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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 …

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.

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  • 1. Simulation  with  Nonlinear   Structural  Materials  
  • 2. Sponsored By:
  • 3. Before We Start q  This webinar will be available afterwards at & via email 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®   •  North  America   –  –  –  –  –  –  –  –  –  –  Vancouver,  BC   Richardson,  TX   Windsor,  ON   Nashville,  TN   Burlington,  MA   Southfield,  MI   Saskatoon,  SK   Lubbock,  TX   Ithaca,  NY   Buffalo,  NY   •  Europe   –  –  –  –  –  –  –  –  –  –  –  Freiburg,  Germany   Linz,  Austria   Gö]ngen,  Germany   Antwerpen,  Belgium   Bologna,  Italy   Wien,  Austria   Wrocław,  Poland   Toulouse,  France   Lyon,  France   Biella,  Italy   Roma,  Italy   •  Register  for  our  free   hands-­‐on  workshops  at  
  • 39. COMSOL  Conference   Boston  ·∙  Bangalore  ·∙  Roeerdam  ·∙  Singapore  ·∙  Seoul  ·∙  Taipei  ·∙  Tokyo    
  • 40. Contact  Us   •  Ques'ons?   •   –  –  –  –  –  –    User  Stories   Videos     Model  Gallery   Discussion  Forum   Blog   Product  News  
  • 41. Thank You q  This webinar will be available at & email q  Tweet with hashtag #DWwebinar q  Connect with q  Twitter: @DesignWorld q  Facebook: q  LinkedIn: Design World Group q  YouTube: q  Discuss this on