Biomechanics of Living Organs

Hyperelastic Constitutive Laws for Finite Element Modeling

Yohan Payan,Jacques Ohayon

• Publisher: Academic Press
• Year: 2017
• ISBN:
  9780128040607
• Topic: Biological Sciences
• Subtopic: Biophysics
• Index: Biological Sciences

Biomechanics of Living Organs: Hyperelastic Constitutive Laws for Finite Element Modeling is the first book to cover finite element biomechanical modeling of each organ in the human body. This collection of chapters from the leaders in the field focuses on the constitutive laws for each organ.

Each author introduces the state-of-the-art concerning constitutive laws and then illustrates the implementation of such laws with Finite Element Modeling of these organs. The focus of each chapter is on instruction, careful derivation and presentation of formulae, and methods.

When modeling tissues, this book will help users determine modeling parameters and the variability for particular populations. Chapters highlight important experimental techniques needed to inform, motivate, and validate the choice of strain energy function or the constitutive model.

Remodeling, growth, and damage are all covered, as is the relationship of constitutive relationships of organs to tissue and molecular scale properties (as net organ behavior depends fundamentally on its sub components). This book is intended for professionals, academics, and students in tissue and continuum biomechanics.

• Covers hyper elastic frameworks for large tissue deformations
• Considers which strain energy functions are the most appropriate to model the passive and active states of living tissue
• Evaluates the physical meaning of proposed energy functions

Part 1

Constitutive Laws for Biological Living Tissues

Chapter 1

Hyperelasticity Modeling for Incompressible Passive Biological Tissues

Grégory Chagnon*; Jacques Ohayon*^,†; Jean-Louis Martiel*; Denis Favier* ^* TIMC-IMAG Laboratory, University Grenoble Alpes, CNRS, Grenoble, France
^† University of Savoie Mont-Blanc, Engineering School Polytech Annecy-Chambéry, Le Bourget du Lac France

Abstract

Soft tissues are mainly composed of organized biological media giving them an anisotropic mechanical behavior. Soft tissues also have the ability to undergo large elastic reversible deformations. Many constitutive models were developed to describe these phenomena. In this chapter, we discuss several varying models and their constitutive equations which are defined by means of strain components or strain invariants. The notion of tangent moduli will be plotted for two well-known constitutive equations, and we will illustrate how to implement explicitly a structural kinematics constraint in a constitutive law to derive the resulting Cauchy stress tensor.

Keywords

Hyperelasticity; Anisotropy; Kinematics constraint; Lagrange multiplier; Strain-energy density functions

1 Introduction

In the last decades, there has been a significant growth in interest in characterizing the passive anisotropic mechanical properties of soft incompressible biological tissues based on nonlinear continuum mechanics theory. Such a constitutive approach is suitable to describe a wide variety of physical material behaviors in which the strain may be large (Ogden, 1984; Cowin and Humphrey, 2000; Holzapfel, 2000; Taber, 2004; Holzapfel and Ogden, 2006).

Biological tissues are heterogeneous composite materials made of different media including epithelial, connective, muscular, neuronal etc. (Marieb and Hoehn, 2010). In these composite materials, the distributions of the internal constituents are assumed to be locally uniform on the continuum scale. These tissues are often regarded as oriented cells surrounded by an extra cellular matrix, the whole behaving as anisotropic continuous media reinforced by different families of fibers of distinct orientations. The proportion of matrix and fibers, as well as their orientations, depends on the type of soft tissues (artery, skin, cornea, muscle, etc.). All these materials present a complex mechani...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Contributors
• Preface
• Part 1: Constitutive Laws for Biological Living Tissues
• Part 2: Passive Soft Organs
• Part 3: Active Soft Organs
• Part 4: Musculo-Skeletal Models
• Index