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

Persistent Link:
http://hdl.handle.net/10150/578889
Title:
A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth
Author:
Armstrong, Michelle Annemarie Hine
Issue Date:
2015
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Embargo:
Release 15-Dec-2018
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.
Type:
text; Electronic Dissertation
Keywords:
growth; porohyperelastic; porous media; remodeling; transport; Applied Mathematics; finite element
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Vande Geest, Jonathan P.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleA Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growthen_US
dc.creatorArmstrong, Michelle Annemarie Hineen
dc.contributor.authorArmstrong, Michelle Annemarie Hineen
dc.date.issued2015en
dc.publisherThe University of Arizona.en
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en
dc.description.releaseRelease 15-Dec-2018en
dc.description.abstractThe 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.en
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectgrowthen
dc.subjectporohyperelasticen
dc.subjectporous mediaen
dc.subjectremodelingen
dc.subjecttransporten
dc.subjectApplied Mathematicsen
dc.subjectfinite elementen
thesis.degree.namePh.D.en
thesis.degree.leveldoctoralen
thesis.degree.disciplineGraduate Collegeen
thesis.degree.disciplineApplied Mathematicsen
thesis.degree.grantorUniversity of Arizonaen
dc.contributor.advisorVande Geest, Jonathan P.en
dc.contributor.committeememberVande Geest, Jonathan P.en
dc.contributor.committeememberBrio, Moyseyen
dc.contributor.committeememberTabor, Michaelen
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