A New Continuum-Based Thick Shell Finite Element for Soft Biological Tissues in Dynamics: Part 1 - Preliminary Benchmarking Using Classic Verification Experiments

TL;DR

This paper introduces a new nonlinear thick continuum-based shell finite element designed for simulating soft biological tissues in dynamics, demonstrating high accuracy, efficiency, and robustness in benchmark tests involving large 3D deformations and complex geometries.

Contribution

The paper presents a novel nonlinear thick CB shell finite element based on Mindlin-Reissner theory, capable of handling large deformations and irregular geometries in soft tissue simulations.

Findings

Accurate and efficient in benchmark experiments

Handles large 3D deformations and curved geometries

Insensitive to shear, membrane, and volumetric locking

Abstract

For the finite element simulation of thin soft biological tissues in dynamics, shell elements, compared to volume elements, can capture the whole tissue thickness at once, and feature larger critical time steps. However, the capabilities of existing shell elements to account for irregular geometries, and hyperelastic, anisotropic 3D deformations characteristic of soft tissues are still limited. As improvement, we developed a new general nonlinear thick continuum-based (CB) shell finite element (FE) based on the Mindlin-Reissner shell theory, with large bending, large distortion and large strain capabilities, embedded in the updated Lagrangian formulation and explicit time integration. We performed numerical benchmark experiments available from the literature that focus on engineering linear elastic materials, which, verified and proved the new thick CB shell FE to: 1) be accurate an efficient 2) be powerful in handling large 3D deformations, curved geometries, 3) accommodate coarse distorted meshes, and 4) achieve comparatively fast computational times. The new element was also insensitive to three types of locking (shear, membrane and volumetric), and warping effects. The capabilities of the present thick CB shell FE in the biomedical realm are illustrated in a companion article (Part 2), in which anisotropic incompressible hyperelastic constitutive relations are implemented and verified.