A Comparative Study of Several Material Models for Prediction of Hyperelastic Properties: Application to Silicone‐Rubber and Soft Tissues

TLDR

Accurate constitutive modeling is essential for analyzing the mechanical behavior of solids, particularly soft tissues whose nonlinear properties necessitate hyperelastic models that depend on experimentally determined parameters. The study aims to evaluate several hyperelastic models—including Martins's model for the first time—using a computational/experimental approach on soft tissues under uniaxial tension, and to identify which models to adopt in future analyses. Seven hyperelastic models were calibrated by inverse methods with a Levenberg–Marquardt algorithm on soft tissues and silicone‑rubber under uniaxial tension, and the fit quality of stress–strain curves was assessed. Martins's hyperelastic model successfully fits experimental data, demonstrating its applicability to soft tissues for the first time.

Abstract

Abstract: The correct modelling of constitutive laws is of critical importance for the analysis of mechanical behaviour of solids and structures. For example, the understanding of soft tissue mechanics, because of the nonlinear behaviour commonly displayed by the mechanical properties of such materials, makes common place the use of hyperelastic constitutive models. Hyperelastic models however, depend on sets of variables that must be obtained experimentally. In this study the authors use a computational/experimental scheme, for the study of the nonlinear mechanical behaviour of biological soft tissues under uniaxial tension. The material constants for seven different hyperelastic material models are obtained via inverse methods. The use of Martins's model to fit experimental data is presented in this paper for the first time. The search for an optimal value for each set of material parameters is performed by a Levenberg–Marquardt algorithm. As a control measure, the process is fully applied to silicone‐rubber samples subjected to uniaxial tension tests. The fitting accuracy of the experimental stress–strain relation to the theoretical one, for both soft tissues and silicone‐rubber (typically nonlinear) is evaluated. This study intents also to select which material models (or model types), the authors will employ in future works, for the analysis of human soft biological tissues.