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Presentation used for Ian Nieves dissertation. It summarizes using FEA simulation to model impact mechanics and damping in a novel materials characterization device, and in biomedical materials designed to promote bone regeneration.
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Modeling the Percussion Modeling the Percussion Response of Laminated Response of Laminated
Materials and Glass Columns Materials and Glass Columns through the use of through the use of
Computational MethodsComputational Methods
Ian NievesIan Nieves
ObjectivesObjectives• Damping and PercussionDamping and Percussion• PeriometerPeriometer• Modeling with Finite Element Modeling with Finite Element
Analysis (FEA)Analysis (FEA)• Modeling Periometer TestingModeling Periometer TestingLaminated Materials - DampingLaminated Materials - DampingGlass Columns - DefectsGlass Columns - Defects
DampingDamping• Energy dissipation during mechanical actionEnergy dissipation during mechanical action• Intrinsic dampingIntrinsic damping: energy thermally : energy thermally
dissipated through microstructural changesdissipated through microstructural changes• Damping a function of material structureDamping a function of material structure
U
D
2 tan
'
"
E
E
Intrinsic Damping and Tissue Intrinsic Damping and Tissue RegenerationRegeneration
• Dominant paradigm of bone maintenance (Mechanostat) = skeletal remodeling and repair mediated by damping + dynamic stresses
• Clinical studies implement damping in prosthetics integration2
22James C. Earthman, Cherilyn Sheets, J. Paquete, et al, Tissue EngineeringJames C. Earthman, Cherilyn Sheets, J. Paquete, et al, Tissue Engineering in Dentistry, in Dentistry, Clin. Plastic Surg.Clin. Plastic Surg., Vol. 30, pp. 621 – 639, 2003, Vol. 30, pp. 621 – 639, 2003
22James C. Earthman, Cherilyn Sheets, J. Paquete, et al, Tissue EngineeringJames C. Earthman, Cherilyn Sheets, J. Paquete, et al, Tissue Engineering in Dentistry, in Dentistry, Clin. Plastic Surg.Clin. Plastic Surg., Vol. 30, pp. 621 – 639, 2003, Vol. 30, pp. 621 – 639, 2003
PercussionPercussion
• Generate mechanical pulses through impactGenerate mechanical pulses through impact• Pulse parameters (intensity, duration, etc.) Pulse parameters (intensity, duration, etc.)
modified in situ through dampingmodified in situ through damping• Pulsate mechanics similar to biological Pulsate mechanics similar to biological
activities (Running, etc.)activities (Running, etc.)
*Bakos et al., Acta Veterinaria Hungarica (2003).
PeriometerPeriometerWorkstation with Workstation with
Virtual Virtual
InstrumentationInstrumentation
Percussion Percussion ProbeProbe
Control Control InstrumentInstrumentation and ation and SensorsSensors
PeriometerPeriometer
Calculation of Force and Calculation of Force and AccelerationAcceleration
fivvmKE 22
2
1
UCUER
22
maF
0
0.5
1
1.5
2
2.5
3
0 1 2 3 4 5 6 7
En
erg
y R
etu
rn (
erg
s)E
ner
gy
Ret
urn
(e
rgs)
Time (ms)Time (ms)
Energy Return = Energy Return = ERER = = CC11 xx FF2 2
Periometer Wave DynamicsPeriometer Wave Dynamics
DEFECT DETECTIONDEFECT DETECTION
Modeling Percussion Modeling Percussion
• Validate percussion responseValidate percussion response• Elucidate mechanisms underlying Elucidate mechanisms underlying
responseresponse• Predict facets of percussion profilePredict facets of percussion profile• Taylor and refine detection capabilitiesTaylor and refine detection capabilities• Facilitate construction of “Percussion Facilitate construction of “Percussion
Spectrum”Spectrum”
Finite Element Analysis (FEA)Finite Element Analysis (FEA) Creates representations of geometry Creates representations of geometry Uses geometry as template for network (mesh) Uses geometry as template for network (mesh)
of discrete lattice points (nodes)of discrete lattice points (nodes) Nodes are vertices for line, planar or polyhedral Nodes are vertices for line, planar or polyhedral
elementselements Uses Shape Functions to solve to produce Uses Shape Functions to solve to produce
predictions of nodal (acceleration, displacement) predictions of nodal (acceleration, displacement) and elemental (stress) results in response to and elemental (stress) results in response to inputs (initial and boundary conditions)inputs (initial and boundary conditions)
ElementsElements
Idealized Hexagonal element used forIdealized Hexagonal element used for virgin testing materials and full-scalevirgin testing materials and full-scale
