Computational investigation of blast survivability and off-road performance of an up-armoured high-mobility multi-purpose wheeled vehicle

Computational investigation of blast survivability and
off-road performance of an up-armoured high-mobility
multi-purpose wheeled vehicle
M Grujicic*, G Arakere, H Nallagatla, W C Bell, and I Haque
Department of Mechanical Engineering, Clemson University, Clemson, SC, USA
The manuscript was received on 10 November 2008 and was accepted after revision for publication on 27 November 2008.
DOI: 10.1243/09544070JAUTO1063
Abstract: Since ballistic and blast survivability and off-road handling and stability of military
vehicles, such as the high-mobility multi-purpose wheeled vehicle (HMMWV), are two critical
vehicle performance aspects, they both (including the delicate balance between them) have to
be considered when a new vehicle is being designed or an existing vehicle retrofitted (e.g. up-
armoured). Finite-element-based transient non-linear dynamics and multi-body longitudinal
dynamics computational analyses were employed in the present work to address the following
two specific aspects respectively of the performance of an HMMWV: firstly, the ability of the
vehicle to survive detonation of a landmine shallow buried into sand underneath the right
wheel of the vehicle and, secondly, the ability of the vehicle to withstand a simple straight-line
brake manoeuvre during off-road travel without compromising its stability and safety of its
occupants. Within the first analysis, the kinematic and structural responses (including large-
scale rotation and deformation, buckling, plastic yielding, failure initiation, fracture, and
fragmentation) of the HMMWV to the detonation of a landmine were analysed computationally
using the general-purpose transient non-linear dynamics analysis software ABAQUS/Explicit.
The second analysis was carried out using Simpack, a general purpose multi-body dynamics
program, and the main purpose of this analysis was to address the vehicle stability during the
off-road travel. The same sand model was used in both types of analysis. Finally, the
computational results obtained are compared with general field-test observations and data in
order to judge the physical soundness and fidelity of the present approach.
Keywords: high-mobility multi-purpose wheeled vehicle, blast survivability, off-road vehicle
performance, abaqus, simpack
1 INTRODUCTION
The high-mobility multi-purpose wheeled vehicle
(HMMWV) is the standard utility vehicle used in
virtually all military branches and has been tradi-
tionally devoted primarily to logistical support and
convoy operations. There are also exceptions to this
traditional application of the HMMWV, such as its
use in Cavalry and Infantry Scout units where this
vehicle is utilized in offensive and defensive mis-
sions and where, in order for the HMMWV to fulfil
functional requirements of these missions, it is
usually fully or partially up-armoured. However,
the tactical and operational environments of Opera-
tion Iraqi Freedom and Operation Enduring Free-
dom have resulted in a major role change for the
HMMWV. That is, as clearly evidenced in these
operations, enemy contact is no longer defined as a
discernible front line that can be physically identi-
fied on a map. Instead, the battlefield can be more
accurately described as being non-linear and asym-
metrical and, consequently, units are forced to
operate in zones that are susceptible to enemy
contact from any direction at any time. This means
that supply lines and logistical missions that were
historically secure now operate in potentially hostile
areas and are always vulnerable to attack [1, 2].
Hence, the majority of (non-armoured) HMMWVs
*Corresponding author: Department of Mechanical Engineering,
Clemson University, 241, Engineering Innovation Building,
Clemson, SC, 29634-0921, USA. email: 1-864-656-5639
1
JAUTO1063 F IMechE 2009 Proc. IMechE Vol. 000 Part D: J. Automobile Engineering

are now operating in conditions that they were not
designed for and are subjected to harsh manoeuvres
that they would not traditionally have to conduct.
This situation has resulted in a significant increase in
rollover and instability-related HMMWV accidents
during such transient manoeuvres and, in turn, to an
increase in soldier injuries and fatalities.
To make the situation even worse, in order to
address the problem associated with road landmines
and improvised explosive devices (IEDs), units have
responded with force protection measures to have
all HMMWVs up-armoured (either by contractors,
using retrofit add-on armour kits or armour intern-
ally fabricated from ballistic steel, sandbags, etc.).
While the additional armour has increased vehicle
ballistic protection, it has also degraded its riding-
stability performance because suspension compo-
nents and tyres have not been modified to keep pace
with the added weight of installed armour (the mass
of additional armour can be up to 2000 kg). This has
further contributed to the increase in HMMWV
instability-related accidents and soldier injuries
and fatalities. In addition, frequent accidents have
also occurred when, owing to excessive weight of the
up-armoured HMMWV, the roadside would col-
lapse, causing the vehicle to land in the water and
soldier injuries and fatalities.
The HMMWV was originally introduced as the
replacement for the MI51 Jeep vehicle and, as
discussed above, comes in various configurations
such as the M998 pickup truck, the M996 ambu-
lance, and the M1025 four-door hard-top version.
These vehicles utilize full frames to which the body,
engine, and suspension are attached. A photograph
of the HMMWV M1025 (the model analysed in the
present work) is displayed in Fig. 1.
