Technical Papers and Briefs

  1. Testing Elastomers for Hyperelastic Material Models in Finite Element Analysis (PDF: 2.7 MB / 7 pages)
  2. The paper provides pictures of the various experiments and discusses the relationship between experimental loadings and hyperelastic material models.

  3. Testing Plastics for Material Models in Finite Element Analysis (PDF: 7.1 MB / 12 pages)
  4. The physical testing of plastic materials for the purpose of defining material constitutive models in finite element analysis can be very simple or incredibly complex depending on the objective of the analysis. Linear analysis of structural parts is routinely performed using only a couple simple parameters. More complex analysis may involve elevated temperatures, severe plastic deformation and strain rate sensitivity requiring customized material model development and rigorous experimentation. The purpose of this discussion is to introduce laboratory experiments that may be used to evaluate the physical properties defined in material constitutive models.

  5. Measuring the Dynamic Properties of Elastomers for Analysis (PDF: 2.8 MB / 7 pages)
  6. This paper provides an outline for the dynamic testing of elastomers for the characterization of dynamic properties needed to define analytical models where small dynamic strains are present on large nonlinear mean strains. This includes acoustic characterization.

  7. Fatigue and Failure Testing of Elastomers for Analysis (PDF: 2.9 MB / 10 pages)
  8. By Kurt Miller, Axel Products, Inc. Mechanical fatigue and failure in elastomers is about starting and growing cracks. This document reviews some of the experiments used at Axel Products to investigate the fatigue and failure of elastomers for material selection, comparison, and analysis.

  9. Capturing Set and Plastic Behavior in Thermo-plastic Elastomers and Elastomers used Near Tg (PDF: 0.86 MB / 3 pages)
  10. This brief describes the steps taken to fit a hyperelastic, Mullins and plastic material model in Abaqus to capture complex material behaviors.

  11. Measuring Rubber and Plastic Friction for Analysis (PDF: 1.3 MB / 4 pages)
  12. The frictional forces generated between plastic, rubber and various hard surfaces are often represented with a simple coefficient of friction (COF) value yet in reality can be a function of material, surface finish, temperature, rate of relative movement, time and normal pressure. Using frictional measurements where these parameters are matched to the application conditions will help to create a more realistic analysis. Issues and experiments are described.

  13. Testing at High Strain Rates (PDF: 2.3 MB / 3 pages)
  14. Issues and pictures related to high strain testing are presented. Data for high strain rate testing of sheet steel, structural plastic and crushable foams is shown.

  15. Measuring the Long Term Creep Properties of Plastic Materials for Finite Element Analysis (PDF: 3.0 MB / 4 pages)
  16. Long term creep experiments provide valuable data for analysis of plastics. The experiments used at Axel Products are described.

  17. Long Term Creep and Long Term Stress Relaxation Experiments for Rubber and Plastic Materials (PDF: 3.4 MB / 4 pages)
  18. Related information is the same as above.

  19. Fitting a Hyperelastic Material Model for a Stabilized-Loading Application (PDF: 0.84 MB / 3 pages)
  20. This brief describes the steps taken to fit a hyperelastic material model to capture the stabilized loading of an elastomeric bushing in service.

  21. Measuring Dynamic Properties of Elastomers between 400 Hz. and 10,000 Hz. (PDF: 0.6 MB / 3 pages)
  22. Measuring the dynamic properties of elastomeric materials in the range of 400 Hz. to 10,000 Hz. is important because this is a significant range in human hearing. Elastomers are often used to control or reduce vibrational frequencies in this range. An outline for the experimental determination of the dynamic material properties at vibration frequencies between 400 Hz. and 10,000 Hz. using a wave propagation approach is provided herein.

  23. Testing Fine Wire (PDF: 0.6 MB / 2 pages)
  24. This brief examines some of the difficulties encountered in wire testing and outlines some techniques that may be successful in overcoming these difficulties.

