al Symposium onr-like Materials

, Inc. (ARDL)

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Elastomer Analysis Using MARC

Prepared for: Elastomer - Fea Forum ‘99 3rd InternationFinite Element Analysis of Rubber and Rubbe

May 19th and 20th, 1999The University of AkronE. J. Thomas HallAkron, Ohio USA

Organized by: Akron Rubber Development Laboratory

Prepared by: Daniel S. WolfMARC Analysis Research Corp.

260 Sheridan Ave., Suite 309Palo Alto, CA 94306

ngineering from the Schoolte instructor he taught many

der Professor C.T. Sun and spe-lems on Interfacial Cracks”.onsible for teaching, research,nt of Ocean Engineering at

me a project engineerper utilization of all structuralWhitney. He has significantsystems including nonlinear as combustors and turbineuction for Turbine Vaneearch Corporation andin the service of MARC’s val-

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Vita for Dr. Daniel S. Wolf

Daniel S. Wolf received his Ph. D., M.S. and B.S. in Aeronautical Eof Aeronautics and Astronautics at Purdue University. As a graduaundergraduate mechanics and laboratory courses. He studied uncialized in continuum mechanics. His thesis title was “Some ProbUpon graduation in 1976, he became an assistant professor, respand expanding laboratory and computing facilities in the departmeFlorida Atlantic University in Boca Raton Florida. In 1979 he becaresponsible for an advanced finite element group to insure the proanalysis simulation programs used by many engineers at Pratt & experience with finite element application programs and computingthermal/structural analysis of hot section engine components suchairfoils. He was awarded patent 4,477,222 titled “Mounting ConstrAssembly”, in 1984. In 1989 he moved on to MARC Analysis Resbecame responsible for customer service, where he remains todayued customers.

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ContentsElastomer Analysis Using MARC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Vita for Dr. Daniel S. Wolf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3What Is New About Neo-Hookean? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Reduce Measured Data And Fit For Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Fit Uniaxial Compression Data To 2 Term Mooney . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Fit Biaxial Data To 2 Term Mooney . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Biaxial Tension = Compression Strain State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8This Is A Reasonable Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Mullins Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Miehe Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Viscoelastic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123D Packer Seal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Axisymmetric Packer Seal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Zero Leak ABS Piston Seal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Constant Velocity Boot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Tires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Tire Model Running MARC K73 Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Coupled Acoustic-Structural Modal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Automatic Rubber Remeshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Intravenous Medical Tube Clamp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Knee Implant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Experimental Elastomer Analysis Training Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

n?

γ

Gγ

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What Is New About Neo-Hookea

Hookean (1660)

Neo-Hookean (1940)

σ 2 1 υ+( )Gε= τ G=

σ G 1 ε+( ) 1 ε+( ) 2––[ ]= τ =

nalysis

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Reduce Measured Data And Fit For A

εc

σm εm,

σ ε,( )

Equal Biaxial Test

Mooney

Too Stiff

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Fit Uniaxial Compression Data To 2 Term

y

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Fit Biaxial Data To 2 Term Moone

State

nd is more reliable.

λ3 Λ=

λ1 Λ

12---–

=λ2

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Biaxial Tension = Compression Strain

Biaxial Tension is the same strain state as compression a

Λ

12---–

=

λ1 λ=

λ2 λ=

λ3 λ 2–=

Λ λ 2–=

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This Is A Reasonable Fit

Three Basic Strain States

α β,( )W0

ov factor, , isd in MARC

K α β,( )

l Predictions

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Mullins Effect

W K=

The Kachanimplemente

These factors can be entered directlyor by fitting data in Mentat

Lab Data

Mode

α β,( )W0

ov factor, , isd in MARC

K α β,( )

l Predictions

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Miehe Effect

W K=

The Kachanimplemente

These factors can be entered directlyor by fitting data in Mentat

Lab Data

Mode

oefficientsMentat

nt λn⁄–( )exp

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Viscoelastic Effects

Prony series cgenerated by

Lab Data

W W∞

Wn 1=

N∑+=

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3D Packer Seal

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Axisymmetric Packer Seal

Seal

6 weeks

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Zero Leak ABS Piston Seal

Typical Seal New

See Customer Profile: Acushnet Rubber Company,On The MARC Newsletter, Spring 1999 (PDF, 591

KB) at www.marc.com

Prototypes for testing were required in

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Constant Velocity Boot

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Tires

allel

7-32 Hosts 1-16

Hosts 33-48

osts; 1 GBytes RAM/Host

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Tire Model Running MARC K73 ParShared: 64 400-MHz CPUs; 1 GBytes RAM/CPU

Hosts 1

Hosts 49-64

Distributed: 64 H

S64 58.3=

al

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Coupled Acoustic-Structural Mod

al

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Coupled Acoustic-Structural Mod

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Automatic Rubber Remeshing

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Automatic Rubber Remeshing

.htm

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Intravenous Medical Tube ClampSee www.marc.com/Theater/movies/ivclamp

rimental: Fuji Film

ctions: MARC FEA

hio

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Knee Implant

Expe

Predi

Orthopedic Research Laboratory, Cleveland, O

ng Class

oom then walking toa, Standard Prod-

data reduction, elas- using FEAfor anyone involved

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Experimental Elastomer Analysis Traini

“The experience of obtaining the experimental data in one rthe next room and using it in FEA was invaluable”,Greg Reucts;

“Excellent. My understanding of experimental testing and tomer material modeling, and material model confirmationincreased tremendously. This workshop should be requiredwith the FEA of elastomers”,Ken Ogilvie, BTR;

“The EEA workshop providesvaluable guidance as to whatone can expect and cannotexpect elastomer FEA models topredict, and when correctlyapproached, how powerful FEAof elastomers is in a field tradi-tionally viewed as art”, LarryCastleman, Busak & Shamban.