Bone Biomechanics:

1
Bone Biomechanics
Bone Group Presentation 2/23/06

• Relating Mechanics Concepts to Bone

Presented by Jeffrey M. Leismer, MEng Edward K.
Walsh, PhD
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Introduction

• Definitions
• Statics, dynamics, mechanics of materials,
  failure
• Concepts to be learned
• What are stresses and strains?
• How can knowledge of loads and deformations be
  used to obtain stresses and strains?
• How does bone fail?
• Audience background/interests?

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Agenda

• Ed Jeff_________________________________________
  (25 minutes)
• Bone mechanics overview
• Mechanical influences on the skeleton
• Statics
• Mechanics of materials
• Stress-strain relationship
• Mechanical testing
• Failure modes in bone
• Jeff______________________________________________
  _(5 minutes)
• Application Manatee bone fracture study

4
Overview
BONE MECHANICS
Mechanics (effects of forces on a body)
To Prof. Walsh
5
Bone Mechanics Overview
To Jeff
6
Mechanical Influences on the Skeleton

• Internal/external loading factors
• Loading site, direction, magnitude, speed,
  repetition, duration
• Physiological loading concepts
• Muscle forces
• Tendon and ligament attachment points
• Moment arms (bicep curl example)

7
Mechanical Lever System
Mechanical Lever System
bfulcrum dmoment arm F1/d
F
d
To Prof. Walsh
8
Vocabulary

• Load (N lbf)
• Deformation (mm in)
• Stress (N/m2Pa psi)
• Strain (mm/mm in/in)
• Moment/Torque (NmJ in-lb)
• Moment of Inertia (mm4 in4)

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Overview
Statics (equilibrium of forces and moments)
Statics (equilibrium of forces and moments)
Dynamics (bodies in motion)
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Statics Overview
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Statics

• Equilibrium of forces
• ?F0
• Equilibrium of moments
• ?M0
• Bicep curl example

To Jeff
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Static Analysis
Static Analysis
-To solve for the muscle force, remove rigid body
bc and replace the section with reaction forces
at b
F
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useful angles
Static Analysis
Use the figure to find the forces and moments in
each direction
Now lets plug in some realistic values and solve
for the forces
What happens to F if we increase the moment arm,
d?
Sum the forces and moments and set them equal to
zero
F
Resolve muscle force vector into x and y
components
To Prof. Walsh
14
Overview
Mechanics (effects of forces on a body)
Mechanics (effects of forces on a body)
Mechanical Testing (response to loading)
Statics (equilibrium of forces and moments)
Dynamics (bodies in motion)
15
Mechanics of Materials Overview
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Mechanics of Materials
(can be used to show the state of stress at a
point)
state of stress
Types of stresses and their equations
To Jeff
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Mechanics of Materials
Mechanics of Materials
-To find the stresses at point e
-Make a cut at e
-Remove all components to the right of the cut
-Replace the removed section with reaction forces
and a moment at point e
M
a
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Mechanics of Materials
Solve for the reaction forces and moment
M
L-d
a
q
Simplify analysis by rotating the coordinate
system and force vectors
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Mechanics of Materials
Bending stress at e due to moment M sbMc/I
cro Ip(ro4-ri4)/4 For M89 in-lb, ro0.75 in,
ri0.25 in I0.245 in4 sb272 lb/in2 272 psi
Cross-section of bone at e
failure strength (bending) ltlt sf30,250 psi
Normal stress at e due to Rx sNRx/A
sN4.4 psi Ap(ro2-ri2)1.57 in2 RxWxWcos(q)
6.8 lbf
Shear stress at point e due to Ry sNRy/A
sN12 psi RyWyWsin(q)18.8 lbf
M
L-d
q
The stresses found above were calculated for a
point at the top of the cross-section. The
stresses will be lower at any other point about
the cross-section.
To Prof. Walsh
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Stress-Strain Relationship Constitutive Law

• Hookes Law
• sCe
• where C is the stiffness matrix
• eSs,
• where S is the compliance matrix
• Inverse relationship
• SC-1
• Material properties
• Elastic modulus E
• Poissons ratio u
• Shear modulus G

To Jeff
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Overview
Mechanical Testing (response to loading)
Mechanics (effects of forces on a body)
Mechanics (effects of forces on a body)
Statics (equilibrium of forces and moments)
Dynamics (bodies in motion)
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Mechanical Testing of Bone

• Handling considerations
• Hydration, temperature, strain rate
• Types of tests
• Tension/compression, bending, torsion, shear,
  indentation, fracture, fatigue, acoustic
• Equipment
• Mechanical testing machine, deformation
  measurement system, recording instrumentation
  (load-deflection)
• Other considerations
• Specimen size orientation, species, sampling
  location

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Mechanical Testing

• Outcome measures (uniaxial test)
• Ultimate load reflects integrity of bone
  structure
• Stiffness related to mineralization
• Work to failure energy required to break bone
• Ultimate displacement inversely related to
  brittleness
• Etc.