It is well established that light-armoured vehicles
such as HMMWVs and their occupants are highly
vulnerable to anti-vehicular mine blasts (see, for
example, reference [3]). The development of anti-
mine protection systems aimed at reducing the
vulnerability of the vehicles and vehicle occupants
to mine blasts typically includes extensive experi-
mental test programmes. Such experimental pro-
grammes are critical for ensuring the utility and
effectiveness of the anti-mine protection systems.
However, the use of the experimental programmes is
generally expensive and time-consuming, involves
destructive testing of the vehicles, and is often
limited to vehicles that were already damaged
beyond repair or phased out of service. Experimental
testing of vehicles currently being produced or under
development is often cost prohibitive. The develop-
ment of effective mine protection systems for light-
armoured vehicles requires a comprehensive under-
standing of two distinct groups of phenomena:
(a) detonation of high-energy explosive mines
buried in soil, interaction of the detonation
products with surrounding soil, and interaction
of mine blast fragments, gaseous detonation
products, and soil ejecta with the target vehicle;
(b) the structural and ballistic response of the target
vehicle and their occupants when subjected to
transient highly non-linear dynamic or impulse
loading resulting from the mine detonation.
While the role of experimental test programmes
remains critical, they are increasingly being comple-
mented with the corresponding computation-based
engineering analyses and simulations. One of the
main objectives of the present paper is to help with
further development of these computational engineer-
ing analyses and simulations so that they can become
a reliable method or alternative in the effective mine
protection systems development process.
In recent years, major advances have been made
in modelling the detonation phenomena, the con-
stituent response of the materials under high-
deformation-rate large-deformation ballistic condi-
tions, and the interactions between detonation
products, soil, and target vehicle or structure. In
particular, these models have enabled the coupling
between Eulerian representations (typically applied
to the gaseous detonation products and air) and
Lagrange representations (typically applied to the
target vehicle or structure, mine-casing fragments,
and soil). These advances in the modelling of the
phenomena accompanying detonation of a shallow-
buried mine in the vicinity of a target vehicle or
structure combined with the major advances in the
computational software and hardware are gradually
Fig. 1 Photograph of an HMMWV M1025, the vehicle
analysed in the present work @
2 M Grujicic, G Arakere, H Nallagatla, W C Bell, and I Haque
Proc. IMechE Vol. 000 Part D: J. Automobile Engineering JAUTO1063 F IMechE 2009

enhancing the fidelity of the aforementioned com-
putational engineering analyses to the level that, in
the near future, virtual design, development and
validation of the effective mine protection systems
may become a reality [4, 5].
A review of the public-domain literature carried
out in the present work revealed that most of the
reported computational analyses pertaining to the
phenomena accompanying the detonation of a
shallow-buried mine in the vicinity of a target
vehicle or structure emphasize one of the following:
(a) an accurate modelling of mine detonation,
interactions between the detonation products
and the surrounding soils, and the determina-
tion of the spatial and temporal evolutions of
the resulting specific impulse (see, for example,
references [6] and [7];
(b) an accurate quantification of the interactions
between the mine-blast waves and the (rigid
and stationary) target vehicle or structure (see,
for example, reference [8];
(c) a detailed numerical analysis of the structural
and ballistic response of the target vehicle or
structure when subjected to (simplified empiri-
cally based) mine-blast-induced impulse load-
ing (see, for example, references [4] and [5].
All these analyses suffer from serious limitations.
For example, in the analyses of type (a), no
interactions between mine-casing fragments, deto-
nation products and soil ejecta, on one hand, and
the target vehicle or structure, on the other hand, are
considered. Such interactions are considered in the
analyses of type (b), but the target vehicle or
structure is not allowed to deflect or move and only
provides rigid and stationary walls which define a
spatial region within which the gaseous detonation
products are confined. In the analyses of type (c), the
structural response of the target vehicle or structure
is enabled but the interactions between the gaseous
detonation products, soil ejecta, and the target
vehicle or structure is oversimplified by replacing
them with empirically based relations for the initial
velocity or the impulse force. Hence, two of the main
objectives of the present work are: firstly, to combine
the formulation for modelling detonation of mines
shallow buried in sand [7] with a computational
analysis dealing with the interactions of detonation
products, mine fragments, and sand ejecta with the
target structure [9, 10] and, secondly, to apply this
combined formulation to the HMMWV.
As discussed earlier, as the existing HMMWVs are
being up-armoured to enhance their ballistic protec-
tion performance and survivability, the driving
performance, stability, and safety of these vehicles
(particularly during off-road travel) are being ser-
iously compromised, because of extra weight asso-
ciated with the added armour. Consequently, the
second main objective of the present work is to carry
out a series of conventional multi-body (longitudi-
nal) vehicle-dynamics computational analyses of the
off-road performance of an HMMWV. The key
feature of this portion of the work is that the same
sand material model which was used in the afore-
mentioned mine detonation vehicle-survivability
analyses is also used here to derive the appropriate
tyre–sand interaction model needed in the off-road
vehicle-dynamics computational analyses.
