Improved Carroll's hyperelastic model considering compressibility and its finite element implementation

Abstract

In engineering component design, material models are increasingly used in finite element simulations for an expeditious and less costly analysis of the design prototypes. As such, researchers strive to formulate models that are less complex, robust, and accurate. In the realm of hyperelastic materials, phenomenological-based Carroll's model is highly promising due to its simplicity and accuracy. This work proposes its further improvement by modifying the strain energy density function to comply with the restriction that it should vanish at reference configuration and adding a compressible term to capture the practical behavior of elastomeric materials and to avoid numerical problems during finite element implementation. The model constants for both the original and the modified versions were obtained by fitting their respective expressions to the classical Treloar's experimental data using the Levenberg–Marquardt algorithm. The modified model was implemented using Abaqus CAE 2016 via a vectorized user material (VUMAT) subroutine. Comparisons of the model predictions with Treloar's experimental data demonstrated the superiority of the modified version particularly in the equibiaxial loading mode. Moreover, the simulated and the experimentally observed behavior agreed to a great accuracy thus making the modified model suitable for simulating the loading response of components fabricated of elastomeric materials. In this work, the Carroll's hyperelastic model strain energy density expression is modified to comply with the mathematical restriction that it should vanish at the undeformed configuration. Furthermore, a compressible term is added to capture the practical behavior of elastomers and to avoid numerical problems during finite element implementation. Numerical and finite element predictions are compared with classical experimental data upon which the modified model demonstrated superior predictive capabilities particularly in the equibiaxial loading mode.