Finite Element Modeling of TireTerrain Interaction
SALLY A. SHOOP
INTRODUCTION
terrain are highly deformable. A rigid approximation
of either is an oversimplification of the problem and
would yield erroneous contact conditions, which are
Vehicle mobility on unpaved surfaces is important
critical to obtaining correct solutions. The incorpora-
to the military as well as to agriculture, forestry, min-
tion of the third (lateral) dimension is similarly nec-
ing, and construction industries. The problems can be
essary, as the lateral movement of the terrain (in ad-
grouped into two major categories: predicting vehicle
dition to deformation in front and beneath the tire) is
performance on various terrains (will it get stuck;
readily apparent for most soft terrain materials (soils
how much traction or pull is available to climb or
and snow). The effect of the lateral dimension is also
pull) and estimating the consequences of the vehicle
evident in equations for rolling resistance, which is a
passage (rut formation, shearing/tearing of roots, soil
function of the width of the rolling object (Bowden
compaction, and the effects of these on vegetation
and Tabor 1964, Ludema 1996a). Similarly, empiri-
and erosion).
cal sinkage and motion resistance equations by Bek-
The objective of this project is to produce a three-
ker (1969) for soil and Richmond (1995) for snow
dimensional finite element model of tire-terrain inter-
include the tire or track width, indicating the impact
action that can be used to explore the effects of tire
of the third dimension on the performance of the tire
and terrain variables on vehicle mobility (traction and
or track.
motion resistance) and terrain deformation (rut for-
The details of the tiresoil modeling problem are
mation and shearing). Such a model would enable
divided into three topic areas: 1) material models for
detailed analysis of the complex interactions resulting
the terrain material, 2) tire models for use on a de-
from contact friction and would further the under-
formable substrate, and 3) the combined tireterrain
standing of off-road vehicle mobility by defining
model and the treatment of the interface. These are
critical mechanisms involved in vehicle traction and
presented after a brief historical perspective on tire
motion resistance. Ultimately the model generated
terrain interaction.
would be used for tire design and specification for
off-road vehicles (for construction, mining, and rec-
reation), for vehicle performance prediction, and for
BACKGROUND
terrain damage prediction and reduction of the
environmental impact of off-road travel. Previously a
Off-road vehicle performance prediction
three-dimensional simulation of contact between a
Off-road vehicle performance analysis is a three-
deformable tire and deformable terrain had been too
dimensional, nonlinear, dynamic problem. Major
difficult and computationally time consuming. Re-
early efforts were led by Bekker, at the University of
cent advancements in the contact formulations of
Michigan and the U.S. Army Land Locomotion
general-purpose finite element codes (e.g. ABAQUS,
Laboratory (Bekker 1956, 1960, 1969), and his con-
HKS 1998) and increases in computer processing
temporaries at the National Tillage Laboratory at
speeds have brought such a model into the realm of
Auburn, Alabama (Gill and Vanden Berg 1967).
possibility.
Karafiath and Nowatzki (1978) extended the state of
The originality of this research lies in accounting
the art to include modeling of soil deformation under
for the deformable nature of both the tire and the ter-
the wheel or track based on theoretical soil mechan-
rain in a fully three-dimensional model. Both tire and
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