ANSYS Users Group_Hyperelastic Materials

Midwest ANSYS Users GroupMay 18, 2005 Analyzing Hyperelastic Materials w/ Some Practical Considerations Prepared by: Paris Altidis; Borg Warner Updated by: Vince Adams; IMPACT ©2004 – IMPACT Engineering Solutions, Inc. 1 1 What Is a Hyperelastic Material ? ? ? ? ? ? ? Can experience large strains (up to 500%) and most of it - if not all - is recoverable. Rubber is a hyperelastic material; behavior is reminiscent of a viscous fluid during its processing to shape. The vulcanization and/or curing of rubber type materials causes their polymer chains to crosslink which allows the material to fully recover from elastic deformations. Load-Extension behavior is nonlinear Nearly incompressible – Exception is some rubber foam materials where large volume changes can be achieved. Low Cost / Flexible / Resilient - Work in many environments (moisture, pressure, heat) www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 2 2 2 Where are Hyperelastic Materials Used? ? ? ? ? ? Automotive (Tires, Belts, Hoses, Mounts) Aerospace (Remember the failed O-ring on the Space Shuttle ??) Biomedical/Dental Industries (artificial organs, wheelchairs, implantable surgical devices) Packaging (Styrofoam) Sports (Equipment safety, Shoes, Helmets) www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 3 3 3 Gent.com ©2005 – IMPACT Engineering Solutions. Inc.Available Hyperelastic Material Models in ANSYS 9. Yeoh ? For special apps like foam: Use Blatz-Ko and Ogden Compressible Foam ? www. NeoHookean.impactengsol. 4 4 4 . Polynomial Form.0 Mooney-Rivlin. Ogden Potential. Arruda-Boyce. Inc.0 ? ? User-Programmable Features (UPFs) are available to code your own material model.impactengsol. 5 5 5 . Currently available UPFs for hyperelasticity use HYPERxx types of elements.com ©2005 – IMPACT Engineering Solutions. www.Beyond the available models in ANSYS 9. Inc. Do a Curve Fit and plot both test and fitted data on same plot.17 give you all the available AND equivalent testing modes www.impactengsol.Material Modeling Basics… ? A poor material model will ? ? ? Minimum Data: Uniaxial tension ? ? ? ? Prevent your FE model from running MOST likely will give you erroneous results and you will not even know it…. 6 6 6 .com ©2005 – IMPACT Engineering Solutions. Chapter 4 Structures with Material Nonlinearities in ANSYS ? Figures 4. Try a NeoHookean Material Best Scenario: Uniaxial AND Biaxial Tension + Pure Shear.16 and 4. com ©2005 – IMPACT Engineering Solutions.impactengsol.16 – Deformation Modes Source: ANSYS 9. Inc.6 www.0 Theory – Chapter 4.Material Modeling Basics… Figure 4. 7 7 7 . Inc.17 – Equivalent testing modes Source: ANSYS 9. 8 8 8 .impactengsol.0 Theory – Chapter 4.6 www.com ©2005 – IMPACT Engineering Solutions.Material Modeling Basics… Figure 4. e.com ©2005 – IMPACT Engineering Solutions.Equibiaxial vs. No Friction Friction Affects Compression Test Data www. Compression Testing • Pure Compression Requires: • Uniaxial Loading • No Lateral Constraints • i. Inc.impactengsol. 9 9 9 . Inc. Compression Testing While not intuitive.Equibiaxial vs. Equibiaxial testing gives same response as pure compression www.impactengsol. 10 10 10 .com ©2005 – IMPACT Engineering Solutions. the stress strain function is sensitive to the maximum strain ever experienced. There is some degree of permanent deformation. 4. 5. The stress strain function for the 1st time an elastomer is strained is never again repeated.Observations on Material Testing 1.impactengsol. The stress strain function will again change significantly if the material experiences strains greater than the previous stabilized level. 11 11 11 . 3. 2.com ©2005 – IMPACT Engineering Solutions. In general. The stress strain function of the material while increasing strain is different than the stress strain function of the material while decreasing strain. Inc. It is a unique event. The stress strain function does stabilize after between 3 and 20 repetitions for most elastomers. www. the material does not return to zero strain at zero stress. After the initial straining. 