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