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