Development of a Thick Continuum-Based Shell Finite Element for Soft Tissue Dynamics

Abstract

The goal of the present doctoral research is to create a theoretical framework and develop a numerical implementation for a shell finite element that can potentially achieve higher performance (i.e. combination of speed and accuracy) than current Continuum-based (CB) shell finite elements (FE), in particular in applications related to soft biological tissue dynamics. Specifically, this means complex and irregular geometries, large distortions and large bending deformations, and anisotropic incompressible hyperelastic material properties. The critical review of the underlying theories, formulations, and capabilities of the existing CB shell FE revealed that a general nonlinear CB shell FE with the abovementioned capabilities needs to be developed. Herein, we propose the theoretical framework of a new such CB shell FE for dynamic analysis using the total and the incremental updated Lagrangian (UL) formulations and explicit time integration. Specifically, we introduce the geometry and the kinematics of the proposed CB shell FE, as well as the matrices and constitutive relations which need to be evaluated for the total and the incremental UL formulations of the dynamic equilibrium equation. To verify the accuracy and efficiency of the proposed CB shell element, its large bending and distortion capabilities, as well as the accuracy of three different techniques presented for large strain analysis, we implemented the element in Matlab and tested its application in various geometries, with different material properties and loading conditions. The new high performance and accuracy element is shown to be insensitive to shear and membrane locking, and to initially irregular elements.