On homogeneous and inhomogeneous deformation response of some generalized linear incompressible transversely isotropic hyperelastic potentials

Abstract

To accurately predict the mechanical behavior of soft materials, continuum mechanics-based phenomenological constitutive models are analyzed. This work examines three compatible standard incompressible transversely isotropic hyperelastic potentials. These potentials are derived from the neo-Hookean strain energy model, which extends linear elasticity theory to account for non-linear responses. They are characterized by quadratic dependencies on the fourth and fifth invariants, or their product, and are defined by three material parameters. The responses of these models under homogeneous deformations, such as simple tensile and simple shear, and non-homogeneous inflation, are examined and evaluated. The findings provide insights into the influence of linear theory on model development and its effectiveness in representing realistic stress responses in soft materials. The study highlights the importance of the building model methodology, especially concerning material instabilities.