A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth

Abstract

The purpose of this dissertation is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. The theory of volumetric growth is combined with the theory of mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid-fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To demonstrate the difference of the GMPHETS model from a traditional hyperelastic (HE) growth model, several finite element test problems with example growth laws are considered, including time-dependent, concentration-dependent, and stress-dependent growth. In particular, this work demonstrates that the solid-only growth of an MPHETS model of a stylized artery results in a more uniform hoop stress than in a HE model under solid-only growth for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To my knowledge, this is the first description of an MPHETS model with growth. The developed computational framework can be used together with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues.