A viscoelastic model for particle-reinforced composites in finite deformations

In this paper, we propose a constitutive model for viscoelastic particle-reinforced composites undergoing finite deformations based on the homogenization framework developed in Chen et al. (Chen et al. in Mechanics of Materials 131 (2019), 102–112), where the effective free energy density function of each composite phase was decomposed into the corresponding volumetric, isochoric and dissipative parts. The long-term (pure elastic) behaviors of both the matrix and particles are governed by the incompressible neo-Hookean models. The effective elastic free energy density functions of the two phases are computed based on the homogenization method in Guo et al. (Guo et al. in Mechanics of Materials 70 (2014), 1–17). The average stress of each phase is then derived using the homogenization framework. The viscoelastic constitutive model of the particle-reinforced composites is obtained by combing the contributions of the two phases. Cubic units with 27 non-overlapping randomly distributed same-sized spheres are created as the representative volume element (RVE) models of the particle-reinforced composites. The finite element simulations of various deformations with different strain rates are performed for the RVE models of different particle volume fractions and material parameters to validate the constitutive model. The simulation results show that the constitutive model can well estimate the effective viscoelastic responses of the particle-reinforced composites undergoing finite deformations.