The elements of continuum biomechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Wiley
2012
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xiv, 371 S. Ill., graph. Darst. |
| ISBN: | 9781119999232 |
Internformat
MARC
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| 008 | 130318s2012 ad|| |||| 00||| eng d | ||
| 020 | |a 9781119999232 |9 978-1-119-99923-2 | ||
| 035 | |a (OCoLC)809612003 | ||
| 035 | |a (DE-599)BVBBV040891270 | ||
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| 100 | 1 | |a Epstein, Marcelo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The elements of continuum biomechanics |c Marcelo Epstein |
| 264 | 1 | |a Chichester |b Wiley |c 2012 | |
| 300 | |a xiv, 371 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Biomechanics | |
| 650 | 4 | |a Biomechanics / Case studies | |
| 650 | 0 | 7 | |a Biomechanik |0 (DE-588)4006880-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804150173642784768 |
|---|---|
| adam_text | Contents
Preface
xiii
Part I A ONE-DIMENSIONAL CONTEXT
1
Material Bodies and Kinematics
3
1.1
Introduction
3
1.2
Continuous versus Discrete
5
1.3
Configurations and Deformations
9
1.4
The Deformation Gradient
13
1.5
Change of Reference Configuration
14
1.6
Strain
15
1.7
Displacement
17
1.8
Motion
18
1.9
The Lagrangian and Eulerian Representations
of Fields
20
1.10
The Material Derivative
22
1.11
The Rate of Deformation
24
1.12
The Cross Section
25
2
Balance Laws
29
2.1
Introduction
29
2.2
The Generic Lagrangian Balance Equation
30
2.2.1
Extensive Properties
30
2.2.2
The Balance Equation
31
2.3
The Generic Eulerian Balance Equation
35
2.4
Case Study: Blood Flow as a Traffic Problem
37
2.5
Case Study: Diffusion of a Pollutant
39
2.5.1
Derivation of the Diffusion Equation
39
2.5.2
A Discrete Diffusion Model
41
2.6
The Thermomechanical Balance Laws
42
2.6.1
Conservation of Mass
42
2.6.2
Balance of (Linear) Momentum
43
2.6.3
The Concept of Stress
44
2.7
Case Study: Vibration of Air in the Ear Canal
45
2.8
Kinetic Energy
50
2.9
The Thermodynamical Balance Laws
55
2.9.1
Introduction
55
Vlil
Contents
2.9.2
Balance of Energy
56
2.9.3
The Entropy Inequality
58
2.10
Summary of Balance Equations
60
2.11
Case Study: Bioheat Transfer and Malignant Hyperthermia
61
References
67
3
Constitutive Equations
69
3.1
Introduction
69
3.2
The Principle of Determinism
70
3.3
The Principle of Equipresence
72
3.4
The Principle of Material Frame Indifference
72
3.5
The Principle of Dissipation
75
3.6
Case Study: Memory Aspects of Striated Muscle
79
3.7
Case Study: The Thermo(visco)elastic Effect in Skeletal Muscle
83
3.8
The Theory of Materials with Fading Memory
88
3.8.1
Groundwork
88
3.8.2
Fading Memory
91
3.8.3
Stress Relaxation
93
3.8.4
Finite Linear Viscoelasticity
94
References
97
4
Mixture Theory
99
4.1
Introduction
99
4.2
The Basic Tenets of Mixture Theory
99
4.3
Mass Balance
102
4.4
Balance of Linear Momentum
103
4.4.1
Constituent Balances
103
4.4.2
Mixture Balance
103
4.5
Case Study: Confined Compression of Articular Cartilage
106
4.5.1
introduction
106
4.5.2
Empirical Facts
107
4.5.3
Field Equations
109
4.5.4
Non-linear Creep
113
4.5.5
Hysteresis
117
4.5.6
The Linearized Theory
118
4.6
Energy Balance
119
4.6.1
Constituent Balances
119
4.6.2
Mixture Balance
120
4.7
The Entropy Inequality
121
4.8
Chemical Aspects
122
4.8.1
Stoichiometrv
¡22
4.8.2
Thermodynamics of Homogeneous Systems
127
4.8.3
Enthalpy and Heats of Reaction
128
4.8.4
The Meaning of the Helmholtz Free Energy
131
4.8.5
Homogeneous Mixtures
132
4.8.6
Equilibrium and Stability
134
4.8.7
The Gibbs Free Energy as
a Le gendre
Transformation
135
4.9
Ideal Mixtures
137
Contents
4.9.1 The Ideal Gas
Paradigm 137
4.9.2
Mixtures of
Ideal Gases 139
4.9.3
Other
Ideal
Mixtures 142
4.10
Case Study: Bone as a Chemically Reacting Mixture
143
References
. .,
140
Part II TOWARDS THREE SPATIAL DIMENSIONS
5
Geometry and Kinematics
ţgj
5.1
Introduction j^j
5.2
Vectors and Tensors 15j
5.2.1
Why Linear Algebra
? 151
5.2.2
Vector Spaces I53
5.2.3
Linear Independence and Dimension I55
5.2.4
Linear Operators, Tensors and Matrices
156
5.2.5
Inner-product Spaces
[59
5.2.6
The Reciprocal Basis
150
5.3
Geometry of Classical Space-time
162
5.3.1
A Shortcut
162
5.3.2
M3 as a
Vector Space
163
5.3.3
Έ?
