Finite Element Modeling of TireTerrain Interaction
CONTENTS - TR-01-160005
ILLUSTRATIONS - TR-01-160006
ILLUSTRATIONS - continued
NOMENCLATURE - TR-01-160008
NOMENCLATURE - continued - TR-01-160009
INTRODUCTION - TR-01-160010
Vehicle movement on snow
Figure 3. Snow cross sections showing pressure bulb formation
Tire terminology
TERRAIN MATERIAL MODELS
Yield surface
Figure 10. Yield surfaces in deviatoric space
Hardening law
Figure 15. Piecewise linear modeling of the hardening law. (After HKS 1998.)
Modified DruckerPrager cap model
Figure 17. Modified DruckerPrager cap yield surface in the pt plane. (After HKS 1998.)
Figure 20. Plastic flow surface for the crushable foam model
Material parameter determination
Yield surface.
Table 1. Initial material model parameters
Figure 24. Compression of natural snow at 0 to 3C. (After Abele and Gow 1975.)
Figure 26. Pressurevolume data from compression tests of Abele and Gow (1975)
Figure 27. Comparison of model and experimental data for uniaxial
Figure 28. Deformed meshes for field plate sink- age simulations
Figure 29.
Figure 30. Modeled snow density (kg/m ) for plate sinkage test for DruckerPrager cap material
Figure 32. Deformation of fresh snow under a plate. (From Fukue 1979.)
Figure 34. Validation of McCormick Ranch sand DruckerPrager cap model with uniaxial strain test data from DiMaggio and Sandler (1976). (After HKS 1996.)
TIRE MODELS FOR A DEFORMABLE SUBSTRATE
Figure 36. Tires used in the experiments: Goodyear Wrangler HT Michelin XCH4, and Goodyear Wrangler AT
Figure 37. Deflection measurements for the tires used in the experi- ments at inflation pressures of 241 kPa (35 psi) and 179 kPa (26 pir
Rigid tire model
Figure 39. Construction elements of the Darnell tire model. (After Darnell et al. 1997.)
Table 7. Bending stiffness of tire sections
Figure 42. ShoopDarnell tire model (user elements not shown)
Figure 42 (cont.). Shoop-Darnell tire model
Figure 43. Modal analysis tire model with smooth tread
Figure 44. Modal analysis tire model with ribbed tread
Figure 44 (cont.). Modal analysis tire model with ribbed tread
Evaluation of tire models on a rigid surface
Figure 48. Measured contact areas at three inflation pressures
Figure 49. Comparison of measured and modeled contact areas at three inflation pressures
Figure 51. Comparison of the smooth and ribbed modal analysis tire models with measured contact areas
Figure 52. Measured and modeled contact stress distribution for half carcass on a hard surface (207 kPa inflation and 6627 N load)
Figure 55. Measured and modeled sidewall profiles for the Shoop Darnell tire model
Table 10. Qualitative summary of runtime analysis
Friction
Figure 57. Comparison of standard mesh (top) and ALE mesh (bot- tom). (From Shoop et al. 1999.)
Motion resistance forces and sinkage
Table 11. Measured sinkage and resistance in snow
ing the NRMM algorithm. (From Richmond 1995.)
Figure 62. Finite element model, measured data, and NRMM predictions for sinkage and motion resistance in fresh snow.
Figure 63. Finite element simulations at zero slip and at unlimited slip and NRMM motion resistance predictions for 240-kg/m snow
Figure 64. Marking the snow to observe snow deformation after vehicle passage
Figure 66. Comparison of measured (19-cm snow) and modeled (20-cm snow) displacement in a cross section transverse to the direction of travel
Deformable tire on soil
Figure 68. Rolling tire on an elastic material (sand)
Figure 69. Rolling ShoopDarnell tire on a DruckerPrager cap model of the McCormick Ranch sand
CONCLUSIONS - TR-01-160063
Significant findings
Recommended applications and future research needs
LITERATURE CITED - TR-01-160066
LITERATURE CITED - continued - TR-01-160067
LITERATURE CITED - continued - TR-01-160068
REPORT DOCUMENTATION PAGE - TR-01-160069
TR-01-16
CONTENTS - TR-01-160005
ILLUSTRATIONS - TR-01-160006
ILLUSTRATIONS - continued
NOMENCLATURE - TR-01-160008
NOMENCLATURE - continued - TR-01-160009
INTRODUCTION - TR-01-160010
Vehicle movement on snow
Figure 3. Snow cross sections showing pressure bulb formation
Tire terminology
TERRAIN MATERIAL MODELS
Yield surface
Figure 10. Yield surfaces in deviatoric space
Hardening law
Figure 15. Piecewise linear modeling of the hardening law. (After HKS 1998.)
