Constitutive modelling of strain-induced crystallisation in rubber

The phenomenon of strain-induced crystallisation (SIC) is still challenging nowadays in the context of material modelling. The focus of the presented constitutive equations is to depict the stress response of unfilled natural rubber when uni-axially stretched. Here, the capture of the hysteresis is of highest interest, where SIC is the main hysteresis source for unfilled natural rubber. he paper is based on a thermomechanical approach presented in former publications which uses an additive split of the hybrid free energy. The model uses a multiphase approach, i.e. one rubber fibre includes three different contributions: a crystalline phase and an amorphous phase which is compounded by a crystallisable amorphous part and a noncrystallisable amorphous part. Thus, different hyperelastic material models for each part are used for the formulation of the stress and the strain energy, which are an essential part of the first order differential equation of crystallinity. The presented model is based on the concept of representative directions and is therefore formulated one dimensional. The model is validated via the time dependence of the material in two ways; stress relaxation simulations and simulations of uniaxial cycles with varying stretch rate. The constitutive equations are physically and chemically motivated and ensure the thermodynamic consistency.