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    Relationships Among Microstructural Featuresand Crack Propagation in Osteonal BoneIdentified Using Finite Element Analysis

    Erin K. Oneida, Marjolein C.H. van der Meulen, Anthony R. Ingraffea

    Cornell University

    Ithaca, NY

    12 th International Conference on FractureOttawa, CanadaJuly 12-17, 2009

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    Outline

    Motivation

    Review

    Objective Research Procedure

    Results Discussion

    Acknowledgements

    (Mohsin et al., 2006)

    Crack PropagatingAroundMicrostructuralFeature

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    Motivation

    Each year, 2 million Americans over age 50 suffer a skeletal fracture 1

    Increased mortality 2 Related financial costs of more than $17 billion 1

    Understanding relationships among geometry, material properties,and damage propagation could explain fracture risk and providedirection for preventative treatment development

    1. Burge et al ., 2007 2. Center et al ., 1999

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    Cancellous Bone

    Cortical BoneOsteon Haversian

    Canal

    Lamella

    3-7 m10-500 m

    Bone: Complex, Hierarchical Material

    Osteon HaversianCanal

    Cross-section of cortical bonemicrostructure

    150 mFemur(cm)

    (Rho et al. , 1998 and Rho et al., 2002 )

    InterstitialBone

    Einterstitial > Eosteonal

    CementLine

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    Femoral Fracture 4

    (cm)

    Crack in Humerus 2

    (m)

    Atomic Separation 1

    (angstrom)

    1. Abraham et al ., 1998 2. Nalla et al. , 2003 3. Mohsin et al. , 2006 4. Perren, 2002

    Fracture Events at Different Length Scales

    Crack Around Osteon 3

    (mm)

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    Response upon encountering an osteondepends on crack length (Mohsin et al ., 2006):

    100 m or less = stopped at cement lines 100-300 m = deflected at cement lines 400 m = able to penetrate cement lines

    100 m

    Osteon

    Osteon

    Crack Propagation Affected by Microsctructure

    (Koester et al ., 2008)

    A B C D

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    Objective

    To use computational modeling together with detailedexperimental data to identify the relationships amongmicrostructural features and damage evolution in cortical bone

    100 m

    + Explain?

    FE Model Experimental Data Crack Propagation Behavior

    at the Microscale

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    Research Plan Overview

    Develop Representative Finite ElementModels

    Incorporate Damage

    Propagate Damage According toSpecific Criteria

    Identify Relationships Among Geometry,Material Properties, and Damage Evolution

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    From Data to Digital Bone

    INPUT: Osteon Geometry : Radii: Outer, Haversian canal, lamellar layer Material Properties : Different elastic moduli for each region And More : Porosity, osteon percent area

    Finite Element Model

    (Rho et al., 2002)

    Experimental Data

    Developed code for automatic generation of cortical microstructure

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    Examples of Generated Digital Bone

    1 2

    3 4

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    Geometry :PorosityHaversian Canal DiameterOsteon DiameterOsteon % Area

    Material Properties:EinterstitialEosteonal

    Model and mesh generated in a few min. on

    desktop computer

    Osteon

    Have rsian Canal

    Microstructure Parameters of Interest

    1 m m

    Interstitial Bone

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    Applied Boundary Conditions

    1 m m

    0.0625 mm thick

    Plane

    Displaced0.005 mm

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    Research Plan Overview

    Develop Representative Finite ElementModels

    Incorporate Damage

    Propagate Damage According toSpecific Criteria

    Identify Relationships Among Geometry,Material Properties, and Damage Evolution

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    Damage Incorporation Example

    Penny-shaped crack template (radius = 0.06 mm) inserted using FRANC3D/NG (finiteelement-based fracture mechanics software developed in-house)

    Crack explicitly represented as a geometric discontinuity and adaptive re-meshingemployed

    CrackTemplate

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    Penny-shaped crack template (radius = 0.06 mm) inserted using FRANC3D/NG (finiteelement-based fracture mechanics software developed in-house)

    Crack explicitly represented as a geometric discontinuity and adaptive re-meshingemployed

    Damage Incorporation Example

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    Penny-shaped crack template (radius = 0.06 mm) inserted using FRANC3D/NG (finiteelement-based fracture mechanics software developed in-house)

    Crack explicitly represented as a geometric discontinuity and adaptive re-meshingemployed

    Damage Incorporation Example

    Deformed View

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    Research Plan Overview

    Develop Representative Finite ElementModels

    Incorporate Damage

    Propagate Damage According toSpecific Criteria

    Identify Relationships Among Geometry,Material Properties, and Damage Evolution

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    Damage Propagation Framework

    : Increment of Crack Growthat th Point

    : Mode I Stress IntensityFactor at th Point

    IN: Modelwith InitialCrack

    Repeat CrackGrowth?

