A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications

This paper presents a viscoelastic model for the fully three-dimensional st ress and deformation response of fiber-reinforced composites that experienc e finite strains. The composites are thought to be (soft) matrix materials which are reinforced by two families of fibers so that the mechanical prope rties of the composites depend on two fiber directions. The relaxation and/ or creep response of each compound of the composite is modeled separately a nd the global response is obtained by an assembly of all contributions. We develop novel closed-form expressions for the fourth-order elasticity tense r (tangent moduli) in full generality. Constitutive models for orthotropic, transversely isotropic and isotropic hyperelastic materials at finite stra ins with or without dissipation are included as special cases. In order to clearly show the good performance of the constitutive model, we present 3D and 2D numerical simulations of a pressurized laminated circular tube which shows an interesting 'stretch inversion phenomenon' in the low pressure do main. Numerical results are in good qualitative agreement with experimental data and approximate the observed strongly anisotropic physical response w ith satisfying accuracy. A third numerical example is designed to illustrat e the anisotropic stretching process of a fiber-reinforced rubber bar and t he subsequent relaxation behavior at finite strains. The material parameter s are chosen so that thermodynamic equilibrium is associated with the known homogeneous deformation state. (C) 2001 Elsevier Science B.V. All rights r eserved.