as an
Affine
Space
164
5.3.4
Frames
165
5.3.5
Space-time and Observers
167
5.3.6
Fields and the Divergence Theorem
168
5.4
Eigenvalues and Eigenvectors
j
74
5.4.1
General Concepts
174
5.4.2
More on Principal Invariants
176
5.4.3
The Sxmmetric Case
178
5.4.4
Functions of Symmetric Matrices
180
5.5
Kinematics
181
5.5. ƒ
Material Bodies
181
5.5.2
Configurations, Deformations and Motions
181
5.5
J
The Deformation Gradient
182
5.5.4
Local Configurations
184
5.5.5
A Word on Notation
185
5.5.6
Decomposition of the Deformation Gradient
186
5.5.7
Measures of Strain
191
5.5.
S 77?e
Displacement Field and its Gradient
192
5.5.9
The Geometrically Linearized Theory I94
5.5. /0
Vo/í/we ««ŕ/
Лгга
195
5.5.
/У
The Material Derivative
198
5.5.72
Change of Reference Configuration
200
5.5.7
і
The Velocity Gradient
202
6
Balance Laws and Constitutive Equations
205
6.1
Preliminary Notions
205
6.1.1
Extensive Properties
205
Contents
6.1.2 Transport Theorem 206
6.2 Balance
Equations
208
6.2.1 The General Balance
Equation
208
6.2.2 The Balance
Equations
of Continuum Mechanics
212
6.3
Constitutive Theory
221
6.3.1
Introduction and Scope
221
6.3.2
The Principle of Material Frame Indifference
and Its Applications
222
6.3.3
The Principle of Thermodynamic Consistency
and Its Applications
226
6.4
Material Symmetries
229
6.4.1
Symmetries and Groups
229
6.4.2
The Material Symmetry Group
230
6.5
Case Study: The Elasticity of Soft Tissue
233
6.5.1
Introduction
233
6.5.2
Elasticity and Hyperelasticity
234
6.5.3
Incompressibility
235
6.5.4
Isotropy
238
6.5.5
Examples
239
6.6
Remarks on Initial and Boundary Value Problems
245
References
250
7
Remodelling, Ageing and Growth
251
7.1
Introduction
251
7.2
Discrete and Semi-discrete Models
256
7.2.1
Challenges
256
7.2.2
Cellular Automata in Tumour Growth
258
7.2.3
A Direct Model of Bone Remodelling
259
7.3
The Continuum Approach
262
7.3.1
Introduction
262
7.3.2
The Balance Equations of Volumetric Growth and Remodelling
263
7.4
Case Study: Tumour Growth
267
7.5
Case Study: Adaptive Elasticity of Bone
271
7.5.1
The Isothermal Quasi-static Case
274
7.6
Anelasticity
276
7.6.1
Introduction
276
7.6.2
The Notion of Material Isomorphism
276
7.6.3
Non-uniqueness of Material Isomorphisms
279
7.6.4
Uniformity and Homogeneity
280
7.6.5
Anelastic Response
282
7.6.6
Anelastic Evolution
283
7.6.7
The Eshelby Stress
289
7.7
Case Study: Exercise and Growth
294
7.7. /
Introduction
294
7.7.2
Checking the Proposed Evolution Law
294
7.7.3
A Numerical Example
296
7.8
Case Study: Bone Remodelling and Wolffs Law
298
References
301
Contents
x¡
8
Principles of the Finite-Element Method
303
8.1
Introductory Remarks
ЗОЗ
8.2
Discretization Procedures
304
8.2.1
Brief Review of the Method of Finite Differences
304
8.2.2
Non-Traditional Methods
307
8.3
The Calculus of Variations
307
8.3.1
introduction
307
8.3.2
The Simplest Problem of the Calculus of Variations
309
8.3.3
The Case of Several Unknown Functions
315
8.3.4
Essential and Natural Boundary Conditions
317
8.3.5
The Case of Higher Derivatives
319
8.3.6
Variational Problems with More than One Independent Variable
322
8.4
Rayleigh,
Ritz
and Galerkin
324
8.4.1
Introduction
324
8.4.2
The Rayleigh-Ritz Method
326
8.4.3
The Methods of Weighted Residuals
328
8.4.4
Approximating Differential Equations by Galerkin
s
Method
330
8.5
The Finite-Element Idea
335
8.5.1
Introduction
335
8.5.2
A Piecewise Linear Basis
337
8.5.3
Automating the Procedure
342
8.6
The
FEM
in Solid Mechanics
347
8.6.1
The Principle of Virtual Work
347
8.6.2
The Principle of Stationary Potential Energy
352
8.7
Finite-Element Implementation
353
8.7.1
General Considerations
353
8.7.2
An Ideal Element
354
8.7.3
Meshing, Insertion Maps and the Isoparametric Idea
356
8.7.4
The Contractibility Condition and its Consequences
357
8.7.5
The Element 1VW Routine
359
8.7.6
The Element EVW Routine
362
8.7.7
Assembly and Solution
362
References
366
Index
367
THE ELEMENTS OF
CONTINUUM
BIOMECHANICS
MARCELO
EPSTEIN, University of Calgary, Canada
An appealing and engaging introduction to Continuum Mechanics in