The organization of the paper is as follows. A brief
description of the problem definition, geometrical
models for the vehicle, mine, and sand mechanical
material models, and details of the computational
procedure used in the finite-element-based transient
non-linear dynamics analyses in modelling the inter-
actions between mine detonation products, sand
ejecta, and targeted vehicles are all presented in
section 2.1. The problem definition, topology of the
vehicle model, details regarding the derivation of the
tyre–sand interaction model, and those pertaining to
the multi-body dynamics (MBD) computational pro-
cedure used in the analysis of the off-road vehicle
performance are all presented in section 2.2. The
results obtained in the present work are presented and
discussed in section 3. The main conclusions resulting
from the present work are summarized in section 4.
2 MODELLING AND COMPUTATIONAL
PROCEDURES
2.1 Finite element modelling of mine detonation
under an HMMWV
In this section, a brief description is given of the
computational analysis used to simulate the inter-
actions between the detonation products and soil
ejecta resulting from the explosion of a mine shallow
buried in sand under the front wheel of an HMMWV
M1025 and the vehicle. The computational model-
ling of these interactions involved two distinct steps:
firstly, geometric modelling of the HMMWV M1025
together with the adjoining mine and sand regions;
secondly, the associated transient non-linear dy-
namics analysis of the impulse loading (momentum
transfer) from the detonation products and soil
ejecta to the vehicle and the kinematic and structural
response of the vehicle.
Off-road performance of a HMMWV 3

All the calculations carried out in this portion of
the work were made using the general-purpose
transient non-linear dynamics analysis software
ABAQUS/Explicit [11]. In previous work [9], a
detailed account was provided of the basic features
of ABAQUS/Explicit, emphasizing those that are
most relevant for modelling detonation of shallow-
buried and ground-laid mines and the subsequent
interactions between detonation products, soil
ejecta and target vehicle or structure. Therefore,
only a brief overview of ABAQUS/Explicit is given in
this section.
A typical transient non-linear dynamics problem
such as the interactions between shallow-buried
mine detonation products and soil ejecta with the
target vehicle or structure is analysed within ABA-
QUS/Explicit by solving simultaneously the govern-
ing partial differential equations for the conservation
of momentum, mass, and energy together with the
material constitutive equations and the equations
defining the initial and the boundary conditions. The
aforementioned equations are solved numerically
using a second-order accurate explicit scheme. The
ABAQUS/Explicit computational engine solves the
governing equations within a Lagrange framework,
i.e. the computational finite element grid is tied to
the components or materials (sand, the mine and
the HMMWV, in the present case) and moves and
deforms with them.
The interactions between different components or
materials as well as self-interactions are analysed in
ABAQUS/Explicit using a penalty contact method in
which the penetration of the surfaces into each other
is resisted by linear spring forces with values propor-
tional to the distance of penetration. These forces,
hence, tend to pull the surfaces into an equilibrium
position with no penetration.
2.1.1 Geometric model for HMMWV M1025
The finite element model of the HMMWV M1025
(with an overall length of 4.84 m, a wheelbase of
3.4 m, a curb mass of 3075 kg and a gross mass of
4672 kg) used in the present work consists of
approximately 140 000 elements. The computer-
aided design (CAD) model originally developed by
D. Wilson was purchased from 3DCAD.com [12] and
preprocessed for ABAQUS/Explicit finite element
program [11] using the general purpose pre-proces-
sing program HyperMesh from Altair, Inc. [13]. The
model includes the following subsystems: chassis,
front and rear suspension, four wheels, steering,
engine, transmission, cabin, hood, and four doors
and four seats. Each subsystem, in turn, consists of a
number of parts or components. For example, the
front left wheel subsystem includes a tyre tread, tyre
body, wheel rim, and eight lug nuts. The parts are
meshed with shell elements, three-dimensional
beam elements, and three-dimensional solid ele-
ments and assembled either by using various
connector elements, tying their adjacent edges or
faces or by having the connected parts share their
edge nodes. The engine block, brake assemblies,
front and rear differentials, transfer case, and chassis
frame rear axle are modelled as rigid parts in order to
take advantage of the high stiffness of these parts
relative to other parts. A summary of the main parts
which were included in the pickup truck finite
element model is given in Table 1.
The finite element model of the HMMWV M1025
displayed in Fig. 2 is oriented in such a way that the
positive x direction goes from the rear to the front of
the vehicle, the positive y direction goes from the
passenger (right-hand) side to the driver (left-hand)
side, and the positive z direction is upwards.
The materials used in the HMMWV M1025 model
are idealized as rigid (used only in some beam
connectors, brakes, and brake assemblies) linear
elastic, hyperelastic, elastic–plastic, or elastic–plastic
with failure. Suitable adjustments are made to the
material properties in order to account for non-
modelled features of various parts such as the
internal details of the engine, differentials, and
transfer case. Essentially, three classes of non-rigid
materials were used in the construction of the
HMMWV M1025:
(a) steel (of various grades);
(b) ballistic glass (used in windshields and win-
dows);
(c) rubber (used in tyres).
