An I₂-enhanced hyperelastic model to capture secondary strain-stiffening

Soft elastomers, undergoing large deformation, are prevalent in broad class of engineering applications ranging from continuum robotics to artificial skin. Hyperelastic material models are commonly employed to predict the mechanical response of such elastomers. Unstable deformation is often seen when soft elastomer components are subjected to extreme loads. A phenomenological hyperelastic model is formulated in this work to capture one of the experimentally found instabilities in the deformation exhibited by certain class of soft elastomers, namely the secondary strain-stiffening . The issues that restrict the existing invariant based hyperelastic models from reproducing the secondary strain-stiffening are addressed by combining the salient features of Knowles model and the exponent of the second invariant I ₂ of the left Cauchy-Green stretch tensor (named Knowles-Exp-Ln model). The capability of the developed model is demonstrated by comparing the model predictions with the results of balloon-inflation experiment. Further, the behavior of the Knowles-Exp-Ln model is analytically explored in the case of other instability-prone homogeneous tests such as the inflation of thin cylindrical shells and the expansion of the spherical cavity. Practical guidelines for the estimation of relevant material parameters are also given, considering Baker-Ericksen inequality. The results obtained in this work suggest that the proposed hyperelastic model captures, apart from usually observed limit-point instabilities, the secondary strain-stiffening accurately. The model can be readily used to solve the boundary value problems involving the particular class of elastomers that experience the secondary strain-stiffening as well as to train surrogate models over a wide range of unstable deformations.