Biosciences
This book presents the elements of Continuum Mechanics to people interested
in applications to biological systems. It is divided into two parts, the first of which
introduces the basic concepts within a strictly one-dimensional spatial context.
This policy has been adopted so as to allow the newcomer to Continuum Mechanics
to appreciate how the theory can be applied to important issues in Biomechanics
from the very beginning. These include mechanical and thermodynamical balance,
materials with fading memory and chemically reacting mixtures.
In the second part of the book, the fully fledged three-dimensional theory is presented
and applied to hyperelasticity of soft tissue, and to theories of remodeling, aging and
growth. The book closes with a chapter devoted to Finite Element analysis. These and
other topics are illustrated with case studies motivated by
biomedical
applications, such
as vibration of air in the air canal, hyperthermia treatment of tumours, striated muscle
memory, biphasic model of cartilage and adaptive elasticity of bone. The book offers
a challenging and appealing introduction to Continuum Mechanics for students and
researchers of biomechanics, and other engineering and scientific disciplines.
Key features:
•
Explains continuum mechanics using examples from biomechanics for a uniquely
accessible introduction to the topic
•
Moves from foundation topics, such as kinematics and balance laws, to more
advanced areas such as theories of growth and the finite element method
•
Transition from a one-dimensional approach to the general theory gives the
book broad coverage, providing a clear introduction for beginners new to the
topic, as well as an excellent foundation for those considering moving to more
advanced applications.
Marcelo
Epstein is Professor of Mechanical and Manufacturing Engineering and
Adjunct Professor of Kinesiology at the University of Calgary. He is a fellow of the
American Academy of Mechanics, recipient of the CANCAM prize and University
Professor of Rational Mechanics.
Also available
as an e-book
ISBN
978-1-119-99923-2
WILEY
wiley.com
1 1
19 999232
|
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| id | DE-604.BV040891270 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:34:43Z |
| institution | BVB |
| isbn | 9781119999232 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025870923 |
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| physical | xiv, 371 S. Ill., graph. Darst. |
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| publisher | Wiley |
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| spelling | Epstein, Marcelo Verfasser aut The elements of continuum biomechanics Marcelo Epstein Chichester Wiley 2012 xiv, 371 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Biomechanics Biomechanics / Case studies Biomechanik (DE-588)4006880-8 gnd rswk-swf (DE-588)4522595-3 Fallstudiensammlung gnd-content Biomechanik (DE-588)4006880-8 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025870923&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025870923&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Epstein, Marcelo The elements of continuum biomechanics Biomechanics Biomechanics / Case studies Biomechanik (DE-588)4006880-8 gnd |
| subject_GND | (DE-588)4006880-8 (DE-588)4522595-3 |
| title | The elements of continuum biomechanics |
| title_auth | The elements of continuum biomechanics |
| title_exact_search | The elements of continuum biomechanics |
| title_full | The elements of continuum biomechanics Marcelo Epstein |
| title_fullStr | The elements of continuum biomechanics Marcelo Epstein |
| title_full_unstemmed | The elements of continuum biomechanics Marcelo Epstein |
| title_short | The elements of continuum biomechanics |
| title_sort | the elements of continuum biomechanics |
| topic | Biomechanics Biomechanics / Case studies Biomechanik (DE-588)4006880-8 gnd |
| topic_facet | Biomechanics Biomechanics / Case studies Biomechanik Fallstudiensammlung |
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