The components of the transmission, suspension,
and steering systems were assumed to be made of
AISI 4340 steel. The remaining components of the
vehicle were taken to be made of one of the two mild
steel grades with initial yield strengths of 270 MPa
and 350 MPa respectively. A more detailed account
of the models used to represent the structural and
the ballistic response of these materials is presented
in section 2.2.3.
2.1.2 Geometrical modelling of the mine and sand
regions
The mine and sand computational domains used in
the present study are shown in Fig. 2. The size and

circular disc shape of the mine computational
domain are selected to match that of a typical
10 kg anti-vehicle C4 mine used in reference [10].
The mine computational domain was meshed using
eight-node reduced-integration solid elements with
a typical size of 5 mm by 5 mm by 5 mm and filled
with a C4 HE material.
The sand computational domain was model as a
solid cuboid with L6W6H 5 3000 mm62400 mm6
900 mm. The domain was divided into three con-
centric subdomains. All three subdomains were
meshed using eight-node reduced-integration solid
elements with a typical mesh size of 5 mm by 5 mm
by 5 mm in the innermost subdomain and a
maximum mesh size of 50 mm by 50 mm by 5 mm
in the outermost subdomain. Finally, the lateral and
the bottom faces of the sand domain were sur-
rounded with eight-node CIN3D8 infinite elements
in order to model far-field sand regions and to avoid
unphysical stress-wave reflection at the sand-do-
main lateral and bottom surfaces. The sand domains
containing C3D8R elements were filled with CU-
Army Research Laboratory (ARL) sand material
(discussed later) while the infinite elements were
filled with an elastic sand material with Young’s
modulus and Poisson’s ratio matching those of the
CU-ARL sand.
The mine–sand and sand–pendulum interactions
were modelled using the hard contact pair type of
contact algorithm. Within this algorithm, contact
pressures between two bodies are not transmitted
unless the nodes on the slave surface contact the
master surface. No penetration or over-closure is
Table 1. Names and descriptions of the parts used in the finite element analysis of the HMMWV M1025
Part name Number of parts Part description and/or function
Tyres, wheel and braking
Tyres 4 Provide traction with the road
Rims 4 Connect the tyre to the brake assembly
Brake discs 4 Are represented by a simple model
Wheel hubs 4 Connect the wheel to the steering assembly
Suspension
Upper A-arms 4 Allow for vertical motion of the wheels
Lower A-arms 4 Allow for vertical motion of the wheels and shock mount
Spring–shock absorbers 4 Absorb shock and dampens vibrations
Shock absorber mounts 4 Support the damper–shock absorber
Cross members 4 Connect the lower A-arms
Steering
Steering system 1 Allows driver to control the vehicle
Chassis
Main frame 1 Provides longitudinal bending and torsional stiffness
Cross members 2 Provide transverse connection in the main frame
Engine and transmission
Engine 1 Provides the power to the vehicle
Differential 2 Supplies torque independently to the wheels
Transfer case 1 Transmits input transmission power to the front and rear
wheels
Engine gearbox 1 Consists of engine gearing and transfer of power to drive shaft
Drive shaft 3 Drives the train members
Front and rear axles 2 Transmit power to the wheels
Body
Cabin floor 1 Is represented by a simple model of the driver compartment
Roof and roof closure 1 Are represented by a simple model of a roof and roof closure
Interior panel 2 Provides support to the driver compartment
Windshield and window 6 Are represented by a simple model of the windshield and
window
Doors 4 Are represented by a simple model of the cabin doors
Hood 1 Provides upper closure to the engine compartment
Seat 4 Consists of interior driver and passenger seating
Fig. 2 Geometrical meshed models for HMMWV
M1025 and a sand domain containing a land-
mine. The mine computational domain (not
visible) is situated within the sand, underneath
the front right wheel

allowed and there is no limit to the magnitude of the
contact pressure that could be transmitted when the
surfaces are in contact. Transmission of shear
stresses across the contact interfaces is defined in
terms of a static and a kinematic friction coefficient
and an upper-bound shear stress limit (a maximum
value of shear stress which can be transmitted before
the contacting surfaces begin to slide).
A standard mesh-sensitivity analysis was carried
out in order to ensure that the results obtained are
insensitive to the size of the elements used.
At the beginning of the simulation, the vehicle was
assumed to be at rest (with the gravitational force
acting downwards), while the mine and sand
domains were filled with stationary materials (sand
and C4 respectively). Mine detonation was initiated
first along the bottom face of the mine.
2.1.3 Material constitutive models
As discussed above, the complete definition of a
transient non-linear dynamics problem entails the
knowledge of the material models that define the
relationships between the flow variables (pressure,
mass density, energy density, temperature, etc.).
These relations typically involve an equation of state,
a strength equation, a failure equation, and an
erosion equation for each constituent material.
