Neo-Hookean fiber-reinforced composites in finite elasticity |
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Authors: | G. deBotton I. Hariton E.A. Socolsky |
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Affiliation: | The Pearlstone Center for Aeronautical Studies, Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva, 84105, Israel |
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Abstract: | The response of a transversely isotropic fiber-reinforced composite made out of two incompressible neo-Hookean phases undergoing finite deformations is considered. An expression for the effective energy-density function of the composite in terms of the properties of the phases and their spatial distribution is developed. For the out-of-plane shear and extension modes this expression is based on an exact solution for the class of composite cylinder assemblages. To account for the in-plane shear mode we incorporate an exact result that was recently obtained for a special class of transversely isotropic composites. In the limit of small deformation elasticity the expression for the effective behavior agrees with the well-known Hashin-Shtrikman bounds. The predictions of the proposed constitutive model are compared with corresponding numerical simulation of a composite with a hexagonal unit cell. It is demonstrated that the proposed model accurately captures the overall response of the periodic composite under any general loading modes. |
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Keywords: | Hyperelastic composites Nonlinear composites Fiber-reinforced composites Finite elasticity Effective properties Constitutive law Micromechanics |
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