  25. The Effects of Large Temperature Changes on Elastomer Seal Performance (PDF: 0.7 MB / 5 pages)
  26. This paper describes the effects of large temperature changes on elastomer seals and an experimental approach to measuring these effects.

  27. Combining Plastic and Hyperelastic Material Models to Describe Complex PEEK Thermoplastic Behavior (PDF: 0.5 MB / 3 pages)
  28. This brief describes the steps taken to fit a plastic, hyperelastic material model to describe the deformation and stiffness in a PEEK bearing. Uniaxial tension test experimental data is shown to be insufficient to fit the complex model.

  29. Thermal Conductivity of Rubber and Plastic Materials (PDF: 1.47 MB / 2 pages)
  30. This is a brief description of the operation of the transient plane source measurement technique used at Axel Products to measure the thermal conductivity of rubber and plastic materials.

  31. Compression or Biaxial Extension? (PDF: 0.7 MB / 3 pages)
  32. Why is the biaxial extension experiment used for elastomers? Why is the compression test an undesirable test when developing test data for finite element analysis? This short paper addresses these questions.

  33. Fitting a Hyperelastic Mullins Model to Describe the Stress Distribution in a Rubber Mount (PDF: 1.4 MB / 3 pages)
  34. This brief describes the steps taken to describe the stress distribution in an elastomeric mount during use using a hyperelastic and Mullins material model.

  35. Elastomer Rate-dependence: A Testing and Material Modeling Methodology (PDF: 6.65 MB / 20 pages)
  36. By Tod Dalrymple and Jaehwan Choi, Dassault Systems Simulia Corp. and Kurt Miller, Axel Products, Inc. Stress relaxation testing at very early times (fraction of a second) combined with test data from a set of constant strain-rate uniaxial tests is used to create hyperelastic/viscoelastic material models. A robust method of testing the material and a robust method of material model calibration is developed to capture the strain-rate sensitivity of elastomeric materials. This material representation is intended for simulations of dynamic transient loadcases. The focus is on the use of the hyperelastic and viscoelastic Prony series representation in the Abaqus/Standard and Abaqus/Explicit simulation software. This technique and resulting material model represents the material’s strain-rate dependence during loading quite accurately and thus can be used effectively to simulate peak load conditions during dynamic transient events. Unfortunately, the resulting hyperelastic plus Prony series viscoelastic material model does not represent the material’s hysteresis loop during the load-unload cycle accurately. This paper presents the test methods developed, a sample of material test data, and the resulting material model and material model responses.

  37. Modeling Carpet for use in Occupant Crash Simulations (PDF: 0.65 MB / 12 pages)
  38. By Dylan Thomas, Honda R&D Americas Prediction of occupant injury using crash simulations can require numerical representation of materials that are not normally included within the structural model. Intuitively, it makes sense that the carpet would be required to predict the tibia index during frontal crash events; however, there appears to be little published on the topic. The tibia index is an injury criterion that needs to be predicted during IIHS frontal offset occupant simulations, but is also looked at during unbelted FMVSS 208 simulations. Since carpet behaves quite differently during compressive and tensile loading, a numerical representation that can stably capture both regimes during occupant modeling is needed. This paper outlines a method to model the carpet using a specific meshing method and two material models. Shell elements in combination with the *PIECEWISE_LINEAR_PLASTICITY material model are used to model the tensile load carrying capacity of the carpet, while brick elements with the *MAT_FU_CHANG_FOAM material model are used to represent the compressibility of the carpet. Validation of using this modeling method with test data is presented, as well as the application of the carpet model in larger occupant models.

  39. Understanding Frequency Domain Viscoelasticity in Abaqus (PDF: 0.13 MB / 13 pages)
  40. By Saurabh Bahuguna, Randy Marlow*, and Tod Dalrymple of Dassault Systèmes Simulia Corp., Great Lakes Region In this paper, the frequency domain viscoelastic model in Abaqus is explored. The input requirement of the model from uniaxial dynamic tests at several frequencies is detailed.

