We propose a microstructure inspired approach for rubberlike materials. These materials are modeled as a mixture of an elastic matrix and a damageable fraction, assigned by a distribution of links with variable activation and rupture thresholds. In particular, the hysteretic behavior is described by considering the recross-linking effect under unloading. Based on the physical interpretation of the material distribution and parameters of the model proposed here, we are able to obtain an effective and numerically efficient three-dimensional, nonlinear damage and hysteresis model for rubberlike solids. To demonstrate the feasibility of this model in reproducing complex deformation histories, we performed cyclic uniaxial and shear tests on ethylene-propylene diene monomer specimens. A comparison with diffusely adopted models clearly demonstrates the advantages of the proposed approach. In particular, we show the possibility, crucial for real applications, of describing a completely different deformation history based on the material parameters calibration on the only uniaxial experiment. (C) 2018 The Society of Rheology.