Constitutive modeling of viscoelastic fiber-reinforced composites at finite deformations

In this paper, a constitutive model is proposed for viscoelastic fiber-reinforced composites at finite deformations. A homogenization framework is constructed for the finite-strain viscoelastic composites, which decomposes the Helmholtz free energy density function of each constituent into volumetric, isochoric and dissipative parts. An effective evolution rule is developed to govern the effective viscous responses of each composite phase. The long-term (purely elastic) behaviors of both the matrix and the fibers are characterized by the incompressible neoHookean model, and the elastic free energy density functions of the matrix and the fibers are derived based on a specific multiplicative decomposition of the deformation gradient. The constitutive model for the viscoelastic fiber-reinforced composites is constructed by combining all the contributions of the components. Representative volume element (RVE) models for unit cells of the composite with various fiber volume fractions are then used to perform numerical simulations based on the proposed constitutive model. The simulation results show that the constitutive model can accurately predict the effective viscoelastic behaviors of fiber-reinforced composites at finite deformations. Furthermore, the steady-state dynamic behaviors of the RVE models are examined and the numerical results illustrate that the constitutive model can capture the responses of the viscoelastic fiber-reinforced composites under oscillatory loadings. In addition, the proposed constitutive model can successfully capture the viscoelastic behaviors of composites with randomly distributed fibers.