Predictive stress-stretch models of elastomers up to the characteristic flex

Non-linear stress-stretch characteristic curves of elastomers are described by means of constitutive equations derived from hyperelastic models. Despite their descriptive ability, these models are not intrinsically predictive a priori, due to their parametric nature, which requires data fitting a posteriori. To overcome this limitation, analytical laws with inherent predictive ability are needed. Here, we present a simple predictive uniaxial law and a simple predictive hyperelastic model. They move from the experimental evidence that during uniaxial tensile loading of different soft elastomers the true stress has a linear dependence on the engineering strain, up to the characteristic oblique flex that shows up in the nominal stress vs engineering strain plot. We show that this behaviour is captured by a predictive hyperbolic stress-stretch law that requires just a single material constant (the Young’s modulus), determinable from few data at very low strains. Also, we formulate a predictive hyperelastic constitutive model, able to accurately describe the stress-stretch curve up to the flex, still by using the initial elastic modulus only. The paper contextualizes the predictive law and model within the field of hyperelastic modelling and presents a comparative experimental validation on three types of elastomers, currently used for electromechanically active polymer devices known as dielectric elastomer transducers. We show that the accuracy of the new predictive models is higher than that of the neo-Hookean equation, and we discuss the potentialities, as well as the limitations, of the derived laws as tools possibly useful to designers.