Hexagonal elements in cylindrical Hexagonal elements in cylindrical probe with nodes adjacent to probe with nodes adjacent to accelerometeraccelerometer
Dytran vs. Dytran vs. MARCMARC• Dytran specialized for Dytran specialized for
ballistic modelingballistic modeling – – more more detailed resultsdetailed results
• Explicit solver – Explicit solver – ∆t∆tCritCrit automatically calculatedautomatically calculated
• DYMAT 24 Piecewise Linear DYMAT 24 Piecewise Linear Plasticity (elastoplastic) Plasticity (elastoplastic) material modelmaterial model
• Matrig rigid material model Matrig rigid material model – only requires mass input– only requires mass input
• MARC capable of ballistic MARC capable of ballistic modeling, specialized for modeling, specialized for elastomeric analysiselastomeric analysis
• Implicit Solver - Implicit Solver - ∆t∆tCritCrit calculated through calculated through inspectioninspection
• Elastic Material modelElastic Material model• Rayleigh damping model Rayleigh damping model
– intrinsic damping input– intrinsic damping input
DytranDytran MARCMARC
Stepped Probe Stepped Probe ConstructionConstruction
Rigid Probe and Glass Column Construction
MeshesMeshes
Boundary Conditions for Boundary Conditions for Laminated MaterialsLaminated Materials
Initial and Boundary Conditions Initial and Boundary Conditions for Rigid Probe and Glass Columnsfor Rigid Probe and Glass Columns
Material ParametersMaterial ParametersMaterial
Model Material E (KPa) ρ (kg/mm3) ν σys (KPa) Code
DYMAT 24
Steel 1.93108 8.00x10-6 0.30 4.40x104
Dytran
Al 6061 7.00x107 2.70x10-6 0.35 3.95x105
PTFE 5.00x105 2.10x10-6 0.40 9.00x104
Glass 7.03x107 2.47x10-6 0.22 6.90x104
PMMA 3.30x106 1.19x10-6 0.37 1.07x105
PLGA 3.50x106 1.19x10-6 0.40 4.4x104
Elastic
Steel 1.93108 8.00x10-6 0.30
MARC
Al 6061 7.00x107 2.70x10-6 0.35
PTFE 5.00x105 2.10x10-6 0.40
Glass 7.03x107 2.47x10-6 0.22
PMMA 3.30x106 1.19x10-6 0.37
PLGA 3.50x106 1.19x10-6 0.40
Intrinsic Damping in MARCIntrinsic Damping in MARC
Material Al PTFE PMMA
η 0.0003 0.1038 0.0400
• Rayleigh Damping Function: C = αM + (β+gt)K, M Rayleigh Damping Function: C = αM + (β+gt)K, M = Mass Matrix, K = Stiffness Matrix, C = Damping = Mass Matrix, K = Stiffness Matrix, C = Damping MatrixMatrix
• Damping is proportional to stiffness and massDamping is proportional to stiffness and mass• Stiffness Matrix Factor(Stiffness Matrix Factor(β) = 2(η)/π(lowest modal β) = 2(η)/π(lowest modal
frequency(Hz))frequency(Hz))• η = Loss Coefficient η = Loss Coefficient • Modal frequency material specific, derived Modal frequency material specific, derived
through MARC modal analysisthrough MARC modal analysis
Al MonolithsAl Monoliths
3.175 mm thick Al Monolith: Results3.175 mm thick Al Monolith: Results
Stepped ProbeStepped Probe
Stepped Probe: MARCStepped Probe: MARC
Cylindrical Probe: DytranCylindrical Probe: Dytran
Cylindrical Probe:Cylindrical Probe: DytranDytran
Cylindrical Probe: MARCCylindrical Probe: MARC
Size Effects: 500 x 500 x 3.175 mm Al Monolith Size Effects: 500 x 500 x 3.175 mm Al Monolith and 27 gram Probeand 27 gram Probe
k
mT
27 gram Probe27 gram Probe 500 mm x 500 mm x 3.175 mm Monolith500 mm x 500 mm x 3.175 mm Monolith
Al – PTFE Scaffolds with Al – PTFE Scaffolds with Rigid ProbeRigid Probe
Al – PTFE Scaffolds with Al – PTFE Scaffolds with Stepped Probe and Intrinsic Stepped Probe and Intrinsic
DampingDamping
3.175 PTFE: 3.175 Al 3.175 PTFE: 3.175 Al 1.58 PTFE: 3.175 Al 1.58 PTFE: 3.175 Al
PMMA Scaffold with Intrinsic PMMA Scaffold with Intrinsic DampingDamping
Scaffold and ProbeScaffold and Probe Layer with DefectLayer with Defect
PMMA Scaffold with Intrinsic PMMA Scaffold with Intrinsic Damping: Origin of ShoulderDamping: Origin of Shoulder
Intrinsic DampingIntrinsic Damping No Intrinsic DampingNo Intrinsic Damping
PLGA Scaffold: Mesh re-Enforcement and PLGA Scaffold: Mesh re-Enforcement and Stress AttenuationStress Attenuation
1J. Calvert, L. Weiss, New Frontiers in Bone Tissue Engineering, Clin. Plast. Surg., Vol. 30, pp. 641 – 648, 2003
• PLGA demonstrated to PLGA demonstrated to stimulate bone stimulate bone and vascular regenerationand vascular regeneration11
Re-enforcedRe-enforced
VirginVirgin
Glass DefectGlass Defect
0.2 mm0.2 mm
Glass used to model rigid biological materials: Glass used to model rigid biological materials: bone, enamel, etc.bone, enamel, etc.