    OUT: Model withGrown Crack

    Finite ElementAnalysis

    Compute Parameters of Interest

    e.g., Stress Intensity Factors(KI, KII, KIII)

    2

    mean

    i I

    giveniK

    K aa

    i

    Grow Crack Front According to ChosenGrowth Rule

    e.g., Linear Elastic Fracture Mechanics:

    i

    I K

    iai

    AutomaticRe-meshing

    YES

    NO

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    Initial Crack

    Edge View(Deformation Scale Factor = 10)

    Uniform Applied Displacement (1 m)

    0 . 1

    3 5 m m

    +4.417e+02

    +1.112e+03

    +3.833e+02

    +5.000e+02

    +2.667e+02

    +3.250e+02

    +1.500e+02+2.083e+02

    +3.333e+01+9.167e+01

    -2.500e+01-8.333e+01-1.417e+02-2.000e+02

    -2.695e+02

    33 , MPa

    (Avg: 75%)

    Crack Growth Illustration

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    Crack Grown 1 Step

    +4.417e+02

    +1.112e+03

    +3.833e+02

    +5.000e+02

    +2.667e+02

    +3.250e+02

    +1.500e+02+2.083e+02

    +3.333e+01+9.167e+01

    -2.500e+01-8.333e+01-1.417e+02-2.000e+02

    -2.695e+02

    33 , MPa

    (Avg: 75%)

    Edge View(Deformation Scale Factor = 10)

    0 . 1

    3 5 m m

    Crack Growth Illustration

    Uniform Applied Displacement (1 m)

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    Crack Grown 3 Steps

    +4.417e+02

    +1.112e+03

    +3.833e+02

    +5.000e+02

    +2.667e+02

    +3.250e+02

    +1.500e+02+2.083e+02

    +3.333e+01+9.167e+01

    -2.500e+01-8.333e+01-1.417e+02-2.000e+02

    -2.695e+02

    33 , MPa

    (Avg: 75%)

    Edge View(Deformation Scale Factor = 10)

    0 . 1

    3 5 m m

    Crack Growth Illustration

    Uniform Applied Displacement (1 m)

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    Crack Grown 2 Steps

    +4.417e+02

    +1.112e+03

    +3.833e+02

    +5.000e+02

    +2.667e+02

    +3.250e+02

    +1.500e+02+2.083e+02

    +3.333e+01+9.167e+01

    -2.500e+01-8.333e+01-1.417e+02-2.000e+02

    -2.695e+02

    33 , MPa

    (Avg: 75%)

    Edge View(Deformation Scale Factor = 10)

    0 . 1

    3 5 m m

    Crack Growth Illustration

    Uniform Applied Displacement (1 m)

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    Crack Grown 4 Steps

    +4.417e+02

    +1.112e+03

    +3.833e+02

    +5.000e+02

    +2.667e+02

    +3.250e+02

    +1.500e+02+2.083e+02

    +3.333e+01+9.167e+01

    -2.500e+01-8.333e+01-1.417e+02-2.000e+02

    -2.695e+02

    33 , MPa

    (Avg: 75%)

    Edge View(Deformation Scale Factor = 10)

    0 . 1

    3 5 m m

    Crack Growth Illustration

    Uniform Applied Displacement (1 m)

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    Crack Grown 5 Steps

    +4.417e+02

    +1.112e+03

    +3.833e+02

    +5.000e+02

    +2.667e+02

    +3.250e+02

    +1.500e+02+2.083e+02

    +3.333e+01+9.167e+01

    -2.500e+01-8.333e+01-1.417e+02-2.000e+02

    -2.695e+02

    33 , MPa

    (Avg: 75%)

    Edge View(Deformation Scale Factor = 10)

    0 . 1

    3 5 m m

    Crack Growth Illustration

    Uniform Applied Displacement (1 m)

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    Crack Grown 6 Steps

    +4.417e+02

    +1.112e+03

    +3.833e+02

    +5.000e+02

    +2.667e+02

    +3.250e+02

    +1.500e+02+2.083e+02

    +3.333e+01+9.167e+01

    -2.500e+01-8.333e+01-1.417e+02-2.000e+02

    -2.695e+02

    33 , MPa

    (Avg: 75%)

    Edge View(Deformation Scale Factor = 10)

