A Multi-Layer Finite Element Model Based on Anisotropic Hyperelastic Fiber Reinforcements within Intestinal Walls

The intestinal wall is considered as a highly composite heterogeneous tissue characterized by a strong nonlinear stress-strain passive response with an exponential stiffening effect at higher deformations. The conventional theory of fiber-reinforced elastic solids allows one to describe the anisotropic strain energy as a function of the pseudo-invariants arising from the coupling of the elastic deformation and the direction of fiber reinforcement. In this paper, a multi-layer finite element model of the intestine walls is developed, based on an anisotropic hyperelastic theory of the layered structure, in which each layer may be considered as a composite reinforced by two families of fibers that are arranged in symmetrical spirals. A potential is proposed to model the intestine walls as a fiber-reinforced composite consisting of two directions of muscle-fiber reinforcement and a cross-ply collagen arrangement. Moreover, finite element simulations of a specimen cut from the intestinal walls were carried out by using the same form of strain-energy function, described by a well-known Gasser-Ogden-Holzapfel (GOH) model, for each layer. The model parameters were optimized by fitting the model to the experimental stress-stretch responses in both longitudinal and circumferential directions. In order to verify the proposed model, finite element analyses were carried out to investigate the distributions of equivalent stress in the intestine after the complete deployment of capsule robot legs.