12 12 12 .Cyclic Damage and Mullins Effect www.com ©2005 – IMPACT Engineering Solutions. Inc.impactengsol. The material model does not differentiate between a 1st time strain and a 100th time straining of the part under analysis. www. Inc. Zero stress is always zero strain. Loading and unloading the part under analysis is the same. 4.impactengsol.Limitations of Hyperelastic Mat’l Models Most material models only allow the analyst to describe only a subset of the structural properties of elastomers. The stress strain functions in the model are stable. The models treat the material as perfectly elastic meaning that there is no provision for permanent strain deformation. 3.com ©2005 – IMPACT Engineering Solutions. There is no provision to alter the stress strain description in the material model based on the maximum strains experienced. 2. The stress strain function is fully reversible so that increasing strains and decreasing strains use the same stress strain function. In the Mooney-Rivlin and Ogden formulations: 1. 13 13 13 . They do not change with repetitive loading. Where is Material Tested ?? ? ? ? Always test your material with loading that is similar to the actual application Contact Axel Products or DatapointLabs for guidelines on what is required.impactengsol. Visit their websites and RTFM (Read Their Fantastic Methods).com ©2005 – IMPACT Engineering Solutions. Inc. Many papers can be downloaded for reference. www.com www. 14 14 14 .datapointlabs.com www.axelproducts. impactengsol. 15 15 15 .Curve Fitting of Hyperelastic Parameters ? ? ? ? The recommended method is the ANSYS Curve Fitting Wizard.net provide in-depth info on these techniques… Most will be posted to the MAG site www. you need 2X the number of M-R Parameters.ansys. Inc. For a decent curve fit using the M-R models. Hardcore users: Use APDL to create your own scripts for the curve fitting portion and post-processing. Papers on www.com ©2005 – IMPACT Engineering Solutions. com > Surveys TIP: DEPENDING ON YOUR DESIGN/APPLICATION NEEDS ANY OR ALL MAY BE REQUIRED FOR THE MATERIAL AT HAND www.polymerfem.impactengsol.Testing Procedures… Source http://www.com ©2005 – IMPACT Engineering Solutions. Inc. 16 16 16 . www.2-P Mooney-Rivlin vs.com ©2005 – IMPACT Engineering Solutions. Worth using it in ANSYS as a firstpass analysis ?? ? I’d rather test the material at hand in tension at least. 17 17 17 . Shore Hardness How good is it ? ? Has been seen in ANSYS and other user groups ? ONLY For Reference ? Experience has shown that it is not consistent for ALL GRADES and TYPES of hyperelastic materials. Inc.impactengsol. 92 14.09 6.285 50.945 5.86 10.79 45.82 78.305 31.245 27.38 6.525 6.61 177. psi From Waltz (XANSYS) www.83 68.71 30.98 18.755 215. 18 18 18 .36 25.22 183.615 43.315 22.845 9. psi Shore-A [°] 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 C10 C01 80 Linear (C10) Linear (C01) 60 40 y = 0.455 12.59 415.62 205.975 8.72 C01 psi 5.63 74.715 494.com ©2005 – IMPACT Engineering Solutions.955 361.275 665.425 9.41 8.76 227. Inc.635 23.045 179.945 5.605 53.15 101.86 434.impactengsol.565 453.585 41.375 26.02 11.92 379.225 196.815 7.475 537.23 26.525 37.555 39.685 252.07 55.185 23.945 6.97 88.705 473.305 637.575 20.965 C10 psi 23.625 762.73 71.33 328.0333x 20 0 0 100 200 300 400 500 600 700 800 900 Young's Modulus.68 Mooney Coefficients 120 y = 0.66 560.2 24.67 312.16 515.5 15.445 296.2-P Mooney-Rivlin vs.075 610.715 585.705 19.035 12.36 25.22 65.79 106.11 17.9 33.54 7.135 189.39 58 60. Shore Hardness E psi 176.32 397.405 28.8 97.805 16.74 92.99 799.195 13.345 84.25 7.425 344.49 23.1333x 100 Mooney Coefficients.615 13.53 17.08 15.465 63.735 266.3 21.01 81.64 35.655 281.985 696 728.505 239.925 24.44 11.965 48. impactengsol. F. 1978. Shore Hardness E (psi) = 11. 1400 Young's Modulus (PSI) 1200 1000 800 600 400 200 0 20 30 40 50 60 70 80 90 100 Hardness (Shore A) www.0071*A^3 Lindemann (XANSYS) From E. 19 19 19 .2-P Mooney-Rivlin vs.4445*A^2 + 0. Rubber Springs Design. Gobel.com ©2005 – IMPACT Engineering Solutions. Inc. John Wiley. New York.427*A -0. 