Cylindrical Probe and Glass ControlCylindrical Probe and Glass Control
MARCMARC
DytranDytran
Stepped Probe and Glass Control: Stepped Probe and Glass Control: Acceleration ResultsAcceleration Results
T ≈ 0.18 msecT ≈ 0.18 msec
T ≈ 0.25 msecT ≈ 0.25 msec
T ≈ 0.25 msecT ≈ 0.25 msec
MARCMARC
DytranDytran
Rigid Probe and Glass ControlRigid Probe and Glass Control
Stepped Probe and Trench DefectStepped Probe and Trench Defect
“T” ≈0.58 msec “T” ≈0.58 msec
Trench Crack: Averaged Probe Trench Crack: Averaged Probe Acceleration (Dytran)Acceleration (Dytran)
Averaged Probe nodal Averaged Probe nodal accelerations accelerations for indicated planesfor indicated planes
Wedge Crack GeometryWedge Crack Geometry
Shoulder Peak
Shoulder Peak
Semi-Circular Aligned Crack: Semi-Circular Aligned Crack: AccelerationAcceleration
1 mmCross Section Cross Section PerpendicularPerpendicular
to Impact to Impact PlanePlane
Crack Boundary EffectsCrack Boundary Effects
Rigid Probe with 1 mm transverse Crack
Glass Controls: FEA vs. PercussionY
– Ax
is A
ccel
erati
on (m
m/s
ecY
– Ax
is A
ccel
erati
on (m
m/s
ec22 )
Time (sec)Time (sec)
Glass control acceleration accurately modeled with stepped probe
Cracked Glass : FEA vs. PercussionY
– Ax
is A
ccel
erati
on (m
m/s
ecY
– Ax
is A
ccel
erati
on (m
m/s
ec22 )
Y –
Axis
Acc
eler
ation
(mm
/sec
Y –
Axis
Acc
eler
ation
(mm
/sec
22 )
Y –
Axis
Acc
eler
ation
(mm
/sec
Y –
Axis
Acc
eler
ation
(mm
/sec
22 )Time (sec)Time (sec) Time (sec)Time (sec)
Time (sec)Time (sec)
Crack Stresses (KPa)
Semi-circular crack with Semi-circular crack with square edgesquare edge
Semi-circular
crack with
round edge
Wedge-form Wedge-form crack crack
with round with round edgeedge
Interference EffectsInterference Effects
Summary• FEA can elucidate mechanical origin of probe signalsFEA can elucidate mechanical origin of probe signals• FEA – based modeling can accurately model defect detection in rigid FEA – based modeling can accurately model defect detection in rigid
materialsmaterials• FEA can qualitatively evaluate energy dissipation in biomedical scaffoldsFEA can qualitatively evaluate energy dissipation in biomedical scaffolds• Modeling indicates dependence of Periometer function on interference Modeling indicates dependence of Periometer function on interference
effectseffects• Further modeling – experimental is required to refine intrinsic damping Further modeling – experimental is required to refine intrinsic damping
modelingmodeling
AcknowledgementsAcknowledgements
• Dr. James Earthman• MSC Software Corporation,
Santa Ana, CA