These equations arise from the fact that, in general,
the total stress tensor can be decomposed into a sum
of a hydrostatic stress (pressure) tensor (which
causes a change in the volume or density of the
material) and a deviatoric stress tensor (which is
responsible for the shape change of the material). An
equation of state then is used to define the
corresponding functional relationship between pres-
sure, mass density, and internal energy density
(temperature). Likewise, a (constitutive material)
strength relation is used to define the appropriate
equivalent plastic strain, equivalent plastic strain
rate, and temperature dependences of the material’s
yield strength. This relation, in conjunction with the
appropriate yield criterion and flow-rule relations, is
used to compute the deviatoric part of stress under
elastic–plastic loading conditions. In addition, a
material model generally includes a failure criterion
(i.e. an equation describing the hydrostatic or
deviatoric stress and/or strain condition(s) which,
when attained, cause the material to fracture and
lose its ability to support (abruptly in the case of
brittle materials or gradually in the case of ductile
materials) normal and shear stresses. Such failure
criterion in combination with the corresponding
material-property degradation and the flow-rule
relations governs the evolution of stress during
failure. The erosion equation is generally intended
for eliminating numerical solution difficulties arising
from highly distorted elements. Nevertheless, the
erosion equation is often used to provide an
additional material failure mechanism especially in
materials with limited ductility.
To summarize, the equation of state together with
the strength and failure equations (as well as with
the equations governing the onset of plastic defor-
mation and failure and the plasticity and failure-
induced material flow) enable assessment of the
evolution of the complete stress tensor during a
transient non-linear dynamics analysis. Such an
assessment is needed where the governing (mass,
momentum, and energy) conservation equations are
being solved. Separate evaluations of the pressure
and the deviatoric stress enable inclusion of the non-
linear shock effects in the equation of state.
In the present work, the following materials are
utilized within the computational domain: C4 HE
explosive, various grades of steel, rubber, ballistic
glass, and soil. Since a detailed account of the
constitutive models used to represent the behaviour
of the materials in question can be found in recent
work [10], only a brief qualitative description of
these models will be provided in the remainder of
this section.
(a) C4 HE explosive. The Jones–Wilkins–Lee equa-
tion of state [14] is used for C4 in the present work
since that is the preferred choice for the equation of
state for high-energy explosives in most hydrody-
namic calculations involving detonation. Within a
typical hydrodynamic analysis, detonation is mod-
elled as an instantaneous process which converts
unreacted explosive into gaseous detonation pro-
ducts, and detonation of the entire high-explosive
material is typically completed at the very beginning
of a given simulation. Consequently, no strength and
failure models are required for high-energy explo-
sives such as C4.
(b) Steel. In the present work, with the exception of
the tyres and few rigid components, all the compo-
nents of the HMMWV M1025 are assumed to be made
of various steel grades. Since hydrostatic stress gives
rise to only minor reversible density changes in steels,
a linear type of equation of state was used for all the
steel grades. To represent the constitutive response of
the steels under deviatoric stress, the Johnson–Cook
[15] strength model is used. This model is capable of
representing the material behaviour displayed under
large-strain high-deformation-rate high-temperature

conditions of the type encountered in problems
dealing with the interactions of detonation products
and sand ejecta with target structures. Since all the
grades of steel considered in the present work exhibit
a ductile mode of failure, their failure condition was
defined using the Johnson–Cook [16] failure model.
Erosion of steel components is assumed to take place
when geometrical (i.e. elastic plus plastic plus
damage) instantaneous strain reaches a maximum
allowable value. Following general practice, the
optimal value for the geometrical instantaneous
strain was approximated as 2.0. When a material
element is eroded, its nodes are retained together
with their masses and velocities in order to conserve
momentum of the system. The momentum is con-
served by distributing the mass and velocities
associated with the eroded elements among the
corner nodes of the remaining elements. Despite the
fact that some loss of accuracy is encountered in this
procedure (owing to removal of the strain energy
from the eroded elements), the procedure is generally
found to yield reasonably accurate results [10].
(c) Rubber. The mechanical response of rubber (the
material used for tyres) was represented using the
extended Blatz–Ko [17] hyperelastic material model.
Within the model, a linear equation of state is used
to account for the nearly incompressible behaviour
of this material. The material constitutive relation is
assumed to be fully (non-linear) hyperelastic (i.e. no
provision is made for plastic deformation). The
Blatz–Ko [17] model used is a special form of the
hyperelastic material response used to describe
large-strain non-linear stress versus strain relations
observed in elastomers. In these materials, the
relationship between the (second Piola–Kirchhoff)
stress and (Green–Lagrange) large-deformation
strain is given implicitly via a strain energy density
function, which depends only on the strain invar-
iants. A complete specification of the strain energy
function typically requires the knowledge of only few
parameters (only one, the initial shear modulus in
the case of the Blatz–Ko rubber model).
Since the vehicle tyres may rupture when sub-
jected to mine detonation loads, a simple failure
model is used to extend the Blatz–Ko rubber model.
This model is based on a (geometrical) failure strain
whose magnitude was set to a value of 5.0 [10]. The
same value of the geometrical strain was used to
define the material erosion strain.
