behavior of an elastomer/steel composite is analysed when elastomer and steel are respectively assumed to obey the Mooney-Rivlin and StVenant-Kirchhoff laws. We then study the validity of simplified formulations of this homogenized law obtained by approximating the local first Piola-Kirchhoff tensor with a Taylor-Young's expansion. In the case of neo-Hookean constituents, we show that the continuum homogenized model can be determined analytically. Since the classic asymptotic is not valid in the neighbourhood of the boundaries, we modify the micromechanical quantities in such a region by introducing a boundary layer expansion. In this way, the effects of respectively only one boundary and two boundaries are treated.

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  1. E. Pruchnicki

    Present address: Laboratoire de Mécanique de Lille CNRS URA 1441 Ecole Centrale de Lille, B. P. 48, F-59651, Villeneuve d'Ascq Cedex, France

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    Pruchnicki, E. Hyperelastic homogenized law for reinforced elastomer at finite strain with edge effects. Acta Mechanica 129, 139–162 (1998). https://doi.org/10.1007/BF01176742

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    • DOI: https://doi.org/10.1007/BF01176742

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