Modified DruckerPrager cap model
Figure 17. Modified DruckerPrager cap yield surface in the pt plane. (After HKS 1998.)
Figure 20. Plastic flow surface for the crushable foam model
Material parameter determination
Yield surface.
Table 1. Initial material model parameters
Figure 24. Compression of natural snow at 0 to 3C. (After Abele and Gow 1975.)
Figure 26. Pressurevolume data from compression tests of Abele and Gow (1975)
Figure 27. Comparison of model and experimental data for uniaxial
Figure 28. Deformed meshes for field plate sink- age simulations
Figure 29.
Figure 30. Modeled snow density (kg/m ) for plate sinkage test for DruckerPrager cap material
Figure 32. Deformation of fresh snow under a plate. (From Fukue 1979.)
Figure 34. Validation of McCormick Ranch sand DruckerPrager cap model with uniaxial strain test data from DiMaggio and Sandler (1976). (After HKS 1996.)
TIRE MODELS FOR A DEFORMABLE SUBSTRATE
Figure 36. Tires used in the experiments: Goodyear Wrangler HT Michelin XCH4, and Goodyear Wrangler AT
Figure 37. Deflection measurements for the tires used in the experi- ments at inflation pressures of 241 kPa (35 psi) and 179 kPa (26 pir
Rigid tire model
Figure 39. Construction elements of the Darnell tire model. (After Darnell et al. 1997.)
Table 7. Bending stiffness of tire sections
Figure 42. ShoopDarnell tire model (user elements not shown)
Figure 42 (cont.). Shoop-Darnell tire model
Figure 43. Modal analysis tire model with smooth tread
Figure 44. Modal analysis tire model with ribbed tread
Figure 44 (cont.). Modal analysis tire model with ribbed tread
Evaluation of tire models on a rigid surface
Figure 48. Measured contact areas at three inflation pressures
Figure 49. Comparison of measured and modeled contact areas at three inflation pressures
Figure 51. Comparison of the smooth and ribbed modal analysis tire models with measured contact areas
Figure 52. Measured and modeled contact stress distribution for half carcass on a hard surface (207 kPa inflation and 6627 N load)
Figure 55. Measured and modeled sidewall profiles for the Shoop Darnell tire model
Table 10. Qualitative summary of runtime analysis
Friction
Figure 57. Comparison of standard mesh (top) and ALE mesh (bot- tom). (From Shoop et al. 1999.)
Motion resistance forces and sinkage
Table 11. Measured sinkage and resistance in snow
ing the NRMM algorithm. (From Richmond 1995.)
Figure 62. Finite element model, measured data, and NRMM predictions for sinkage and motion resistance in fresh snow.
Figure 63. Finite element simulations at zero slip and at unlimited slip and NRMM motion resistance predictions for 240-kg/m snow
Figure 64. Marking the snow to observe snow deformation after vehicle passage
Figure 66. Comparison of measured (19-cm snow) and modeled (20-cm snow) displacement in a cross section transverse to the direction of travel
Deformable tire on soil
Figure 68. Rolling tire on an elastic material (sand)
Figure 69. Rolling ShoopDarnell tire on a DruckerPrager cap model of the McCormick Ranch sand
CONCLUSIONS - TR-01-160063
Significant findings
Recommended applications and future research needs
LITERATURE CITED - TR-01-160066
LITERATURE CITED - continued - TR-01-160067
LITERATURE CITED - continued - TR-01-160068
REPORT DOCUMENTATION PAGE - TR-01-160069
TR-01-16
