tion resistance forces but underestimates sinkage. The
research was to produce a three-dimensional finite
measured deformation patterns are duplicated in the
element model of tireterrain interaction that can be
model, but the modeled displacements are less than
used to explore the effects of tire and terrain variables
what is measured in the field. Model results were also
on vehicle mobility. Such a model can be used for
compared to snow mobility predictions made using
tire design and specification for off-road vehicles, for
the largely empirical NATO Reference Mobility
vehicle performance prediction, and for terrain dam-
Model, with good agreement for forces but underes-
age prediction and reduction of the environmental
timation of sinkage. The amount of wheel slip had a
impact of off-road travel.
major impact on the modeled sinkage.
The details of the tiresoil modeling problem are
Simulations of a tire rolling on soil and snow us-
divided into three topic areas: 1) material models for
ing the ShoopDarnell tire and the modal analysis
the terrain material, 2) tire models for use on a de-
tire model are operational but have not been vali-
formable substrate, and 3) the combined tireterrain
dated. Of significant note, however, is that a simula-
model and the treatment of the interface. The terrain
tion using the modal analysis tire on fresh snow pre-
materials simulated in this study were fresh snow and
dicts very little tire deformation (3 mm, or less than
compacted sandy soil. The two material models used
2% deflection). This suggests that the assumption of
were a modified DruckerPrager cap plasticity model
a rigid tire may be used for soft terrain such as deep,
and a critical-state, crushable foam model. Both
fresh snow without loss of model accuracy.
models were considered suitable for capturing the
highly compressible behavior of fresh, natural snow
(initial density of 200250 kg/m3 at temperatures of
Significant findings
The following summarizes the significant
10 to 1C). Model parameters were generated
achievements of this work:
from field test data and from the literature, matching
1. A material model was developed for fresh snow
this snow type as closely as possible. The snow
and validated with plate sinkage tests in the lab
model was validated using plate sinkage test data for
and field. Good agreement of measured and mod-
snow of similar age and density. The soil model
eled forces, displacements, and changes in mate-
represents sand similar to that used during vehicle
rial density were achieved.
mobility experiments at CRREL. The material was
2. Evaluations of several finite element tire models
modeled using a DruckerPrager cap plasticity model
suitable for rolling on a deformable substrate in-
with input parameters from the literature.
dicate that the Darnell model yielded accurate re-
To apply a tire model to deformable terrain, the
sults and was computationally efficient. The mo-
model must be efficient yet accurately portray the tire
dal analysis type of tire model is also suitable but
structural behavior. Four tire models were evaluated
is more computationally intensive.
for suitability to rolling on deformable terrain: 1) a
3. Combined tireterrain models utilizing the
rigid tire model, 2) a simplified tire model using
ShoopDarnell tire and the modal analysis tire
methodology developed by Darnell at the University
model are operational but have not yet been vali-
of Michigan for use in vehicle dynamics simulations,
dated. Preliminary results of the modal analysis
3) a tire model of the type used for harmonic vibra-
tire model on snow show very little deformation
tion modal analysis, with a smooth tread, and 4) a tire
in the tire, indicating that the rigid wheel simplifi-
model similar to model 3 except with a straight
cation may be valid for soft terrain.
ribbed (longitudinal) tread. All of the models were
4. A model of a rigid wheel on fresh snow, validated
built to represent tires used in the experimental test
experimentally, shows good agreement with
program for comparison to measured tire behavior in
measured motion resistance forces, snow dis-
terms of deflection, contact area, deflected sidewall
placement, and snow compaction and agrees with
profile, contact stress distribution, and rolling resis-
results predicted by the NATO Reference Mobil-
tance forces on deformable terrain (snow and soil).
ity Model.
Three models of the combined tire and terrain
5. The rigid wheel on snow model does not capture
were developed. The first is a rigid tire on fresh
the tread effects of the tireterrain interaction (as
snow. The second is the ShoopDarnell tire model
tread patterns were not expressly modeled). For a
rolling on a soil, and the last is the modal analysis tire
free-rolling wheel, the amount of slip and sinkage
on snow. Model results simulating a rigid tire rolling
is overpredicted. When the model wheel slip is set
on snow were compared to tire forces measured using
to zero, as is measured during shallow snow resis-
an instrumented vehicle. The measured snow defor-
tance tests in the field, sinkage is underpredicted.
mation under the wheel was also compared to model
The most realistic results lie between these two
results. The model exhibits good agreement with mo-
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