Mechanics of finite nonlinear viscoelastic growth for soft biological tissues

Abstract

Many soft biological tissues have a kind of rubbery properties and behave viscoelastic. The main difference between soft biological tissues and rubber-like materials is that they can grow. Studying the growth of these structures is challenging due to their properties. The aim of this study is to develop a computer program and a framework for the finite nonlinear viscoelastic growth of soft body parts such as arteries, skin, intestines and aneurysms, considering a Newtonian fluid for the viscoelastic branches. To deal with nonlinear relationships, a membrane FE formulation is used throughout the total Lagrangian framework. The general formulas work for different types of materials, both isotropic and anisotropic. To solve the equations for how the internal variables for growth and the viscoelastic branches change over time, two implicit Euler-backward methods are used. To see whether the model works correctly, we compare the numerical results with experimental data on skin and artery growth. The numerical results show that the described framework can accurately predict the experimental findings. In addition, the model allows us to study different shapes of biostructures such as intestinal growth and aneurysm growth. This study may serve as a benchmark for a better understanding of the complex phenomena in the biomechanics of growth.