Introduction to continuum biomechanics
This book is concerned with the study of continuum mechanics applied to biological systems, i.e., continuum biomechanics. This vast and exciting subject allows description of when a bone may fracture due to excessive loading, how blood behaves as both a solid and fluid, down to how cells respond to...
| Main Author: | |
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| Other Authors: | |
| Format: | Electronic |
| Language: | English |
| Published: |
San Rafael, Calif. (1537 Fourth St, San Rafael, CA 94901 USA) :
Morgan & Claypool Publishers,
c2008.
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| Series: | Synthesis lectures on biomedical engineering,
#19. |
| Subjects: | |
| Online Access: | Abstract with links to resource |
Table of Contents:
- Introduction
- Tensor calculus
- Indicial notation
- Tensors
- Tensor symmetry, principle values, and principal directions
- Other useful tensor relationships
- Kinematics of a continuum
- Description of the motion of a continuum
- Material vs. spatial description
- Material derivative
- Deformation-induced strain
- Principal strains
- Dilatation
- Rate of deformation
- Continuity equation (conservation of mass)
- Stress
- Stress vector ("traction")
- Stress tensor and its components
- Principle of moment of momentum (proof of stress tensor symmetry)
- Principal stresses
- Maximum shear stress
- Equations of motion (conservation of linear momentum)
- Boundary condition for the stress tensor
- Alternative stress definitions
- Demonstrations
- Problems
- Elasticity
- General elasticity
- Experimental observations of infinitesimal linear elasticity
- Linearly elastic solid
- Isotropic linearly elastic solid
- Material properties of elastic materials
- Equations of the infinitesimal theory of elasticity
- Compatibility conditions for infinitesimal strain conditions
- Classical problems in elasticity
- Planar approximations (D simplification)
- Anisotropic linear elasticity
- Problems
- Fluids
- Introduction to fluids
- Hydrostatics
- Newtonian viscous fluid
- Meaning of l and m
- Incompressible Newtonian fluid
- Navier-Stokes equations
- Boundary condition
- Important definitions
- Classical flows
- Non-Newtonian fluids
- Vorticity vector
- Irrotational flow
- Irrotational flow of an inviscid incompressible fluid
- Blood and circulation
- Basics and material properties of blood
- Reynolds numbers for blood
- Non-Newtonian behavior of blood
- Casson equation
- Blood rheology
- Laminar flow of blood in a tube
- Viscoelasticity
- Definition of viscoelasticity
- 1-D linear viscoelasticity (differential form based on mechanical circuit models)
- 1-D Linear Viscoelasticity (Integral Formulation)
- 3-D Linear Viscoelasticity
- Boundary value problems and the correspondence principle
- Dynamic behavior of viscoelastic materials
- Limiting cases of linear viscoelasticity are the Hookean solid and Newtonian viscous fluid
- Poroelasticity and thermoelasticity
- Poroelasticity
- Thermoelasticity
- Biphasic theory
- Conservation of mass
- Conservation of momentum
- Constitutive equations
- Summary and equations of motion
- Confined compression
- Unconfined compression.