    0 . 1

    3 5 m m

    Crack Growth Illustration

    Uniform Applied Displacement (1 m)

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    crk8

    Crack Grown 7 Steps

    +4.417e+02

    +1.112e+03

    +3.833e+02

    +5.000e+02

    +2.667e+02

    +3.250e+02

    +1.500e+02+2.083e+02

    +3.333e+01+9.167e+01

    -2.500e+01-8.333e+01-1.417e+02-2.000e+02

    -2.695e+02

    33 , MPa

    (Avg: 75%)

    Edge View(Deformation Scale Factor = 10)

    0 . 1

    3 5 m m

    Crack Growth Illustration

    Uniform Applied Displacement (1 m)

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    Crack Grown 8 Steps

    +4.417e+02

    +1.112e+03

    +3.833e+02

    +5.000e+02

    +2.667e+02

    +3.250e+02

    +1.500e+02+2.083e+02

    +3.333e+01+9.167e+01

    -2.500e+01-8.333e+01-1.417e+02-2.000e+02

    -2.695e+02

    33 , MPa

    (Avg: 75%)

    Edge View(Deformation Scale Factor = 10)

    0 . 1

    3 5 m m

    Crack Growth Illustration

    Uniform Applied Displacement (1 m)

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    Research Plan Overview

    Develop Representative Finite ElementModels

    Incorporate Damage

    Propagate Damage According toSpecific Criteria

    Identify Relationships Among Geometry,Material Properties, and Damage Evolution

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    Parameter Study: 3 Variations

    GeometryPorosity 1: 5.5%Haversian Canal Diameter 2: 58.8 mOsteon Diameter 3: 246.8 mOsteon % Area 1: 41.0 %

    Material Properties

    Einterstitial1

    : 25 GPaEosteonal : 25 GPa

    Model #1 (Reference Model)

    Geometry

    Porosity: 5.5%Haversian Canal Diameter: 58.8 mOsteon Diameter: 246.8 mOsteon % Area: 41.0%

    Material PropertiesEinterstitial : 25 GPaEosteonal : 12.5 GPa

    Model #2 (Vary Materials)Geometry

    Porosity: 12.7%Haversian Canal Diameter: 117.6 mOsteon Diameter: 246.8 mOsteon % Area: 41.0%

    Material PropertiesEinterstitial : 25 GPaEosteonal : 25 GPa

    Model #3 (Vary Geometry)

    1. Rho et al., 2002 2. Wang and Ni, 2003 3. Wachter et al. , 2002

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    Model #1 (Reference Model)

    Model #2 (Vary Materials) Model #3 (Vary Geometry)

    Parameter Study: 3 Variations

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    Parameter Study: Methods Overview

    Generate

    ModelApply BCs Insert Crack FE Analysis

    Grow Crack

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    Results: Crack Front After 1 Growth Step

    Canal (Models #1 and #2)

    Canal (Model #3)

    Osteon

    Outer BoundaryCrack

    X Coordinate (mm)

    Y C o o r d i n a t e

    ( m m

    )

    Original Crack Front

    Model #2 Crack Front

    - - -Model #1 Crack Front

    Model #3 Crack Front

    Osteonal BoneInterstitial Bone

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    Discussion of Results

    Variation in crack front growth apparent between Models #1 and #2-When inside an osteon, crack grew less when modulus was lower

    Future Studies will explore : Additional variations in material properties and geometry

    apparent at the microscale

    Different crack growth formulations (e.g., cohesive zone modeling) Variations in crack orientation, size, and number of cracks Different loading scenarios

    Same crack front growth observed in Models #1 and #3

    Cracks behaved as expected in all models for given loading scenario

    Ultimately, developed modeling capabilities will be validated using

    experimental data related to crack growth at the microscale

    -Due to loading conditions and crack location, different radius had no effect

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    Overall Discussion

    Modeling framework created and used to study crack propagationin bone at the microscale: Model generation tool allowed for quick creation of variable

    digital models of bone

    Cracks were successfully inserted and grown according to chosencriteria Small parametric study allowed for investigation of effects of

    material property and geometry variations on crack growth

    With basic tools in place, a broader parametric investigation canbe performed in the future

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    Acknowledgements

    Thanks for financial support: Ross-Tetelman Fellowship Cornell Center for Materials Research (NSF DMR 0089992) NIH Grant AR 053571

    Thanks for technical assistance: Dr. Bruce Carter Dr. Paul Wawryznek

    Cornell Fracture Group Members

    Thank-you for your time!