(d) Sand. Sand is a very complicated material
whose properties vary greatly with the presence or
absence and relative amounts of various constituent
materials (sand particles, clay, silt, gravel, etc.),
particle sizes, and particle size distribution of the
materials. In addition, the moisture content and the
extent of precompaction can profoundly affect the
sand properties. To account for all these effects,
Clemson University (CU) and the ARL, Aberdeen
Proving Ground, Maryland, USA, jointly developed
[6] and subsequently parameterized (using the
results of a detailed investigation of dynamic
response of sand at different saturation levels, as
carried out by researchers at the Cavendish Labora-
tory, Cambridge, UK [18, 19]) the new sand model
[20]. This model (used in the present work) is
capable of capturing the effect of moisture on the
dynamic behaviour of sand and was named the CU–
ARL sand model.
For the CU–ARL sand model, a saturation-depen-
dent porous-material or compaction equation of
state is used which, as shown in our previous work
[20], is a particular form of the Mie–Gruneisen
equation of state [22]. Within this equation there
are separate pressure versus density relations de-
fined for plastic compaction (giving rise to the
densification of sand) and for unloading or elastic
reloading. Within the CU–ARL sand strength model,
the yield strength is assumed to be pressure
dependent and to be controlled by saturation-
dependent inter-particle friction. In addition to
specifying the yield stress versus pressure relation-
ship, the strength model entails the knowledge of the
density and saturation-dependent shear modulus.
Within the CU–ARL sand failure model, failure is
assumed to occur when the negative pressure falls
below a critical saturation-dependent value, i.e. a
hydro-type failure mechanism was adopted. After
failure, the failed material element loses the ability to
support tensile or shear loads while its ability to
support compressive loads is retained. Erosion of a
sand element is assumed, within the CU–ARL sand
erosion model, to take place when geometrical (i.e.
elastic plus plastic plus damage) instantaneous
strain reaches a maximum allowable value. The
investigation reported in reference [6] established
that the optimal value for the geometrical instanta-
neous strain is about 1.0.
2.2 Multi-body (longitudinal) dynamics
modelling of the off-road performance of an
HMMWV
2.2.1 A multi-body dynamics model for HMMWV
M1025
A new 36-degrees-of-freedom MBD model for
HMMWV M1025 was developed in this work using

various public-domain data. The model contains 40
rigid bodies and the addition of several force and
control elements. A topological map of the HMMWV
M1025 MBD model is shown in Fig. 3. The basic
kinematics of the model can be described as follows.
1. The vehicle chassis, including cargo/load, is
represented by a single rigid body.
2. Eight rigid bodies are used to represent four
lower A-arms and four upper A-arms. Each of the
A-arms is connected to the chassis body by a
Fig. 3 Topological map for the HMMWV M1025 MBD model

single revolute joint with the axis of revolution
initially aligned in the global x direction.
3. Four additional rigid bodies are used to repre-
sent the four wheel hubs, each connected to a
lower A-arm–upper A-arm pair. In the front of
the vehicle, universal joints with their axes of
revolution initially aligned in the global x and z
directions are used for connection while, in the
rear, revolute joints were used with their axis of
revolution initially aligned in the global x direc-
tion.
4. Four rigid bodies are used to represent the
wheels which are connected to the wheel hubs
using transverse revolute joints with their axis of
revolution initially aligned in the global y direc-
tion (i.e. along the wheels axis).
5. Within the steering system, four rigid bodies are
used to represent the steering column, the
steering rack and two steering rods respectively.
A single revolute joint is assigned to the steering
column with its axis of revolution aligned with
the axis of the column. A control element is used
to provide input to this joint in order to enable
controlled steering. Two prismatic joints with
their translational axis initially aligned in global y
direction are used to connect the steering rack
with the steering rods (one at each side of the
vehicle). The steering rods were connected to the
wheel hub using universal joints which enable
revolutions to occur other than that along the
axis of the steering rod. A torque-to-force con-
straint is placed between the steering column
and the steering rack.
6. Several hard and soft mechanical stops were
used in order to account for inter-component
contacts adequately. These stops were modelled
as non-linear axial or rotational springs.
7. Compliance of the suspension system was
represented by connecting axial springs and
shock absorbers between the upper shock mount
of the chassis and the lower shock mounts
located on the lower A-arm, and the appropriate
spring rates and damping coefficients were
assigned.
8. The vertical force developed between the stan-
dard tyre used on an HMMWV and a rigid-
ground surface as a function of the vertical tyre
deflection was taken from tests performed on
this tyre and includes bottoming-out hardening
effects.
9. The non-linear longitudinal friction and shear
behaviours of the tyre in contact with the rigid
road were modelled using the Pacejka [22] magic
formula and the tyre–road interaction forces are
set to zero when the tyre is not in contact with
the ground. The longitudinal force is a function
of the relative velocities between the bottom of
the tyre and the ground (i.e. the longitudinal
slip), the normal force, and the tyre–road friction
coefficient. Similarly, the lateral shear force (not
used in the present work) is a function of the slip
angle (controlled by relative magnitudes of the
longitudinal and lateral tyre-velocity compo-
nents), the friction coefficient, and the vertical
force.
