Hyperelastic_Materials-基于Mooney-Rivlin

11©2004 – IMPACT Engineering Solutions, Inc. Midwest ANSYS Users Group May 18, 2005 Analyzing Hyperelastic Materials w/ Some Practical Considerations Prepared by: Paris Altidis; Borg Warner Updated by: Vince Adams; IMPACT 22www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 2 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) 33www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 3 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) 44www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 4 Available Hyperelastic Material Models in ANSYS 9.0 ? Mooney-Rivlin, Polynomial Form, Neo- Hookean, Ogden Potential, Arruda-Boyce, Gent, Yeoh ? For special apps like foam: Use Blatz-Ko and Ogden Compressible Foam 55www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 5 Beyond the available models in ANSYS 9.0 ? User-Programmable Features (UPFs) are available to code your own material model. ? Currently available UPFs for hyperelasticity use HYPERxx types of elements. 66www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 6 Material Modeling Basics… ? A poor material model will ? Prevent your FE model from running ? MOST likely will give you erroneous results and you will not even know it…. ? Minimum Data: Uniaxial tension ? Try a NeoHookean Material ? Best Scenario: Uniaxial AND Biaxial Tension + Pure Shear. ? Do a Curve Fit and plot both test and fitted data on same plot. ? Chapter 4 Structures with Material Nonlinearities in ANSYS ? Figures 4.16 and 4.17 give you all the available AND equivalent testing modes 77www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 7 Material Modeling Basics… Figure 4.16 – Deformation Modes Source: ANSYS 9.0 Theory – Chapter 4.6 88www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 8 Material Modeling Basics… Figure 4.17 – Equivalent testing modes Source: ANSYS 9.0 Theory – Chapter 4.6 99www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 9 Equibiaxial vs. Compression Testing • Pure Compression Requires: • Uniaxial Loading • No Lateral Constraints • i.e. No Friction Friction Affects Compression Test Data 1010www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 10 Equibiaxial vs. Compression Testing While not intuitive, Equibiaxial testing gives same response as pure compression 1111www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 11 Observations on Material Testing 1. The stress strain function for the 1st time an elastomer is strained is never again repeated. It is a unique event. 2. The stress strain function does stabilize after between 3 and 20 repetitions for most elastomers. 3. The stress strain function will again change significantly if the material experiences strains greater than the previous stabilized level. In general, the stress strain function is sensitive to the maximum strain ever experienced. 4. The stress strain function of the material while increasing strain is different than the stress strain function of the material while decreasing strain. 5. After the initial straining, the material does not return to zero strain at zero stress. There is some degree of permanent deformation. 1212www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 12 Cyclic Damage and Mullins Effect 1313www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 13 Limitations of Hyperelastic Mat’l Models Most material models only allow the analyst to describe only a subset of the structural properties of elastomers. In the Mooney-Rivlin and Ogden formulations: 1. The stress strain functions in the model are stable. They do not change with repetitive loading. The material model does not differentiate between a 1st time strain and a 100th time straining of the part under analysis. 2. There is no provision to alter the stress strain description in the material model based on the maximum strains experienced. 3. The stress strain function is fully reversible so that increasing strains and decreasing strains use the same stress strain function. Loading and unloading the part under analysis is the same. 4. The models treat the material as perfectly elastic meaning that there is no provision for permanent strain deformation. Zero stress is always zero strain. 