  41. Fitting a Hyperelastic Material Model for a First Time Loading Application (PDF: 0.4 MB / 2 pages)
  42. This brief describes the steps taken to define a hyperelastic material model needed to describe the behavior of a thick elastomer seal during a factory installation operation.

  43. Equibiaxial Stretching of Elastomeric Sheets, An Analytical Verification of Experimental Technique (PDF: 751 KB / 8 pages)
  44. By Jim Day, GM Powertrain and Kurt Miller, Axel Products, Inc. This paper provides an analysis and verification of the radial biaxial test used at Axel Products, Inc. Appendix A of this document provides an analysis of the compression button experiment and details the adverse effects of friction.

  45. Implications of the Mullins Effect on the Stiffness of a Pre-loaded Rubber Component (PDF: 373 KB / 15 pages)
  46. By Ryan E. Paige, Will V. Mars, Cooper Tire & Rubber Company, ABAQUS User's Conference, Cambridge, Massachusetts, May 2004. Many engineered rubber components are pre-loaded during manufacture or installation in such a way that the rubber experiences compressive loads that are partially relieved during operation. In this paper, we investigate the consequences of applying this type of loading when the rubber exhibits a Mullins effect. The Mullins effect is a dependence of the hyperelastic response on the maximum deformation previously experienced. ABAQUS contains a new model for this effect, and we first examine the significance of the model parameters. Then we show that the total stiffness of a rubber component may either decrease or increase significantly by including the Mullins effect.

  47. When F does not Equal Ku, White Paper, by MSC Software (PDF: 3.1 MB / 20 pages)
  48. This easy to read paper explains how to spot a nonlinear problem and discuss the nature of nonlinearities in analysis.

  49. Nonlinear Finite Element Analysis of Elastomers, White Paper, by MSC Software, 2010 (PDF: 12.6 MB / 75 pages)
  50. This white paper discusses the salient features regarding the mechanics and finite element analysis (FEA) of elastomers. Although, the main focus of the paper is on elastomers (or rubber-like materials) and foams, many of these concepts are also applicable to the FEA of glass, plastics, and biomaterials.

  51. Axel Capabilities Sheet (PDF: 0.6 MB / 1 pages)
  52. This page describes the general capabilities of Axel Products, Inc.

  53. Experimental Loading Conditions Used to Implement Hyperelastic and Plastic Material Models (PDF: 930 KB / 14 pages)
  54. Loading variables such as strain rate, strain direction, maximum strain, relaxation, cyclic behavior and plasticity are outlined to provide a context for the design of experiments needed to define hyperelastic and plastic material models based on the needs of the application.

  55. Using Slow Cyclic Loadings to Create Stress Strain Curves for Input into Hyperelastic Curve Fitting Routines (PDF: 565 KB / 4 pages)
  56. This is an Axel Products, Inc. support document which reviews the effects of loading, unloading and strain levels on elastomers. The limitations of hyperelastic material models as they relate to laboratory material data are reviewed.

  57. Application of Energy Based Fatigue Crack Growth to Elastomer Compound Development (PDF: 1.1 MB / 14 pages)
  58. By Don Young, Independent Consultant. Brief theory and background are provided to show the importance and relevance of using a fracture mechanics approach to model and evaluate rubber materials. The experimental approach is briefly discussed, and alternate forms of analysis are described to properly model strain, stress and energy controlled deformations.

  59. Stress Relaxation Tests, Technical Report 98/1, by Mr.Göran Spetz of Elastocon AB, SWEDEN (PDF: 127 KB / 4 pages)
  60. This is a discussion of long term stress relaxation testing and the use of Arrhenius plots to estimate the useful lifetime of elastomeric components.

  61. Characterization of Polymers by TMA, Perkin-Elmer application paper by W.J. Sichina (PDF: 264 KB / 5 pages)
  62. This is a broad based discussion on the use of thermal mechanical analysis (TMA) to investigate the properties of polymers.

