A phenomenological constitutive model for predicting both the moderate and large deformation behavior of elastomeric materials

Constitutive models that describe nonlinear elastic mechanical behavior are indispensable in the design of engineering components fabricated of elastomeric materials. The main drawbacks of the existing models include complexities in calibrating the model to experimental data and erroneous descriptions of multi-axial response. These challenges motivate researchers to continually formulate new or improved models with better predictive capabilities. In this work, we propose a new polynomial-type phenomenological model with linear and logarithmic dependence on the first and the second invariants respectively. Model parameters were obtained by utilizing the Levenberg-Marquardt algorithm to fit the model expression to the strain energy density data calculated from the experimental data of uniaxial tension loading. The predictive performance of our proposed model in comparison to that of three popular existing models was determined by utilizing three sets of classical experimental data from the literature with varying deformation ranges. Quantities used to relate the predicted and the experimental data include the coefficient of determination, relative errors, and average relative error (for overall behavior). The computations demonstrated that the proposed model exhibits superior predictive capabilities for the entire deformation range whilst requiring minimum efforts in obtaining its parameters, thus, exhibits the desirable features of a phenomenological hyperelastic model.

Automated summary

A new polynomial-type phenomenological model was proposed in this study to describe nonlinear elastic mechanical behavior with linear and logarithmic dependence on the first and second invariants. The model parameters were obtained using the Levenberg-Marquardt algorithm and demonstrated superior predictive capabilities for the entire deformation range.