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Overview
Mechanical Testing (response to loading)
Mechanics (effects of forces on a body)
Mechanics (effects of forces on a body)
Statics (equilibrium of forces and moments)
Dynamics (bodies in motion)
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Failure of Bone

• Failure modes
• Ductile Overload Fracture
• Failure results from loading bone in excess of
  its failure strength
• Brittle Fracture
• Stress is intensified at sharp corners
  (micro-cracks or voids) and results in fracture
  without exceeding the failure strength of bone
• Creep
• Slow, permanent deformation resulting from
  application of a sustained, sub-failure magnitude
  load (Silly Putty)
• Fatigue
• Failure due to repetitive loading below the
  failure strength of bone (a.k.a. stress fractures)

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How can this information be put to use?
How can this information be put to use?

• EXAMPLE
• Manatee Bone Fracture Study
• 25 of all manatees die as a result of collisions
  with watercraft
• Reducing boat speed in manatee zones can greatly
  reduce the energy of impact in the event of a
  collision
• Previous researchers correlated the energy
  associated with traveling at various speeds in a
  small boat to the energy required to fracture
  manatee bone
• One of the goals of my dissertation work is to
  build on this information to further reinforce
  speed restrictions in manatee zones so that this
  docile creature can remain in existence for
  future generations to admire

• EXAMPLE
• Manatee Bone Fracture Study
• 25 of all manatees die as a result of collisions
  with watercraft
• Reducing boat speed in manatee zones can greatly
  reduce the energy of impact in the event of a
  collision
• Previous researchers correlated the energy
  associated with traveling at various speeds in a
  small boat to the energy required to fracture
  manatee bone
• One of the goals of my dissertation work is to
  build on this information to further reinforce
  speed restrictions in manatee zones so that this
  docile creature can remain in existence for
  future generations to admire

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Manatee Bone Fracture Study
Manatee Bone Fracture Study

• Aims
• Characterize manatee rib bone
• Determine anisotropic fracture properties
• Predict the anisotropic stress intensity factors
  (KI,KII,KIII) using finite element methods and
  fracture analysis software

• Aims
• Characterize manatee rib bone
• Determine anisotropic fracture properties
• Predict the anisotropic stress intensity factors
  (KI,KII,KIII) using finite element methods and
  fracture analysis software

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Manatee Bone Fracture Study
Rib bone

• Tension
• Torsion
• Compact Tension

Tests
Specimens
Measured Properties
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Manatee Bone Fracture Study
Manatee Bone Fracture Study

• Visual Image Correlation (VIC)

2 cameras take simultaneous pictures of the
specimen as it is loaded
Correlation software maps the specimen surfaces
from the images to digitized 3D space
Images of the loaded specimen are used to
digitally measure deformations relative the
reference photo of the undeformed specimen
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Manatee Bone Fracture Study

• -Six experiments are run, each with the
  application of only a single component of stress
• From the measured strain, we can calculate all of
  the orthotropic elastic constants
• The elastic constants are used as input to a
  finite element model for further analysis

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Manatee Bone Fracture Study

• Finite Element Analysis (FEA)
• Computational Fracture Analysis
• Crack opening displacements (CODs) from FEA are
  used to determine the 3D anisotropic stress
  intensity factors in a specimen
• Numerical results are compared with those from
  experiment to determine the predictive capacity
  of the model for fracture analyses

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Resources
WE HOPE YOU ENJOYED THE PRESENTATION
PROFESSOR WALSH AND I WILL NOW TAKE THE REMAINING
TIME TO ANSWER YOUR QUESTIONS

• Contact Info
• Computational solid mechanics lab (103 MAE-C)
• Email Jeff jeffleismer_at_gmail.com
• Email Ed ekw_at_mae.ufl.edu
• Books
• Bone Mechanics Handbook (Cowin, 2001)
• Mechanical Testing of Bone (An Draughn, 2000)

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