A new constitutive model for particle reinforced rubber-like composites with arbitrary particle contents

Existing meso-mechanical models for particle reinforced rubber-like composites (PRRLCs) can not well predict the mechanical behavior at high particle contents. Based on a differential effective medium (DEM) method as well as iterative techniques, a new constitutive model is proposed according to the continuum theory of finite deformation, which can predict the nonlinear large deformation response of PRRLCs with arbitrary particle contents, in contrast to existing meso-mechanical models only applicable for PRRLCs with a small particle content. An iterative process to form a PRRLC with a given particle content is considered, in each step of which an infinitesimal content of particles is added into an effectively homogeneous rubber-like medium (initially as the pure rubber-like matrix) to obtain a composite with dilute fillers, and such a composite is homogenized to act as the effective rubber-like medium in the next step. An incrementally effective constitutive relation of the PRRLC can be achieved when the total content of added particles reaches the given value. The present model is used to predict stress-strain responses of PRRLCs with different contents of particles under uniaxial and equi-biaxial tensions. Theoretical predictions at either low or high particle content exhibit good agreements with experimental data and numerical results, and the underestimation of mechanical responses at high particle contents in existing meso-mechanical models for PRRLCs can be well overcome. These results prove the accuracy and reliability of the new model, which should be of guiding value for optimal designs of flexible composites with desirable mechanical performances.