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Elements of Continuum Biomechanics [Hardback]

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(University of Calgary)
  • Formāts: Hardback, 392 pages, height x width x depth: 254x175x24 mm, weight: 744 g
  • Izdošanas datums: 20-Jul-2012
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1119999235
  • ISBN-13: 9781119999232
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Elements of Continuum BiomechanicsPalielināt
  • Formāts: Hardback, 392 pages, height x width x depth: 254x175x24 mm, weight: 744 g
  • Izdošanas datums: 20-Jul-2012
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1119999235
  • ISBN-13: 9781119999232
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781119999232.html
Keywords:

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 application
Preface xiii
Part I A ONE-DIMENSIONAL CONTEXT
1 Material Bodies and Kinematics
3(26)
1.1 Introduction
3(2)
1.2 Continuous versus Discrete
5(4)
1.3 Configurations and Deformations
9(4)
1.4 The Deformation Gradient
13(1)
1.5 Change of Reference Configuration
14(1)
1.6 Strain
15(2)
1.7 Displacement
17(1)
1.8 Motion
18(2)
1.9 The Lagrangian and Eulerian Representations of Fields
20(2)
1.10 The Material Derivative
22(2)
1.11 The Rate of Deformation
24(1)
1.12 The Cross Section
25(4)
2 Balance Laws
29(40)
2.1 Introduction
29(1)
2.2 The Generic Lagrangian Balance Equation
30(5)
2.2.1 Extensive Properties
30(1)
2.2.2 The Balance Equation
31(4)
2.3 The Generic Eulerian Balance Equation
35(2)
2.4 Case Study: Blood Flow as a Traffic Problem
37(2)
2.5 Case Study: Diffusion of a Pollutant
39(3)
2.5.1 Derivation of the Diffusion Equation
39(2)
2.5.2 A Discrete Diffusion Model
41(1)
2.6 The Thermomechanical Balance Laws
42(3)
2.6.1 Conservation of Mass
42(1)
2.6.2 Balance of (Linear) Momentum
43(1)
2.6.3 The Concept of Stress
44(1)
2.7 Case Study: Vibration of Air in the Ear Canal
45(5)
2.8 Kinetic Energy
50(5)
2.9 The Thermodynamical Balance Laws
55(5)
2.9.1 Introduction
55(1)
2.9.2 Balance of Energy
56(2)
2.9.3 The Entropy Inequality
58(2)
2.10 Summary of Balance Equations
60(1)
2.11 Case Study: Bioheat Transfer and Malignant Hyperthermia
61(8)
References
67(2)
3 Constitutive Equations
69(30)
3.1 Introduction
69(1)
3.2 The Principle of Determinism
70(2)
3.3 The Principle of Equipresence
72(1)
3.4 The Principle of Material Frame Indifference
72(3)
3.5 The Principle of Dissipation
75(4)
3.6 Case Study: Memory Aspects of Striated Muscle
79(4)
3.7 Case Study: The Thermo(visco)elastic Effect in Skeletal Muscle
83(5)
3.8 The Theory of Materials with Fading Memory
88(11)
3.8.1 Groundwork
88(3)
3.8.2 Fading Memory
91(2)
3.8.3 Stress Relaxation
93(1)
3.8.4 Finite Linear Viscoelasticity
94(3)
References
97(2)
4 Mixture Theory
99(52)
4.1 Introduction
99(1)
4.2 The Basic Tenets of Mixture Theory
99(3)
4.3 Mass Balance
102(1)
4.4 Balance of Linear Momentum
103(3)
4.4.1 Constituent Balances
103(1)
4.4.2 Mixture Balance
103(3)
4.5 Case Study: Confined Compression of Articular Cartilage
106(13)
4.5.1 Introduction
106(1)
4.5.2 Empirical Facts
107(2)
4.5.3 Field Equations
109(4)
4.5.4 Non-linear Creep
113(4)
4.5.5 Hysteresis
117(1)
4.5.6 The Linearized Theory
118(1)
4.6 Energy Balance
119(2)
4.6.1 Constituent Balances
119(1)
4.6.2 Mixture Balance
120(1)
4.7 The Entropy Inequality
121(1)
4.8 Chemical Aspects
122(15)
4.8.1 Stoichiometry
122(5)
4.8.2 Thermodynamics of Homogeneous Systems
127(1)
4.8.3 Enthalpy and Heats of Reaction
128(3)
4.8.4 The Meaning of the Helmholtz Free Energy
131(1)
4.8.5 Homogeneous Mixtures
132(2)
4.8.6 Equilibrium and Stability
134(1)
4.8.7 The Gibbs Free Energy as a Legendre Transformation
135(2)
4.9 Ideal Mixtures
137(6)
4.9.1 The Ideal Gas Paradigm
137(2)
4.9.2 Mixtures of Ideal Gases
139(3)
4.9.3 Other Ideal Mixtures
142(1)
4.10 Case Study: Bone as a Chemically Reacting Mixture
143(8)
References
146(5)
Part II TOWARDS THREE SPATIAL DIMENSIONS
5 Geometry and Kinematics
151(54)
5.1 Introduction
151(1)
5.2 Vectors and Tensors
151(11)
