A comparative study of constitutive relations and variational formulations for modeling gastrointestinal peristalsis

Abstract

Gastrointestinal (GI) peristalsis is a vital process for food transport and digestion. Many methods have been formulated to model this process computationally in recent years. One such approach is the finite element (FE) method, which is efficient and robust to model peristalsis in a single framework. However, to construct a FE model, a suitable constitutive relation is required to represent the intrinsic stress–strain behavior of the tissue. Furthermore, as the GI tissues experience large deformation, an efficient variational formulation is needed to model finite deformation without numerical instabilities and volume locking. Therefore, the objective of this work was to examine the nearly incompressible and purely incompressible versions of different constitutive models and determine the most suited constitutive model for GI tissue characterization. Furthermore, we investigated various variational principles to decide on an appropriate FE approach for modeling GI peristalsis. In our study, the incompressible Humphrey’s material model was efficient in recreating experimental observations, whereas the two-field formulation for an incompressible material was an adequate variational formulation for modeling large deformation. Our model was able to recreate the experimental stress–strain data accurately with $R^2>0.99$.