10. The behaviour of the same tyre on a deformable
sand-based road is discussed in the next section.
An MBD model such as that developed in the
present work requires knowledge of the initial
position and orientation of every component and
any interconnecting joints as well as mass and
inertia properties of individual components. This
yields a relatively simple but yet realistic model of
the suspension and steering including elements such
as upper and lower A-arms, steering link, and tie
rods.
2.2.2 Tyre–sand interaction model
As discussed earlier, owing to normal sinkage of the
wheels in sand, and the accompanying motion
resistance, an off-road computational dynamics
analysis of a wheeled vehicle is somewhat more
complicated than the corresponding analysis dealing
with the same vehicle travelling on a hard-surface
road (an on-road analysis) [23–25]. To account for
the aforementioned off-road vehicle travel effects,
the tyre–road model needed in the multi-body
longitudinal vehicle-dynamics analysis has to be
modified. While very detailed finite-element-based
models of tyre–sand interactions can be developed
(see, for example, references [26] and [27]), these
models are inherently quite expensive computation-
ally and, hence, less attractive. Consequently, the
semianalytical model recently proposed by Lee et al.
[28] has been used. This model appears to be a good
compromise between the physical reality and com-
putational efficiency when dealing with off-road
vehicle travel tyre–sand interactions.
Within the model given by Lee et al. [28], the tyre–
sand interaction is developed by properly modifying
the tyre–hard road model for the tyre in question.
This modification is affected both by the properties
and characteristics of the tyre and by the mechanical
behaviour of sand and involves the following steps.

Step 1. First, for the given tyre–sand pair, at a given
level of tyre inflation pressure, the associated
normal (downward) force versus vertical wheel
sinkage relation needs to be determined.
Step 2. In the absence of motion resistance to tyre
rolling, as is the case when a tyre with zero rolling
resistance (i.e. no viscous energy dissipation) rolls
over a rigid (i.e. non-deformable) surface, a zero
longitudinal force (i.e. traction effort) is required
for the tyre to remain in the pure-rolling (i.e. zero-
slip) condition. In the case of off-road vehicle
travel, forward motion of the wheel requires
compaction of the sand located just ahead of the
wheel. This, in turn, exerts a resisting force (i.e.
motion resistance) to the wheel. Thus for the tyre
to remain in a pure-rolling condition, a non-zero
traction effort must be present. To obtain such a
non-zero longitudinal force from the tyre–hard-
road model (the Pacejka magic formula model, in
the present case), which yields a zero-traction
effort at a zero-slip, an initial driving slip shift has
to be introduced. The introduction of this slip shift
enables the selected tyre–rigid-road longitudinal
force versus slip formula to yield a non-zero force
(required to overcome the motion resistance
force) under pure-rolling (zero-slip) off-road ve-
hicle travel conditions. Thus, within the second
step of the Lee et al. [28] model, the appropriate
relation for the slip shift and its dependence on
the sand properties and the vertical force is
derived;
Step 3. Once the effective (i.e. shifted) slip is
determined, the tyre–rigid-road longitudinal and
transverse force relations have to be corrected by
subjecting them to the combined (longitudinal
plus lateral) slip (i.e. friction circle) condition.
Step 4. Finally, the (wheel’s sinkage-induced) long-
itudinal and (side ploughing-induced) lateral
resistance forces should be computed and com-
bined (as vectors) with their counterparts obtained
in step 3 in order to obtain the net traction or
drawbar-pull forces.
Details pertaining to the implementation of each of
these four steps, in the present work are discussed next.
(a) Step 1: vertical force versus wheel sinkage
relation. While it is customary to derive the
required vertical force versus wheel sinkage
relation (see, for example, reference [29]) using
a smooth-tyre approximation and the Bekker
pressure versus sinkage relation [25] (the
parameters in the relation can be related to
the key physicomechanical properties of the
sand), this was not done in the present work for
two reasons. Firstly, the tyre used in the
present work has very deep treads and is a
serious oversimplification if it is considered as
a smooth tyre. Secondly, the Bekker para-
meters cannot be readily extracted from the
CU–ARL viscoplastic sand model used in the
present work. Therefore, the vertical force
versus wheel sinkage relation is obtained by
carrying out a series of finite element analyses.
Within each such analysis, the tyre is first
inflated to a desired pressure by prescribing a
constant distributed load to the interior walls
of the tyre while holding the wheel centre fixed.
Then, the tyre is lowered to the ground and the
vertical force of a given magnitude is applied to
the wheel centre while the tyre deflection and
wheel sinkage are being monitored. An exam-
ple of the wheel–sand static-equilibrium con-
figuration obtained in these finite element
analyses is displayed in Fig. 4(a). An example
of the results pertaining to the vertical force Fz
versus wheel sinkage uz relation is displayed in
Fig. 4(b).
(b) Step 2: driving slip-shift determination. Lee et al.
