An approximate method to predict the mechanical properties of small volume fraction particle-reinforced composites with large deformation matrix

The aim of this paper is to propose an approximate homogenization method for deriving the effective strain energy density function of small volume fraction particle-reinforced hyperelastic matrix composites. This method is inspired by the finite element (FE) simulation of a single-particle representative volume element (RVE) model, in which an incompressible Yeoh constitutive model is used to describe the mechanical behavior of the matrix and the particle is regarded as a rigid material. According to the FE results, the RVE can be partitioned into different regions with uniform strain distributions, and then, the equivalent strain energy density function of the whole composite can be calculated based on a volume averaging treatment. With the new method, the stress–strain response of a mica particle-filled rubber matrix composite under uniaxial tension is theoretically predicted, and it shows a good agreement with both experimental measurements and numerical calculations, especially when the particle volume fraction is relatively small. Due to the simple derivation and concise formulation of the strain energy density function, the present method should be of practical value for engineering use in predicting the large deformation behavior of hyperelastic composites.