  63. Examination of finite element analysis and experimental results of quasi-statically loaded acetal copolymer gears (PDF: 389 KB / 7 pages)
  64. By Paul Wyluda, Ticona and Dan Wolf, MSC Software. An elastic-plastic finite element analysis of the quasi-static loading of two acetal copolymer gears in contact is preformed. Load versus rotation of the gear set is compared to actual experimental results.

  65. Why it is necessary to use data from more than one strain field in determining the Helmholtz free-energy (strain energy) density function (PDF: 253 KB / 4 pages)
  66. By Kenneth N. Morman, PhD, The ANSOL Corporation A graphical presentation with appropriate references explaining the need for experiments in multiple states of strain to adequately define "hyperelastic" material models.

  67. Using ENDURICA to Compare Two Rubbers Under Multiaxial Spectrum Loading (PDF: 99 KB / 7 pages)
  68. By Will Mars, PhD. In this example, two rubbers of identical stress-strain behavior, but differing fatigue and strain-crystallization properties (filled NR and filled SBR), are compared for their ability to endure a specified loading history.

  69. Fatigue Life Prediction for Elastomers using ENDURICA Introduction (PDF: 1.2 MB / 39 pages)
  70. By Will Mars, PhD. The use of Endurica commercial software to describe and predict the fatigue behavior of elastomers is described.

  71. Integrating Theory, Experiments, and FEA to Solve Challenging Nonlinear Mechanics Problems (PDF: 0.3 MB / 17 pages)
  72. By Ted Diehl. Sometimes great experimental data can be ugly. The use of Kornucopia commercial software to accurately manipulate and analyze all kinds of challenging data to solve engineering problems is described.

  73. C-Therm TCi™ Principles of Operation (PDF: 0.2 MB / 10 pages)
  74. By C-Therm Technologies. This document descibes the instrument used to measure thermal transport properties at Axel.

  75. Measuring the Shear Properties of Plastic Materials for Finite Element Analysis (PDF: 1.7 MB / 4 pages)
  76. By Axel Products. The stress-strain relationship during pure shearing is a desirable measurement. This document describes an experiment used at Axel Products to measure the structural strength of plastic and plastic composite materials in a pure shear strain state during loading and unloading and across a broad range of temperatures. Digital image correlation is used to measure shear strains on the specimen.

  77. Fatigue and Crack Growth in Engineering Plastics (PDF: 1.9 MB / 2 pages)
  78. By Axel Products. This brief descibes fatigue crack growth experiments for plastics at Axel.

  79. What material tests are typically performed to calibrate a hyperelastic material model? (PDF: 1.0 MB / 2 pages)
  80. By Axel Products. This is a simple question and answer sheet with elastomeric experiment pictures and a brief explanation.

  81. Where do the “Pure” and “Shear” come from in the Pure Shear test? (PDF: 0.5 MB / 3 pages)
  82. By Will Mars, Endurica LLC. Many people puzzle over the nomenclature of the pure shear test. They rightly point out that 1) the Pure Shear test piece is loaded in tension by extending the specimen in the axial direction, and 2) a shearing deformation, by definition, involves the lateral motion of parallel planes. They wonder where is the “shear”? and what does it mean to say that the shear is “pure”?

  83. Calibrating the Parallel Rheological Framework (PRF) Material Model to Describe the Structural Response of Polypropylene (PDF: 1.0 MB / 17 pages)
  84. By Tod Dalrymple, Dassault Systems Simulia Corp. The purpose of this document is to describe a variety of test data that we have for a particular grade of polypropylene and demonstrate a calibration recipe that focuses on the nonlinear viscoelastic behavior of the material below yield. The Abaqus material model used to represent nonlinear viscoelasticity is the Parallel Rheological Framework (PRF) model.

