When the stress in a structure becomes sufficiently large, many materials display nonlinear behavior. Some materials may exhibit a nonlinear stress-strain response even at very low stress. Material models including elastoplastic, viscoplastic, creep, and hyperelastic require expressions more sophisticated than the linear Hooke’s law. This webinar presented applications of nonlinear materials modeling in COMSOL Multiphysics and demonstrated how user-defined materials can be incorporated into a simulation. The webinar concluded with a 15-minute Q&A session. Watch the webinar to learn: • which nonlinear material models are predefined in COMSOL • how to simulate nonlinear material behavior • how to combine different sources of material nonlinearity Speaker: Mateusz Stec, Technical Product Manager, Fatigue, COMSOL Bio: Mateusz works as the Technical Product Manager for the Fatigue Module. He studied Aerospace Engineering at the University of Michigan and Vehicle Engineering at the Royal Institute of Technology. In 2008, he completed his PhD in Solid Mechanics at the Royal Institute of Technology. Before joining COMSOL, he worked at SKF’s European Research Centre as a researcher and project leader.

1. Simulation with Nonlinear
Structural Materials

2. Sponsored By:

3. Before We Start
q This webinar will be available afterwards at
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q Q&A at the end of the presentation
q Hashtag for this webinar: #DWwebinar

4. Moderator
Presenter
Leslie Langnau
Mateusz Stec
Design World
COMSOL

5. Simula'on
with
Nonlinear
Structural
Materials
Mateusz
Stec
Technical
Product
Manager
COMSOL

6. Agenda
• Mul'physics
Simula'on
• Structural
Modeling
– Nonlinear
Materials
– Sources
of
Nonlinearity
– Modeling
op'ons
• Video
Demo
• Q&A
• How
To
– Try
COMSOL
Mul'physics
– Contact
Us
Compression of a hyperelastic seal

7. Why
Do
We
Simulate
Nonlinear
Materials?
• Concept
and
understanding
• Design
and
op'miza'on
• Tes'ng
and
verifica'on
Reinforced concrete

8. Modeling
with
COMSOL
Mul'physics
• Electrical,
Mechanical,
Fluid,
and
Chemical
Simula'ons
• Mul'physics
–
Coupled
phenomena
– Two
or
more
physics
phenomena
that
affect
each
other
with
no
limita'on
on
which
combina'ons
or
how
many
combina'ons
• Single
physics
– One
integrated
environment
–
different
physics
and
applica'ons
– One
day
you
work
on
Heat
Transfer,
next
day
Structural
Analysis,
then
Fluid
Flow,
etc.
– Same
workflow
for
any
type
of
modeling
• Enables
cross-­‐disciplinary
product
development
and
a
unified
simula'on
plaUorm

9. Enables
Technology
Design
Innova'ons
Microwave Threeport Circulator
Radiation Pattern
of a Broadband
Conical Antenna
Fluid-Structure
Interaction of a
Solar Panel
Porous
Reactor
Acoustics Speaker
Systems

10. Op'miza'on
for
Green
Technology
Design
• Solar
panels
are
subject
to
wind
loads
• Must
be
engineered
to
bend
with
the
flow
• Fluid-­‐structure
interac'on
(FSI)
– Fluid
flow
– Structural
displacement
Solar panel subjected
to wind load

11. All-­‐Inclusive
Interac've
Modeling
Environment
COMSOL
Desktop™
StraighUorward
to
use,
it
gives
full
insight
and
control
over
the
modeling
process
Model
Builder
Provides
instant
access
to
any
part
of
the
model
se]ngs
• CAD/Geometry
• Materials
• Physics
• Mesh
• Solve
• Results
Graphics
Ultrafast
graphic
presenta'on,
stunning
visualiza'on,
and
mul'ple
plots

12. Product
Suite
–
COMSOL
Version
4.3b

13. Cons'tu've
Modeling
• Structural
– Linear
elas'c
– Linear
viscoelas'c
σ
σ
• Nonlinear
–
–
–
–
Creep
Hyperelas'c
Elastoplas'c
Viscoplas'c
• Geomechanics
– Concrete
– Rock
– Soil
plas'city
ε
Hyperelastic material
ε
Elasto-plastic material

14. Predefined
Creep
Models
•
•
•
•
•
•
•
•
•
•
Norton
Norton-­‐Bailey
Garofalo
Nabarro-­‐Herring
Coble
Weertman
Poten'al
Volumetric
Deviatoric
User-­‐defined
Stress response of a combined
Norton and Norton-Bailey material

15. Predefined
Hyperelas'c
Models
•
•
•
•
•
•
•
•
•
•
•
•
Neo-­‐Hookean
St
Venant-­‐Kirchhoff
Money-­‐Rivlin
Yeoh
Ogden
Storakers
Varga
Arruda-­‐Boyce
Blatz-­‐Ko
Gao
Murnaghan
User
defined
Rubber velocity joint,
model courtesy of
Metelli S.p.A., Italy

16. Predefined
Elastoplas'c
Models
•
•
Large
strain
plas'city
Yield
criteria
•
Hardening
•
Plas'c
flow
•
User
defined
– Tresca
– von
Mises
– Hill
plas'city
– Isotropic
– Orthotropic
– Kinema'c
– Associated
– Non-­‐associated
Stress distribution in a stent
during balloon inflation

17. Predefined
Viscoplas'c
Model
• Anand
Viscoplastic creep in solder
joints under thermal loading

18. Predefined
Concrete
and
Rock
Models
•
•
•
•
Bresler-­‐Pister
Willam-­‐Warnke
Oeosen
Material
op'on
– Tension
cut-­‐off
• Hoek-­‐Brown
• Generalized
Hoek-­‐Brown
Stress distribution in a
concrete beam

