Computational evaluation of viscoelastic effective properties for composite materials via finite element method

With practical relevance in structural design, passive vibration control, and polymer composite development, predicting time-dependent viscoelastic properties has become increasingly important. This work proposes a finite element (FE)-based homogenization methodology to determine effective viscoelastic coefficients of multiphase composites using representative volume elements (RVEs) of unidirectional cells. Periodic boundary conditions (PBCs) and multiple loading scenarios were applied to extract time-dependent constitutive responses, assuming linear isotropic viscoelasticity for each phase. A virtual stress relaxation test was implemented and validated against analytical solutions from the asymptotic homogenization method (AHM) for square RVEs with circular fibers and volume fractions from 10% to 40%, showing relative differences below 1% over 60 s. Two loading histories, step strain and ramp strain, were analyzed to assess strain-rate effects, with ramp responses converging to step-loading results at long times (t > 25 s). Additional simulations on cross-ply RVEs (up to 70% fiber volume fraction) demonstrated the model’s ability to capture orthotropic and shear-dominated viscoelastic behavior. The proposed framework provides a robust numerical tool for predicting effective viscoelastic properties, supporting advanced composite design and optimization.