  85. Measuring the Cutting Resistance of Elastomers (PDF: 0.2 MB / 3 pages)
  86. By Kurt Miller, Axel Products, Inc. Cutting resistance is measured by applying a sharp blade against a pre-strained elastomer specimen while observing the force required to cut into the elastomer. The cutting resistance force can be used directly to evaluate and compare materials, and to provide information about minimum requirements for crack growth. The experiment that we perform at Axel Products is described in this brief.

  87. Geothermal Cooling of Hydraulic Power Units at Axel Products (PDF: 1.0 MB / 4 pages)
  88. The use of geothermal cooling of hydraulic power supplies in the facilities of Axel Products is descibed.

  89. Crack Growth Under Long-Term Static Loads (PDF: 0.6 MB / 6 pages)
  90. By W. V. Mars, Endurica LLC, K. Miller, Axel Products, Inc., S. Ba & A. Kolyshkin, Schlumberger . When a load is carried over an extended period, a crack in a viscoelastic material might grow, even if the load is less than the static tearing strength Tc for unstable rupture, and even in the absence of dynamic cycles.


  1. FEA of Elastomers and Gaskets in ABAQUS, overheads
  2. By Tod Dalrymple, HKS Michigan, presented at the ASTM Finite Element Analysis Focus Event, October 2000, Orlando, Florida. (PDF: 4983 KB / 43 pages)

  3. Rubber Material Curve Fitting with ABAQUS/ CAE, overheads
  4. By Tod Dalrymple, HKS Michigan and Kurt Miller, Axel Products, Inc., presented at the 2000 Michigan Regional ABAQUS Users' Meeting on November 16, 2000. (PDF: 3045 KB / 34 pages)

  5. Experimental Loading Conditions Used to Implement Hyperelastic and Plastic Material Models, overheads
  6. By Kurt Miller, Axel Products, Inc., presented at the MSC 2nd Worldwide Automotive Conference. (PDF: 2911 KB / 30 pages)

  7. Measuring Elastomer Properties at Audible Frequencies, overheads
  8. By Kurt Miller, Axel Products, Inc., presented at the HKS 2000 ABACUS Users' Conference on June 2, 2000. (PDF: 1039 KB / 15 pages)

  9. Analysis of Elastomeric Components & Assemblies: Some Practical Considerations, overheads
  10. By Bill C. Brothers and Alan R. Leewood, AC Engineering, West Lafayette, Indiana, USA presented at Elastomer - Fea Forum 1999, 3rd International Symposium on Finite Element Analysis of Rubber and Rubber- like Materials, May 19 th and 20 th , 1999, Akron, Ohio USA. (PDF: 658 KB / 30 pages)

  11. Measuring Material Properties to Build Material Models in FEA, overheads
  12. By Kurt Miller, Axel Products, Inc. These are the overheads from a general presentation given by Kurt Miller at various venues. The presentation includes laboratory pictures and test data examples. Download MatPropsFEA.pdf. (This is a BIG file): (PDF: 7922 KB / 61 pages)

  13. Elastomer Analysis Using MARC, overheads
  14. Prepared by: Daniel S. Wolf, MARC Analysis Research Corp.,Palo Alto, CA, USA for: Elastomer - Fea Forum 1999, 3rd International Symposium on Finite Element Analysis of Rubber and Rubber- like Materials, May 19 th and 20 th , 1999, Akron, Ohio USA These overheads contain several testing pictures as well as curve fitting examples and actual component examples. (PDF: 1192 KB / 25 pages)

  15. Stress Relaxation of Elastomers under Constant Strain, overheads
  16. Axel Products, Inc. and Elastocon AB sponsored seminar on Stress Relaxation in Elastomers on January 27, 1999. (PDF: 530 KB / 18 pages)

  17. Compressive Stress Relaxation Anomalies, overheads
  18. By Jim Madsen, Materials Laboratory Manager, Freudenberg-NOK.This presentation provides an overview of long term compressive stress relaxation (CSR) experiments and presents some of the challenges associated with the use of CSR data. (PDF: 600 KB / 36 pages)

