A New Continuum-Based Thick Shell Finite Element for Soft Biological Tissues in Dynamics: Part 2 - Anisotropic Hyperelasticity and Incompressibility Aspects

TL;DR

This paper extends a continuum-based shell finite element to model anisotropic incompressible hyperelastic soft biological tissues under large deformations, demonstrating high accuracy and efficiency through experimental validation.

Contribution

It introduces new techniques for modeling nonlinear hyperelastic strains and enforcing incompressibility directly within a continuum-based shell finite element framework.

Findings

Accurate modeling of large 3D strains in soft tissues.

Excellent agreement with experimental data.

Reliable and efficient simulation tool for biomedical applications.

Abstract

In a companion article (Part 1), we presented the development of a thick continuum-based (CB) shell finite element (FE) based on Mindlin-Reissner theory. We verified the accuracy, efficiency and locking insensitivity of the element in modeling large 3D deformations, using linear elastic material properties. In the present article, we developed and implemented the kinetics description, within the updated Lagrangian (UL) formulation, of anisotropic incompressible hyperelastic constitutive relations that enable the CB shell FE to accurately model very large 3D strains and deformations. Specifically, we developed the measures of deformation in the lamina coordinate system, presented three techniques to model nonlinear hyperelastic strains, and enabled the direct enforcement of incompressibility and of the zero normal stress condition without using a penalty factor or a Lagrange multiplier. Moving towards the application of the present work to the biomedical realm, we performed multiple experiments concerning mechanical behavior of rubber-like materials and soft biological tissues in different geometries and loading conditions. Excellent agreements between the present FE results and the analytical and/or experimental data proved the CB shell FE combined with the present constitutive techniques to be a highly reliable and efficient tool for modeling, analyzing, and predicting mechanical behavior of soft biological tissues.