Constitutive modeling for linear viscoelastic fiber-reinforced composites

In this paper, a micromechanics-based constitutive model is proposed for linear viscoelastic fiber-reinforced composites via a homogenization procedure in the time domain. Based on an additive decomposition, a general deformation is split into four simple deformations, namely, longitudinal tension/compression, transversely hydrostatic deformation, along-fiber shear and transverse shear. For each simple deformation, the mechanical response of the composite is reformulated utilizing the effective time-dependent relaxation functions and the effective referred elastic (time-independent) stresses, which are computed based on micromechanics. The constitutive equations for the linear viscoelastic fiber-reinforced composites are then derived through superposing the effective stresses for all the four simple deformations. The constitutive model has a simple form, which facilitates to study the effective mechanical behaviors of the composites in both the time and frequency domains. The representative volume element (RVE) models with different fiber volume fractions are created to simulate the effective viscoelastic behaviors of the fiber-reinforced composites. The comprehensive numerical simulation results reveal that the constitutive model can offer quite consistent effective mechanical responses with the finite element simulations. The experimental results in the literature are also employed to validate the constitutive model, and the findings show that the constitutive model can offer satisfactory prediction accuracy.