  19. Factors that Affect the Fatigue Life of Rubber: A Literature Survey, overheads
  20. By W. V. Mars - Cooper Tire & Rubber Co., A. Fatemi - U. of Toledo. Will provides a terrific overview of the factors that affect the fatigue and durability of rubber. (PPT: 1115 KB / 25 pages)

  21. Experimental Considerations in the Measurement of Thermal Relaxation and Recovery of Strained Seals, overheads
  22. By Kurt Miller, Axel Products, Inc., presented at the Detroit Rubber Group. (PPT: 4.3 MB)

  23. Elastomer Rate-dependence, overheads
  24. By Tod Dalrymple ., Presented at the Fall 172nd Technical Meeting of the Rubber Division of the American Chemical Society, Inc. (PDF: 673 MB / 21 pages)

  25. Physical Testing of Thermoplastics for Input into DIGIMAT, overheads
  26. By Kurt Miller , Presented at the DIGIMAT US Tech Days - Automotive, May, 2011. This is a brief 20 minute presentation on some of the testing issues associated with DIGIMAT input needs. (PDF: 7 MB / 23 pages)

  27. MSC Elastomer Seminar, overheads
  28. By Kurt Miller , Presented at the MSC Elastomer Seminar, April, 2012. This is a 60 minute presentation on some of the testing issues associated with the characterization of elastomers for elastomer material modeling. (PDF: 3.6 MB / 75 pages)

  29. Characterizing Rubber’s Fatigue Design Envelope, overheads
  30. By Will Mars and Kurt Miller , Presented at the 181st Technical Meeting & Educational Symposium April 22-25, 2012. (PDF: 1.0 MB / 24 pages) An efficient approach is devised for characterizing rubber's fatigue design envelope. It is based on measurements of the fatigue crack growth rate law under both relaxing and nonrelaxing conditions.

  31. Testing of Elastomers and Plastics in Support of Analysis, overheads
  32. By Kurt Miller , Presented at ANSYS Regional Conference – Detroit, June 4, 2013. (PDF: 2.5 MB / 26 pages)

  33. Testing of Elastomers and Plastics in Support of Analysis with an Emphasis on new Material Models in ANSYS, overheads
  34. By Kurt Miller , Presented at the ANSYS Regional Conference – Houston, June 12-13, 2013. (PDF: 3.5 MB / 24 pages) Material models in ANSYS are becoming increasingly descriptive. The expanded capabilities of material models require expanded physical testing to assure that these material descriptions define real materials. This session presents direct test and measurement of multiple strain states, strain rate sensitivity, and visco-plasticity with emphasis on the applicability to the calibration of ANSYS material models.

  35. Experiments and Fitting of Advanced Polymer Models in ANSYS, overheads
  36. By Kurt Miller , Presented at the ANSYS Regional Conference – Detroit, June 5, 2014. (PDF: 4.3 MB / 49 pages)

  37. Testing of Elastomers and Plastics in ANSYS, overheads
  38. By Kurt Miller , Presented at the ANSYS Automotive Simulation World Congress – Detroit, June 2-3, 2015. (PDF: 3.0 MB / 38 pages)

  39. Testing of Elastomers and Plastics for Marc Models, overheads
  40. By Kurt Miller , Presented at the MARC User Meeting – Troy, MI, May 17, 2016. (PDF: 5.7 MB / 51 pages)

  41. Crack Growth Under Long-Term Static Loads: Characterizing Creep Crack Growth Behavior in Hydrogenated Nitrile, overheads
  42. By W.V.Mars, K.Miller, S.Ba, A.Lolyshkin , Presented at ECCMR 2017 – Munich, Germany, August, 2017. (PDF: 1.0 MB / 13 pages) Applications with large static loads and long time periods such as seals, packers, mud motors etc. Combined cycle/time dependent crack growth.