An alternative constitutive model for elastic particle-reinforced hyperelastic matrix composites with explicitly expressed Eshelby tensor

Herein, an alternative theoretical model is developed based on a two-phase Mori–Tanaka method within the framework of finite deformation continuum theory, in order to characterize the nonlinear mechanical behavior of particle-reinforced hyperelastic matrix composites (PRHMCs). The equivalent inclusion problems of a hyperelastic medium (HEM) and a reference elastic medium (REM) are analyzed, both of which have the same configuration and elastic property. Based on the equivalence between incremental stress fields in the HEM and REM, the Eshelby tensor for large deformation cases can be explicitly expressed as a closed-form function depending on the elastic modulus and tangent modulus of the hyperelastic matrix and the classical Eshelby tensor for linearly elastic composites. The Eshelby tensor for hyperelastic composites can be easily determined, without requiring time-consuming numerical ellipsoidal integrals in existing meso-mechanical models for PRHMCs. Incremental constitutive relations depending on the material tangent modulus are adopted to describe the mechanical behaviors of hyperelastic matrix and elastic particles. An incrementally effective constitutive relation of PRHMCs is finally achieved with a homogenization procedure, which is used to well reproduce the stress-strain responses of several types of particle-reinforced hyperelastic matrix composites in uniaxially and biaxially tensile experiments. These results demonstrate the feasibility and convenience of the present model not only in predicting the mechanical behavior of particle-reinforced elastomers, but also in guiding the design of advanced flexible composites with desirable mechanical performances.