42 198.com ©2005 – IMPACT Engineering Solutions.02 814.14 619.01 Lindemann Gobel 800 600 400 200 0 20 30 40 50 60 70 80 Hardness.42 412.15 291.2-P Mooney-Rivlin vs.58 463.85 200.00 Lindemann 159.56 244. Shore Hardness Comparison of Fitted Data 1200 Young's Modulus.impactengsol. Inc.63 342. psi. Waltz 1000 Shore A 35 40 45 50 55 60 65 70 Waltz 172.45 541. Shore A www.14 Gobel 154.60 465.23 520.58 1057.16 649.58 255.09 347. 20 20 20 .12 800.84 324.36 398.28 261.75 205. polymerfem. 21 21 21 .impactengsol.com ©2005 – IMPACT Engineering Solutions.com Other material models from the same source may be used in ANSYS via UPFs.Material Model Recommendations Material Hyperelastic Model Acrylate-butadiene rubber Neo-Hookean Chloroprene Rubber Arruda-Boyce / Yeoh Natural Rubber (55 pph CB) Yeoh Nitrile Rubber Neo-Hookean Silicon Rubber Arruda-Boyce Viton Arruda-Boyce Source http://www. Inc. www. com ©2005 – IMPACT Engineering Solutions. 22 22 22 .impactengsol. Inc.Example of O-Ring Compression www. com ©2005 – IMPACT Engineering Solutions.Example of O-Ring Compression ? ? ? Scope: The performance of an O-Ring (used in a medical device) during assembly as a seal needs to be analyzed and the contact forces to the mating parts be extracted. Inc. 23 23 23 . All other parts: Steel www. Element Type: PLANE182 Axisymmetric (Keyopt(1)=0 Full integration with B-bar method (No Hourglass control) Materials: O-Ring: Hyperelastic Material (Other grade information not available).impactengsol. Example of O-Ring Compression www. 24 24 24 .impactengsol. Inc.com ©2005 – IMPACT Engineering Solutions. 25 25 25 . So. Inc. material tested by Axel products as shown below.Example of O-Ring Compression Step 1: The lack of information about the material would not allow any guessing (BAD MOVE).impactengsol.com ©2005 – IMPACT Engineering Solutions. Step 2: Curve fitted to 9P M-R Model (BETTER ) (method APDL) www. Why a 9P Mooney-Rivlin Model • Better Fit for the strain range • A 5-P might have worked just as well • A Curve fit of ALL Available mat.com ©2005 – IMPACT Engineering Solutions. Inc. (BEST CHOICE ) www. Models and parameters were not feasible/available at the time. 26 26 26 .impactengsol. The Assembly as Designed Guess where the Solution bombed out due to highly distorted Elements. Inc. 27 27 27 . (~ 25% into final loadstep – after preliminary contact resolution).impactengsol.com ©2005 – IMPACT Engineering Solutions. www. 28 28 28 .impactengsol.com ©2005 – IMPACT Engineering Solutions. (Rick?) www.The assembly as Modified to help in the Convergence TIP : Use rounded corners in areas where the soft material gets (or is expected to become) highly distorted and causes shear locking and hourglassing. Inc. type.1.impactengsol. Inc.com ©2005 – IMPACT Engineering Solutions.on ! Turn on nodal Forces Pldisp ! Show Displacement plot www..2 ! Colors only esel. 29 29 29 .mat ! Plot Element by material ONLY /num..2 ! Select Solid Elements /nfor.Problem Solved !! Used a Different color to monitor the change in orientation of all points of interest during the animation process /pnum. impactengsol. 30 30 30 .com ©2005 – IMPACT Engineering Solutions. • Next iteration should incorporate friction • Did Rich tell you about friction in contact pairs ?? www. • Mesh deformation is acceptable.Lessons Learned… • The use of the rounded Fillet helped (read: saved me) in completing the O-Ring assembly. • Orientation of “monitor” elements indicate lack of friction at the contact. • Contact resolution w/ mating parts as expected. Inc. 31 31 31 .com ©2005 – IMPACT Engineering Solutions.impactengsol. Inc.Solution with Friction Added… www. com ©2005 – IMPACT Engineering Solutions.8 www. C01=26. 