A fractional order elastoplastic constitutive model for rubber granular mixtures

This study develops a fractional-order elastoplastic constitutive model for rubber granular mixtures (RGMs). Within the critical state framework, a shift stress characterises the nonlinear CSL in space and its dependence on rubber content. A Riemann-Liouville fractional derivative determines the plastic flow direction, yielding a non-associated flow rule without an independent plastic potential parameter. Based on this formulation, a state-dependent dilatancy relation is derived to capture both volumetric contraction and dilation during shearing. Combined with bounding surface plasticity, the model reproduces the response of RGMs under complex stress paths. The results demonstrate accurate predictions of volumetric deformation, hardening/softening response, and stress-state dependent behaviors of RGMs (e.g. rubber-solid waste mixtures, and sand-rubber mixtures) under different confining pressures, loading paths, and rubber contents.