1414www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 14 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. ? Visit their websites and RTFM (Read Their Fantastic Methods). Many papers can be downloaded for reference. www.axelproducts.com www.datapointlabs.com 1515www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 15 Curve Fitting of Hyperelastic Parameters ? The recommended method is the ANSYS Curve Fitting Wizard. ? Hardcore users: Use APDL to create your own scripts for the curve fitting portion and post-processing. ? For a decent curve fit using the M-R models, you need 2X the number of M-R Parameters. ? Papers on www.ansys.net provide in-depth info on these techniques… Most will be posted to the MAG site 1616www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 16 Testing Procedures… Source http://www.polymerfem.com > Surveys TIP: DEPENDING ON YOUR DESIGN/APPLICATION NEEDS ANY OR ALL MAY BE REQUIRED FOR THE MATERIAL AT HAND 1717www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 17 2-P Mooney-Rivlin vs. 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. Worth using it in ANSYS as a first- pass analysis ?? ? I’d rather test the material at hand in tension at least. 1818www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 18 2-P Mooney-Rivlin vs. Shore Hardness Mooney Coefficients y = 0.1333x y = 0.0333x 0 20 40 60 80 100 120 0 100 200 300 400 500 600 700 800 900 Young's Modulus, psi M o o n ey C o ef fic ie n ts , p si C10 C01 Linear (C10) Linear (C01) Shore-A E C10 C01 [°] psi psi psi 35 176.61 23.49 5.945 36 177.045 23.635 5.945 37 179.22 23.925 5.945 38 183.135 24.36 6.09 39 189.225 25.23 6.38 40 196.62 26.245 6.525 41 205.755 27.405 6.815 42 215.76 28.71 7.25 43 227.505 30.305 7.54 44 239.685 31.9 7.975 45 252.735 33.64 8.41 46 266.655 35.525 8.845 47 281.445 37.555 9.425 48 296.67 39.585 9.86 49 312.33 41.615 10.44 50 328.425 43.79 11.02 51 344.955 45.965 11.455 52 361.92 48.285 12.035 53 379.32 50.605 12.615 54 397.59 53.07 13.195 55 415.86 55.39 13.92 56 434.565 58 14.5 57 453.705 60.465 15.08 58 473.715 63.22 15.805 59 494.16 65.83 16.53 60 515.475 68.73 17.11 61 537.66 71.63 17.98 62 560.715 74.82 18.705 63 585.075 78.01 19.575 64 610.305 81.345 20.3 65 637.275 84.97 21.315 66 665.985 88.74 22.185 67 696 92.8 23.2 68 728.625 97.15 24.36 69 762.99 101.79 25.375 70 799.965 106.72 26.68 From Waltz (XANSYS) 1919www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 19 2-P Mooney-Rivlin vs. Shore Hardness E (psi) = 11.427*A -0.4445*A^2 + 0.0071*A^3 Lindemann (XANSYS) From E. F. Gobel, Rubber Springs Design, John Wiley, New York, 1978. 0 200 400 600 800 1000 1200 1400 20 30 40 50 60 70 80 90 100 Hardness (Shore A) Y o u n g 's M o d u lu s (P S I) 2020www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 20 2-P Mooney-Rivlin vs. Shore Hardness Comparison of Fitted Data 0 200 400 600 800 1000 1200 20 30 40 50 60 70 80 Hardness, Shore A Y ou ng 's M od ul us , p si . Waltz Lindemann Gobel Shore A Waltz Lindemann Gobel 35 172.75 159.85 154.42 40 205.58 200.28 198.56 45 255.84 261.09 244.15 50 324.42 347.60 291.63 55 412.23 465.14 342.36 60 520.16 619.02 398.58 65 649.12 814.58 463.45 70 800.00 1057.14 541.01 2121www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 21 Material Model Recommendations Arruda-Boyce Silicon Rubber Arruda-Boyce Viton Neo-HookeanAcrylate-butadiene rubber Arruda-Boyce / YeohChloroprene Rubber YeohNatural Rubber (55 pph CB) Neo-HookeanNitrile Rubber Hyperelastic ModelMaterial Source http://www.polymerfem.com Other material models from the same source may be used in ANSYS via UPFs. 2222www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 22 Example of O-Ring Compression 2323www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 23 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. ? 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); All other parts: Steel 2424www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 24 Example of O-Ring Compression 2525www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 25 Step 1: The lack of information about the material would not allow any guessing (BAD MOVE). So, material tested by Axel products as shown below. Step 2: Curve fitted to 9P M-R Model (BETTER ) (method APDL) Example of O-Ring Compression 2626www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 26 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. Models and parameters were not feasible/available at the time. (BEST CHOICE) 2727www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 27 The Assembly as Designed Guess where the Solution bombed out due to highly distorted Elements. (~ 25% into final loadstep – after preliminary contact resolution). 