19. Predefined
Soil
Models
•
•
•
•
•
•
•
Mohr-­‐Coulomb
Drucker-­‐Prager
Lade-­‐Duncan
Matsuoka-­‐Nakai
Cam-­‐Clay
User-­‐defined
Material
op'ons
– Compressive
cap
– Tension
cut-­‐off
Stress distribution around
an excavated tunnel

20. Model
Builder
and
Se]ngs

21. CAD
&
Meshing
Interoperability
2D
CAD
File
Formats
DXF
3D
CAD
File
Formats
ACIS®
Ca'a®
V5
Creo™
Parametric
IGES
Inventor®
Parasolid®
Pro/ENGINEER®
SolidWorks®
STEP
E-­‐CAD
File
Formats
GDS/NETEX-­‐G
ODB++
Mesh
File
Formats
NASTRAN
STL
VRML
Meshing
Products
Mimics®
+FE
Module
(Simpleware®)
Avizo®

22. Thermal
Stress
• Mul'physics
interface
• Coupled
structural
and
thermal
analysis
• Mechanical
boundaries
– Loads
– Constraints
• Thermal
boundaries
–
–
–
–
Conduc'on
Heat
flow
Heat
genera'on
Radia'on
Bipolar plate in a fuel cell: Thermal stresses
in a constrained plate

23. Joule
Hea'ng
and
Thermal
Expansion
• Mul'physics
interface
• Physics
coupling
–
–
–
–
Electric
current
conduc'on
Heat
conduc'on
Heat
genera'on
Structural
stresses
and
strains
due
to
thermal
expansion
Thermal actuator: Temperature gradient

24. Piezoelectric
Devices
• Mul'physics
interface
• Cons'tu've
modeling
– Piezoelectric
– Purely
solid
– Purely
dielectric
• Ini'al
electric
displacement
• Electrosta'c
boundary
• Piezoelectric
damping
Sandwich beam with piezoelectric ceramic
actuator: Bending deflection due to shear stress

25. Geometric
Nonlinearity
• The
response
of
the
majority
of
the
structures
can
be
analysed
under
the
assump'on
of
small
displacement
theory
• In
some
situa'ons
the
change
in
the
configura'on
cannot
be
ignored
– It
is
necessary
to
calculate
the
equilibrium
with
respect
to
the
deformed
configura'on
• The
classical
strain
measures
(engineering
strains)
are
no
longer
able
to
describe
large
displacements
and/or
large
rota'ons
– New
strain
measures
must
be
considered
(Green-­‐Lagrange
strains)

26. Strain
Evalua'on
Op'on
• Small
plas'c
strains
– Addi've
decomposi'on
of
strains
• Large
plas'c
strains
Necking of an elastoplastic
metal bar
– Mul'plica've
decomposi'on
of
deforma'on
gradient
large
small

27. Modeling
Op'ons
• Enable
plas'city
in
sub-­‐
domain
• Combine
different
material
nonlineari'es
– Plas'city
+
creep
– Creep
+
creep
– Thermal
expansion
+
creep
+
plas'city
• Geometry
directed
material
orienta'on
Plasticity in an orthotropic container

28. Creep
and
Viscoplas'city
Op'ons
• Olen
refer
to
as
rate-­‐
dependent
plas'city
• Creep
strains
are
added
as
inelas'c
strains
• Combine
predefined
materials
• Predefined
temperature
dependency
• Dissipated
energy
• User-­‐defined
creep
proper'es

29. Soil
Plas'city
Op'ons
• Ellip'c
cap
• Tension
cut-­‐off
• Dilata'on
angle
in
plas'c
poten'al
• Parameter
match
to
Mohr-­‐
Coulomb

30. Hyperelas'c
Energy
Evalua'on
• Nearly
incompressible
materials
– Pressure
(mixed
formula'on)
– Prevent
locking
• User-­‐defined
energy
func'ons

31. User-­‐Defined
Inelas'c
Strains
• Materials
which
exhibit
a
nonlinear
stress-­‐strain
rela'on,
even
at
infinitesimal
strains
– Briele
materials
(ceramics,
metal
alloys)
– Ramberg-­‐Osgood
– Damage
func'on
• You
can
add
distributed
ODEs
or
PDEs
to
account
for
inelas'c
strains
• Add
inelas'c
strains
with
the
Ini'al
Stress
and
Strain
node

32. Variable
Material
Parameters
Temperature-dependent
plasticity in a pressure vessel

33. Infinite
Element
Domains

34. Model
Library
•
•
•
•
•
•
•
•
Combined
creep
Arterial
wall
mechanism
Hyperelas'c
seal
Bar
necking
Sheet
metal
forming
Viscoplas'c
solder
joints
Tunnel
excava'on
Concrete
beam

35. Video
Demo:
Orthotropic
Container
• A
container
made
of
rolled
steel
is
subjected
to
an
internal
overpressure
where
one
of
the
three
material
principal
direc'ons
has
a
higher
yield
stress
than
the
other
two
– Hill’s
orthotropic
plas'city
is
used
to
model
the
differences
in
yield
strength

36. Q&A
Session

37. Product
Suite
–
COMSOL
Version
4.3b

38. Try
COMSOL
Mul'physics®
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America
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www.comsol.com/events

39. COMSOL
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41. Contact
Us
• Ques'ons?
www.comsol.com/contact
• www.comsol.com
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42. Thank You
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