Evaluating Hyperelastic and Alternative Deformation Models for Accurate Characterization of the Mechanical Properties of Biological Tissues

Abstract Although hyperelastic models have been studied for almost 80 years, selecting one that accurately describes the mechanical response of materials remains a challenge. The most prominent examples of hyperelastic materials are biological tissues of living organisms. Information on models of hyperelastic biological materials is highly fragmented, typically focusing on specific individual models or particular organ tissues, and is published across various sources, with some applied aspects being insufficiently covered. This paper presents and analyzes the primary analytical formulations of the most common hyperelastic models (neo-Hookean, Mooney–Rivlin, Ogden, Polynomial, Yeoh, Veronda–Westmann) for calculating and analyzing the deformational behavior of materials. Consolidating essential information about these models in a single publication facilitates an informed choice of a model for computations and analysis of the deformation behavior of a hyperelastic material. Stress–strain curves, elastic modulus–strain curves, and statistical modeling parameters constructed based on the examined applied relationships are provided for the duodenum—the initial section of the human small intestine. Finally, formal approximating models: linear, bilinear, trilinear and exponential models of biological tissues are discussed as alternatives to hyperelastic models. The predictive capabilities of these standard analytical models are compared with those of their hyperelastic counterparts.