32 32 32 .Another O-Ring Case Study… 2 Parameter Mooney-Rivlin Model Used C10=107. Inc.impactengsol.18. www.com ©2005 – IMPACT Engineering Solutions. Hourglassing IS NOT LIMITED to full integration elements. Inc. Use full scale plot to see Hourglassing effects. Combination of material model. Use the wrong Stiffness factor w/ the Uniform Reduced Integration method and you’ll see it…. Hourglass-shaped elements can propagate through the mesh IF THERE ARE LESS THAN 2 ROWS OF ELEMENTS IN EACH DIRECTION. Think of it as “Rubber Turbulence” as the deformation change is rapid and violent. In reality. geometry.impactengsol. mesh density and element selection can induce Hourglassing in hyperelastic materials. 33 33 33 .Hourglassing ? ? ? ? ? ? Hourglassing occurs when there is compression in the material. Hourglassing DOES NOT EXIST. Inc. the artificial energy introduced to control the hourglass effect may affect solution accuracy adversely. ? Don’t just increase the Stiffness 10% for every successive iteration ? Bump it up to some high number and then back off ? Chances are ANSYS will solve FASTER using a HIGH HGSTF rather than a LOW and Gradually increasing value.impactengsol.com ©2005 – IMPACT Engineering Solutions. 34 34 34 .Hourglassing ? ? ? Elements Supporting Hourglass control : Plane182/183. Solid 164 / 185 / 186 / 45 Use HGSTF Real Constant to Specify the Hourglass stiffness scaling factor However. www. com ©2005 – IMPACT Engineering Solutions. Inc.impactengsol. More than 5 % ?? Refine the mesh OR reduce the HGSTF.Hourglassing CAUTION: Introducing the HGSTF changes the the problem. ? ? If the Ratio SENE / AENE is < 5 % the solution is acceptable. www. (Especially if the deformation is Bending Dominated) ? Compare the total energy (SENE) to the artificial energy (AENE) that is being introduced by the hourglass stiffness. 35 35 35 . Use the more comprehensive TB. the test data you obtain are Engineering and NOT True Stress and Strain. Inc.com ©2005 – IMPACT Engineering Solutions.Hyper. processing etc.impactengsol. Therefore.Mooney which is for HYPER56/58 elements.THE School of Hard Knocks ? ? ? NEVER ask a forum member to give you their material data.Wisdom on Hyperelastic Materials from XANSYS .option instead of TB. it cost $ to test but this is not the area to cut corners.) The term “Strain” in hyperelastic materials is replaced by “Stretch”. The principal stretch ratio = 1 + eng. Strain. Yes.. 36 36 36 . www. How do you know the material is made from the same stuff ?? (grade. The first and second invariants of M-R and other models are based on Stretch Ratios. The literature is leaning towards M-R or hyperelastic w/ Ogden function. Poisson’s ratio of 0.bham. Inc. use 0.THE School of Hard Knocks ? ? ? For perfectly incompressible material.uk/millsnj/pdf/matpaperkyoto. Polyurethane foams and access to LS-DYNA ?? See this reference: http://web.com ©2005 – IMPACT Engineering Solutions.Wisdom on Hyperelastic Materials from XANSYS .impactengsol.ac.49995 Polyurethane foams ?? Use Hyper56 with Blatz-Ko function (Keyopt(2)=1) IF you have the parameters for it. 37 37 37 .pdf www. To keep ANSYS happy.5 is unacceptable as it makes the bulk modulus infinite. com ©2005 – IMPACT Engineering Solutions.impactengsol. Inc.PolymerFEM.html www.hu/me/2001_1/pdf/me2001_1_11.com/pages/Downloads. SILICONE RUBBER TESTING http://www.pdf www.bme.com As the name suggests it is THE place to start w/ questions pertaining to elastomer modeling.pp. 38 38 38 .axelproducts. (mostly ABAQUS but some ANSYS and LS-DYNA models are readily available).References on the Internet ? ? ? All about Testing Hyperelastic Materials and more… http://www. Is this option something we can expect to see in the near future ??? www. ANSYS Customer Portal – Sample Models Ansys.impactengsol.net Axel Products Datapoint Labs PolymerFEM. Inc. 39 39 39 .Conclusions ? ? ? Test the material at hand Take the Advanced Nonlinearities Class offered by your ASD.com ©2005 – IMPACT Engineering Solutions. Use these RESOURCES ? ? ? ? ? ? ? ? IMPACT Engineering Solutions.com XANSYS – Ask (wisely) and thou shall receive… Wish List : Currently ANSYS does not have the option for Mullins Effect to account for hysteretic damage. Inc.