This presentation is given at Santa Clara Ansys Conference in 2014, where we have presented the viscoelastic modelling capabilities in Ansys and the basic requirements for such modelling. The presentation is simple and a good starting point to understand viscoelastic modeling in Ansys.

1. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
Modeling Viscoelastic Damping
for Dampening Adhesives
ANSYS REGIONAL CONFERENCE
SANTA CLARA 2014
Can Ozcan & Metin Ozen
Ozen Engineering Inc.

2. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
ABSTRACT
Dampening adhesives are widely used in high sensitivity
manufacturing equipment design in order to minimize
vibration. Dampening adhesives exhibit viscoelastic behavior
and needs to be modeled properly to achieve high quality
design criteria.
This presentation discusses the importance of viscoelastic
material modeling, how it is tested and used to design for
vibration control. Ansys Structural nonlinear capabilities are
needed to analyze for time-transient response of structural
damping adhesives with accuracy.
The presentation includes a test case for electronic device
manufacturing equipment design.

3. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
AGENDA
● VISCOELASTICITY
● DAMPENING ADHESIVES
● TESTING METHODS - NO TEMPERATURE DEPENDENCY
• Experimental Static Test Methods
– Uniaxial Tension and Compression
– Equibiaxial Method
– Planar and Simple Shear Methods
• Experimental Dynamic Test Methods
– Creep and Stress Relaxation Methods
– Torsion Pendulum Method
– Forced Vibration Non-Resonance Methods
– Resonance Methods
– Wave Propagation Methods
● INCORPORATING TEMPERATURE DEPENDENCY
● ANSYS MODELING
● DESIGN FOR VISCOELASTIC DAMPING

4. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
Use of Viscoelastic Materials
● Viscoelastic materials are widely used for vibration, shock and noise
control in the automotive, marine, aerospace, electronics, defence,
instrumentation and home appliance industries.
Image: http://www.trelleborg.com/en/Media/Products-and-Solutions-News/Archive/Silence-included/

5. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
Automotive Application
● Dampening adhesives applied in automotive body to minimize vibration
induced sound
Image : http://2.bp.blogspot.com/_U2C8LB0alAM/SffrG46Fm4I/AAAAAAAAABs/Yo0KB-7ghyA/s400/Latio+spare+tyre+well+before+SP.JPG

6. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
Electronics Application
http://solutions.3mcanada.ca/wps/portal/3M/fr_CA/electronics/home/productsandservices/products/TapesAdhesives/ViscoelasticDampingPolymers/
● Used in electronic devices to minimize vibration

7. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
VISCOELASTICITY
● Viscoelastic materials are made up of long-chain molecules.
● Their properties are determined by the degree of mobility or
entanglement of the long-chain molecules.
● Three regimes of viscoelastic behavior
• The rubbery regime
• The rubber-to-glass transition regime
• The glassy regime
● These regimes encompass rubbers, elastomers, polymers, epoxies and
plastics

8. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
VISCOELASTICITY
● Classification of a viscoelastic material is dependent on it’s temperature
● A viscoelastic material which is classed as rubber at 20C can be made to
behave as a glassy or plastic material at a relatively low temperature of -
40C or less.
● Similary, a material defined as plastic at 20C can be made to behave as
rubbery material at higher temperatures of 150C or more.

9. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
VISCOELASTICITY
● Unlike most metallic materials, mechanical properties of viscoelastic
materials are temperature, frequency and time dependent.
● While the mechanical properties of most metallic materials can be
obtained from material data handbooks, the temperature-, frequency-
and time-dependent characteristics of the mechanical properties of
viscoelastic materials have to be determined experimentally.

10. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
LINEAR VISCOELASTICITY
● Behavior of viscoelastic materials is in between elastic solids and viscous
liquids.
● A first approximation can be Hooke’s law of elasticity plus Newton’s law
of viscosity
under simple shear
conditions

11. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
SHEAR RELAXATION MODULUS
● Shear Relaxation Modulus is obtained from response of a viscoelastic
material subjected to a step change in strain as shown below
● Shear Relaxation Modulus is direct input to Ansys simulations through a
Prony series definition so it is important definition to understand

12. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
SHEAR RELAXATION MODULUS
● Shear relaxation modulus is time dependent
● Under very short times of the order 10-3s or less, ie timescale for shock
and impact, modulus is very high as the time is too short for the long-
chain molecules of viscoelastic material to re-arrange
● At very long times of order 10s or more, ie timescale for creep, modulus
becomes relatively low since long chains have time to re-arrange

13. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
COMPLEX MODULUS
● Analyzing viscoelasticty in frequency domain, gives us the concept of
complex modulus
● Under repetitive loading, viscoelasticity can be defined as:
Storage Modulus
Loss Modulus
Loss Factor

14. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
EFFECT OF TEMPERATURE ON VISCOELASTICTY
● Effects of temperature on complex modulus can be divided into three
distinct regions as shown below (glassy, transition, rubbery)
● At very low temperatures, the motion of the long polymer chains of the
material is highly restricted
● The temperature at which the loss factor attains its maximum value is
known as the transition temperature
E0: instantaneous modulus
Ee: long term/equilibrium modulus

15. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
EFFECT OF FREQUENCY ON VISCOELASTICITY
● Frequency effect on dynamic properties is similar but inverse to the
effect of temperature
E0: instantaneous modulus
Ee: long term/equilibrium modulus

16. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
DAMPING ADHESIVES
● Most applications use the damping adhesive as part of a damped metal
laminate (DML) or as part of a Constrained Layer Damper (CLD)
● DML: Viscoelastic layer is sandwiched in between a metal/plastic layer
formed into finished product (valve cover, oil pan, brackets)
● CLD: Constraining layer of metal or plastic/viscoelastic damper is
attached via polymer layer to the structure to be damped (car panels,
disk drive covers)
Example of DML Application Example of CLD Application

17. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
DAMPING ADHESIVES
● Selection of proper damping polymer is dependent on the temperature
and frequency of the application
● As we have seen for maximum damping, loss factor and the storage
modulus should be maximum which is dependent on both temperature
and frequency for each type of viscoelastic material
● Some applications may need different types of polymers in a multi-
layered setup to damp vibrations at different frequencies or
temperatures

18. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
TESTING METHODS
● Hyperelastic behavior can be used to define viscoelastic materials
rubbery state
● Static test methods can be employed to determine the hyperelastic
properties
● We should remember that shear modulus and bulk modulus are required
to define elastic materials mechanical response
● Using theory of elasticity one can measure shear and Young’s modulus to
determine bulk modulus; which is hard to measure accurately for
viscoelastic materials

19. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
STATIC TESTING METHODS
● Uniaxial tension and compression methods
• Usually dog bone shaped specimens of 2mm thickness and 25mm
length
• Determine Young’s modulus
● Equibiaxial method
• Can be achieved by either loading a square sheet of rubber or by
filling a rubber balloon with a gas and subjecting to internal pressure
● Planar and simple shear methods
• Determine pure shear modulus via planar shear test
• Width to Length ratio of the specimen should be 8-10

20. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
DYNAMIC TESTING METHODS
● There are several techniques for the experimental determination of
dynamics properties of viscoelastic materials (namely complex moduli)
● Methods operate either in time or frequency domain and cover different
time/frequency ranges
● Depending on the time/frequency range these methods can be listed as:
• Creep and stress relaxation methods
• Torsion pendulum method
• Forced vibration non-resonance methods
• Resonance methods
• Wave propagation methods
shorter time scales
higher frequencies

21. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
SIMULATION OF VISCOELASTICITY IN ANSYS
● Viscoelasticity brings non-linearity into finite element analysis
● Some considerations when performing viscoelastic nonlinear analysis:
• Choice of element: depends on geometry, due to common use of
dampening adhesive tapes shell elements with composite properies
can be preferred. 3D continuum elements may be needed for thick
bulky parts (shell vs solid element types in Ansys)
• Linear vs Quadratic: since relative thickness of adhesive tapes are
much thinner wrt to metal parts, quadratic elements are preferred
to be able to resolve stress gradients with less elements (solid185 vs
solid186 in Ansys)
• Compressible vs Incompressible: when a viscoelastic material is in
its rubbery regime, its Poisson’s ratio is almost 0.5 ie when
deformed the volume does not change. Hybrid elements need to be
used in such case (keyopt,x,6,1: mixed u-P formulation in Ansys)

22. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
SIMULATION OF VISCOELASTICITY IN ANSYS
● Once a finite element model is build we can perform:
• Static (linear&non-linear)
• Time Domain Dynamic (linear&non-linear)
• Frequency Domain Dynamic (linear only)*
– For a “Full” harmonic analysis, frequency-dependent elastic and
damping behaviors are supported!
analysis in Ansys
● In machine design one uses the adhesive tapes to dampen out certain
frequencies in the design either related to precision or acoustics
● Thus interest is around Dynamic analysis for adhesive tapes

23. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
COMPARISON OF ANALYSIS TYPES
● A two point bending test is usually used to assess damping performance
of adhesive tapes in a three layer laminate design
● We built the setup of such system in Ansys to compare results under
different analysis types:
● A 2-D plane-strain model with half-symmetry is used
Point fixed
invertical y
direction
Symmetry
face

24. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
COMPARISON OF ANALYSIS TYPES
● Modal analysis give same results for natural frequencies, since
nonlinearity and/or frequency dependency is not taken into account
Viscoelastic Material Definition
1st Mode: 108 Hz
Linear Material Definition
1st Mode: 108 Hz

25. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
COMPARISON OF ANALYSIS
● Harmonic analysis give different results
● Ansys takes into account frequency dependent modulus complex
modulus value for “full” solution method harmonic analysis
● Frequency dependency is applied via Prony Series
● Below results compare center displacement under repeated 1N load
Viscoelastic Material Definition
Damped solution around 70Hz
Linear Material Definition
Resonance around 108Hz

26. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
COMPARISON OF ANALYSIS
● Below time-history graph shows the center displacement of a DML plate,
2 point bending vibration under pulse input

27. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
CALCULATING FFT RESPONSE FROM TIME-HISTORY
● Time-history values can be converted to frequency domain via FFT
● Ansys CFD Post can be used to perform FFT operation
● Results compare well with harmonic analysis
● Temperature dependency is applied via WLF functions

28. © 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential
CALCULATION PERCENT DAMPING
● Damping calculations can be performed using the frequency domain
results using “Half-power Bandwidth Methods”