5.2.1 Why Linear Algebra?
151(2)
5.2.2 Vector Spaces
153(2)
5.2.3 Linear Independence and Dimension
155(1)
5.2.4 Linear Operators, Tensors and Matrices
156(3)
5.2.5 Inner-product Spaces
159(1)
5.2.6 The Reciprocal Basis
160(2)
5.3 Geometry of Classical Space-time
162(12)
5.3.1 A Shortcut
162(1)
5.3.2 R3 as a Vector Space
163(1)
5.3.3 E3 as an Affine Space
164(1)
5.3.4 Frames
165(2)
5.3.5 Space-time and Observers
167(1)
5.3.6 Fields and the Divergence Theorem
168(6)
5.4 Eigenvalues and Eigenvectors
174(7)
5.4.1 General Concepts
174(2)
5.4.2 More on Principal Invariants
176(2)
5.4.3 The Symmetric Case
178(2)
5.4.4 Functions of Symmetric Matrices
180(1)
5.5 Kinematics
181(24)
5.5.1 Material Bodies
181(1)
5.5.2 Configurations, Deformations and Motions
181(1)
5.5.3 The Deformation Gradient
182(2)
5.5.4 Local Configurations
184(1)
5.5.5 A Word on Notation
185(1)
5.5.6 Decomposition of the Deformation Gradient
186(5)
5.5.7 Measures of Strain
191(1)
5.5.8 The Displacement Field and its Gradient
192(2)
5.5.9 The Geometrically Linearized Theory
194(1)
5.5.10 Volume and Area
195(3)
5.5.11 The Material Derivative
198(2)
5.5.12 Change of Reference Configuration
200(2)
5.5.13 The Velocity Gradient
202(3)
6 Balance Laws and Constitutive Equations
205(46)
6.1 Preliminary Notions
205(3)
6.1.1 Extensive Properties
205(1)
6.1.2 Transport Theorem
206(2)
6.2 Balance Equations
208(13)
6.2.1 The General Balance Equation
208(4)
6.2.2 The Balance Equations of Continuum Mechanics
212(9)
6.3 Constitutive Theory
221(8)
6.3.1 Introduction and Scope
221(1)
6.3.2 The Principle of Material Frame Indifference and Its Applications
222(4)
6.3.3 The Principle of Thermodynamic Consistency and Its Applications
226(3)
6.4 Material Symmetries
229(4)
6.4.1 Symmetries and Groups
229(1)
6.4.2 The Material Symmetry Group
230(3)
6.5 Case Study: The Elasticity of Soft Tissue
233(12)
6.5.1 Introduction
233(1)
6.5.2 Elasticity and Hyperelasticity
234(1)
6.5.3 Incompressibility
235(3)
6.5.4 Isotropy
238(1)
6.5.5 Examples
239(6)
6.6 Remarks on Initial and Boundary Value Problems
245(6)
References
250(1)
7 Remodelling, Ageing and Growth
251(52)
7.1 Introduction
251(5)
7.2 Discrete and Semi-discrete Models
256(6)
7.2.1 Challenges
256(2)
7.2.2 Cellular Automata in Tumour Growth
258(1)
7.2.3 A Direct Model of Bone Remodelling
259(3)
7.3 The Continuum Approach
262(5)
7.3.1 Introduction
262(1)
7.3.2 The Balance Equations of Volumetric Growth and Remodelling
263(4)
7.4 Case Study: Tumour Growth
267(4)
7.5 Case Study: Adaptive Elasticity of Bone
271(5)
7.5.1 The Isothermal Quasi-static Case
214(62)
7.6 Anelasticity
276(18)
7.6.1 Introduction
276(1)
7.6.2 The Notion of Material Isomorphism
276(3)
7.6.3 Non-uniqueness of Material Isomorphisms
279(1)
7.6.4 Uniformity and Homogeneity
280(2)
7.6.5 Anelastic Response
282(1)
7.6.6 Anelastic Evolution
283(6)
7.6.7 The Eshelby Stress
289(5)
7.7 Case Study: Exercise and Growth
294(4)
7.7.1 Introduction
294(1)
7.7.2 Checking the Proposed Evolution Law
294(2)
7.7.3 A Numerical Example
296(2)
7.8 Case Study: Bone Remodelling and Wolff's Law
298(5)
References
301(2)
8 Principles of the Finite-Element Method
303(64)
8.1 Introductory Remarks
303(1)
8.2 Discretization Procedures
304(3)
8.2.1 Brief Review of the Method of Finite Differences
304(3)
8.2.2 Non-Traditional Methods
307(1)
8.3 The Calculus of Variations
307(17)
8.3.1 Introduction
307(2)
8.3.2 The Simplest Problem of the Calculus of Variations
309(6)
8.3.3 The Case of Several Unknown Functions
315(2)
8.3.4 Essential and Natural Boundary Conditions
317(2)
8.3.5 The Case of Higher Derivatives
319(3)
8.3.6 Variational Problems with More than One Independent Variable
322(2)
8.4 Rayleigh, Ritz and Galerkin
324(11)
8.4.1 Introduction
324(2)
8.4.2 The Rayleigh-Ritz Method
326(2)
8.4.3 The Methods of Weighted Residuals
328(2)
8.4.4 Approximating Differential Equations by Galerkin's Method
330(5)
8.5 The Finite-Element Idea
335(12)
8.5.1 Introduction
335(2)
8.5.2 A Piecewise Linear Basis
337(5)
8.5.3 Automating the Procedure
342(5)
8.6 The FEM in Solid Mechanics
347(6)
8.6.1 The Principle of Virtual Work
347(5)
8.6.2 The Principle of Stationary Potential Energy
352(1)
8.7 Finite-Element Implementation
353(14)
8.7.1 General Considerations
353(1)
8.7.2 An Ideal Element
354(2)
8.7.3 Meshing, Insertion Maps and the Isoparametric Idea
356(1)
8.7.4 The Contractibility Condition and its Consequences
357(2)
8.7.5 The Element IVW Routine
359(3)
8.7.6 The Element EVW Routine
362(1)
8.7.7 Assembly and Solution
362(4)
References
366(1)
Index 367
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.