Comparing finite viscoelastic constitutive relations and variational principles in modeling gastrointestinal soft tissue deformation

The mechanical attributes of soft tissues within the gastrointestinal (GI) tract are crucial for the effective operation of the GI system, and alterations in these properties may play a role in motility-related disorders. Various constitutive modeling approaches have been suggested to comprehend the response of soft tissues to diverse loading conditions. Among these, hyperelastic constitutive models based on finite elasticity have gained popularity. However, these models fall short in capturing rate- and time-dependent tissue properties. In contrast, finite viscoelastic models offer a solution to overcome these limitations. Nevertheless, the development of a suitable finite viscoelastic model, coupled with a variational formulation for efficient finite element (FE) implementation, remains an ongoing challenge. This study aims to address this gap by developing diverse finite viscoelastic constitutive relations and applying them to characterize soft tissue. Furthermore, the research explores the creation of compressible, nearly incompressible, and incompressible versions of viscoelastic constitutive relations, along with their variational formulation, to facilitate efficient FE implementation. The proposed model demonstrates remarkable accuracy in replicating experimental results, achieving an $R^2$ value exceeding 0.99.