Simulation with Nonlinear Structural Materials
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Simulation with Nonlinear Structural Materials
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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.
Transcript of Simulation with Nonlinear Structural Materials
Simulation with Nonlinear Structural Materials
Sponsored By:
q This webinar will be available afterwards at designworldonline.com & via email
q Q&A at the end of the presentation q Hashtag for this webinar: #DWwebinar
Before We Start
Moderator
Leslie Langnau Design World
Presenter
Mateusz Stec COMSOL
Simula'on with Nonlinear Structural Materials
Mateusz Stec Technical Product Manager
COMSOL
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
Why Do We Simulate Nonlinear Materials?
• Concept and understanding
• Design and op'miza'on
• Tes'ng and verifica'on
Reinforced concrete
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
Enables Technology Design Innova'ons
Microwave Three-port Circulator
Porous Reactor
Fluid-Structure Interaction of a
Solar Panel
Acoustics Speaker Systems
Radiation Pattern of a Broadband Conical Antenna
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
All-‐Inclusive Interac've Modeling Environment
Graphics Ultrafast graphic presenta'on, stunning visualiza'on, and mul'ple plots
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
Product Suite – COMSOL Version 4.3b
Cons'tu've Modeling • Structural
– Linear elas'c – Linear viscoelas'c
• Nonlinear – Creep – Hyperelas'c – Elastoplas'c – Viscoplas'c
• Geomechanics – Concrete – Rock – Soil plas'city
σ
ε
σ
ε Hyperelastic material Elasto-plastic material
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
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
Predefined Elastoplas'c Models • Large strain plas'city • Yield criteria
– Tresca – von Mises – Hill plas'city
• Hardening – Isotropic – Orthotropic – Kinema'c
• Plas'c flow – Associated – Non-‐associated
• User defined
Stress distribution in a stent during balloon inflation
Predefined Viscoplas'c Model • Anand
Viscoplastic creep in solder joints under thermal loading
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
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
Model Builder and Se]ngs
CAD & Meshing Interoperability 3D CAD File Formats ACIS® Ca'a® V5 Creo™ Parametric IGES Inventor® Parasolid® Pro/ENGINEER® SolidWorks® STEP
Meshing Products Mimics® +FE Module (Simpleware®) Avizo®
2D CAD File Formats DXF
E-‐CAD File Formats GDS/NETEX-‐G ODB++ Mesh File Formats
NASTRAN STL VRML
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
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
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
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)
Strain Evalua'on Op'on • Small plas'c strains
– Addi've decomposi'on of strains
• Large plas'c strains – Mul'plica've decomposi'on of
deforma'on gradient large
small
Necking of an elastoplastic metal bar
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
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
Soil Plas'city Op'ons • Ellip'c cap • Tension cut-‐off • Dilata'on angle in plas'c
poten'al • Parameter match to Mohr-‐
Coulomb
Hyperelas'c Energy Evalua'on • Nearly incompressible materials
– Pressure (mixed formula'on) – Prevent locking
• User-‐defined energy func'ons
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
Variable Material Parameters
Temperature-dependent plasticity in a pressure vessel
Infinite Element Domains
Model Library • Combined creep • Arterial wall mechanism • Hyperelas'c seal • Bar necking • Sheet metal forming • Viscoplas'c solder joints • Tunnel excava'on • Concrete beam
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
Q&A Session
Product Suite – COMSOL Version 4.3b
Try COMSOL Mul'physics® • North America
– Vancouver, BC – Richardson, TX – Windsor, ON – Nashville, TN – Burlington, MA – Southfield, MI – Saskatoon, SK – Lubbock, TX – Ithaca, NY – Buffalo, NY
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• Register for our free hands-‐on workshops at www.comsol.com/events
COMSOL Conference
Boston ·∙ Bangalore ·∙ Roeerdam ·∙ Singapore ·∙ Seoul ·∙ Taipei ·∙ Tokyo
Contact Us • Ques'ons?
www.comsol.com/contact
• www.comsol.com – User Stories – Videos – Model Gallery – Discussion Forum – Blog – Product News
Thank You q This webinar will be available at designworldonline.com & email
q Tweet with hashtag #DWwebinar
q Connect with q Twitter: @DesignWorld
q Facebook: facebook.com/engineeringexchange
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q Discuss this on EngineeringExchange.com
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