A constitutive model for particle filled non-Gaussian rubber-like composites

Particle-filled non-Gaussian rubber-like composites (PFNGRCs) always exhibit bimodal stress-strain responses with a stress upturn at large deformation. Such a bimodal mechanical behavior at a high particle content is difficult to be accurately predicted by existing constitutive models due to the use of a linear comparison composite (LCC) concept and an overlook of the non-uniform matrix deformation around particles. Based on a nonlinear comparison composite (NCC) with non-uniform matrix deformations, a novel constitutive model is proposed in this paper to predict bimodal mechanical behaviors of PFNGRCs with arbitrary particle contents. A particle filled neo-Hookean rubber-like composite is introduced as the NCC system, in which the neo-Hookean matrix around particles is divided into multiple layers with varying deformations, and the strain energy density function of the matrix is determined according to the equivalent effective tangent moduli in NCC and PFNGRC systems. The incremental effective constitutive relation of such a NCC is further achieved with a differential effective medium (DEM) scheme, which could be directly used to describe the bimodal mechanical behavior of PFNGRCs. The present model can well reproduce experimental data of uniaxially and equi-biaxially tensile responses of PFNGRCs with either low or high particle contents, showing an apparent advantage over existing constitutive models, especially in accurately characterizing the stress upturn behavior at large deformation. The theoretical tool provided herein should be useful for the design of strong and flexible composite materials.