2828www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 28 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. (Rick?) 2929www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 29 Problem Solved !! Used a Different color to monitor the change in orientation of all points of interest during the animation process /pnum,mat ! Plot Element by material ONLY /num,2 ! Colors only esel,,type,,1,2 ! Select Solid Elements /nfor,on ! Turn on nodal Forces Pldisp ! Show Displacement plot 3030www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 30 Lessons Learned… • The use of the rounded Fillet helped (read: saved me) in completing the O-Ring assembly. • Mesh deformation is acceptable. • Contact resolution w/ mating parts as expected. • Orientation of “monitor” elements indicate lack of friction at the contact. • Next iteration should incorporate friction • Did Rich tell you about friction in contact pairs ?? 3131www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 31 Solution with Friction Added… 3232www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 32 Another O-Ring Case Study… 2 Parameter Mooney-Rivlin Model Used C10=107.18, C01=26.8 3333www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 33 ? Hourglassing occurs when there is compression in the material. ? Hourglass-shaped elements can propagate through the mesh IF THERE ARE LESS THAN 2 ROWS OF ELEMENTS IN EACH DIRECTION. ? Hourglassing IS NOT LIMITED to full integration elements. Use the wrong Stiffness factor w/ the Uniform Reduced Integration method and you’ll see it…. ? Think of it as “Rubber Turbulence” as the deformation change is rapid and violent. ? In reality, Hourglassing DOES NOT EXIST. Combination of material model, geometry, mesh density and element selection can induce Hourglassing in hyperelastic materials. ? Use full scale plot to see Hourglassing effects. Hourglassing 3434www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 34 ? Elements Supporting Hourglass control : Plane182/183, Solid 164 / 185 / 186 / 45 ? Use HGSTF Real Constant to Specify the Hourglass stiffness scaling factor ? However, 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. Hourglassing 3535www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 35 CAUTION: Introducing the HGSTF changes the the problem. (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. ? If the Ratio SENE / AENE is < 5 % the solution is acceptable. ? More than 5 % ?? Refine the mesh OR reduce the HGSTF. Hourglassing 3636www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 36 Wisdom on Hyperelastic Materials from XANSYS - THE School of Hard Knocks ? NEVER ask a forum member to give you their material data. Yes, it cost $ to test but this is not the area to cut corners. How do you know the material is made from the same stuff ?? (grade, processing etc.) ? The term “Strain” in hyperelastic materials is replaced by “Stretch”. The first and second invariants of M-R and other models are based on Stretch Ratios. The principal stretch ratio = 1 + eng. Strain. Therefore, the test data you obtain are Engineering and NOT True Stress and Strain. ? Use the more comprehensive TB,Hyper,,option instead of TB,Mooney which is for HYPER56/58 elements. 3737www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 37 Wisdom on Hyperelastic Materials from XANSYS - THE School of Hard Knocks ? For perfectly incompressible material, Poisson’s ratio of 0.5 is unacceptable as it makes the bulk modulus infinite. To keep ANSYS happy, use 0.49995 ? Polyurethane foams ?? Use Hyper56 with Blatz-Ko function (Keyopt(2)=1) IF you have the parameters for it. The literature is leaning towards M-R or hyperelastic w/ Ogden function. ? Polyurethane foams and access to LS-DYNA ?? See this reference: http://web.bham.ac.uk/millsnj/pdf/matpaperkyoto.pdf 3838www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 38 References on the Internet ? All about Testing Hyperelastic Materials and more… http://www.axelproducts.com/pages/Downloads.html ? www.PolymerFEM.com As the name suggests it is THE place to start w/ questions pertaining to elastomer modeling. (mostly ABAQUS but some ANSYS and LS-DYNA models are readily available). ? SILICONE RUBBER TESTING http://www.pp.bme.hu/me/2001_1/pdf/me2001_1_11.pdf 3939www.impactengsol.com ©2005 – IMPACT Engineering Solutions, Inc. 39 Conclusions ? Test the material at hand ? Take the Advanced Nonlinearities Class offered by your ASD. ? Use these RESOURCES ? IMPACT Engineering Solutions, Inc. ? ANSYS Customer Portal – Sample Models ? Ansys.net ? Axel Products ? Datapoint Labs ? PolymerFEM.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. Is this option something we can expect to see in the near future ???