[28] also provided a relationship for the
calculation of the initial slip shift. Since this
relation is also based on the smooth-tyre
approximation and the Bekker pressure versus
sinkage relation, it was not used in the present
work. Instead, a tyre–sand interaction finite
element analysis was again carried out. Within
this analysis, the wheel is translated long-
itudinally and rotated under a pure-rolling
condition, by prescribing the appropriate long-
itudinal and rotational velocities to the wheel
centre. The longitudinal shear force obtained is
next substituted in the Pacejka [22] magic
formula and the resulting equation solved for
the unknown longitudinal slip (i.e. for the slip
shift). For clarity, however, it can be briefly
stated here that the slip shift at a given level of
the vertical force is obtained by determining
the wheel’s rotational speed and its long-
itudinal velocity at which there is a zero net
longitudinal force acting on the wheel centre.
This procedure, thus, simultaneously yields
both the driving slip shift and the longitudinal
motion-resistance force. An example of the
wheel–sand dynamic equilibrium configura-
tion obtained in these finite element analyses
after the wheel has rolled a short distance is

displayed in Fig. 5(a). An example of the results
pertaining to the longitudinal motion resis-
tance Rx versus vertical force Fz relation is
displayed in Fig. 5(b).
(c) Step 3: net traction force relations. As discussed
earlier, the net longitudinal and lateral drawbar
forces are obtained by combining (in a vector
sense), the tyre–rigid-road force relations
(based on the shifted slip) with the correspond-
ing resistance forces. Since, in the present work,
straight driving manoeuvres were exclusively
considered, only the net longitudinal force (i.e.
drawbar pull) versus slip relation was derived. A
simple schematic diagram is used in Fig. 6 to
show the relations between the vertical force Fz,
the longitudinal force Fx, the longitudinal
resistance force Rx, and the maximum wheel
sinkage z0. An example of the results pertaining
to the net longitudinal force Fx 2 Rx versus
Fig. 5 (a) An example of the tracks left in sand after
wheel roll obtained in the finite element
analyses which will be reported in more details
in a future communication; (b) longitudinal
force versus vertical force relation at a tyre
inflation pressure of 180 kPa; (c) the effect of
slip on the total longitudinal force (traction
effort), motion resistance, and net longitudinal
force (drawbar pull) at a tyre inflation pressure
of 180 kPa and a vertical force of 8000 N
Fig. 4 An example of the wheel–sand interaction
results obtained in the finite element analysis
of tyre–sand interactions: (a) wheel–sand static
equilibrium configuration; (b) vertical force
versus wheel sinkage relation at a tyre inflation
pressure of 180 kPa

longitudinal slip relation is displayed in
Fig. 5(c). It should be noted, as correctly
pointed out by one of the reviewers of the
present work, that the approach used here does
not explicitly include the effect of sand-particle
motion, the effect of which may become
significant when the wheel is near a locking
condition or when it is slipping in the traction
direction.
(d) Step 4: tyre–sand model implementation. The
implementation of the aforementioned rela-
tions in Simpack [30], a general purpose MBD
program, was carried out using the utyr-
e_spck.f user tyre-model subroutine. Within
this subroutine, the current values of the
wheel-centre kinematic parameters (e.g. ver-
tical displacement, longitudinal displacement,
and rotational speed around the wheel axis)
are used to calculate the vertical force, the
slip, and the longitudinal drawbar pull force.
3 RESULTS AND DISCUSSION
3.1 Survivability of HMMWV to detonation of a
mine buried in underlying sand
In this section, the computational results are pre-
sented, which were obtained in the transient non-
linear dynamics analysis of the interaction of detona-
tion products and sand ejecta with the HMMWV after
detonation of a landmine, buried in sand under the
vehicle’s front right wheel. While most HMMWV
models are not required by the US military to have
any armour protection, armament carriers and the
hard-shelled ambulance models were designed to
provide some minor level of protection. The basic
armour package used is a combination of steel,
KevlarH-reinforced composites, and laminated glass–
polycarbonate windshield and windows designed to
stop a fragment of mass less than 1.5 g. The supple-
mental armour provides an additional level of
protection to stop a fragment of mass less than 4 g.
Clearly, neither basic nor supplemental armour is
capable of defeating commonly used bullets at full
muzzle velocity or average-size IED fragments. In this
work, an up-armoured configuration of the HMMWV
was considered in which additional steel and KevlarH-
reinforced composite armour panels were applied to
the vehicle’s underbody and doors and larger-gauge
laminated transparent-armour panels were used for
the windshield and windows. Because of the sensitive
nature of the subject matter and the potential for
misuse of the up-armoured vehicle model, no further
details could be provided here.
3.1.1 Impulse loading functions
Traditionally, the effect of mine blast on the target
vehicle is analysed by replacing the interactions
between the detonation products, the soil ejecta, and
the target with some form of simplified empirically
based loading function. Two such functions that are
most commonly used are conventional weapon
(CONWEP) air-blast loading function [31] and the
loading-function proposed by Westine et al. [32].
Within the loading-function approach, temporal and
spatial evolutions of the detonation loads (previously
determined by multiple-regression analyses of the
data collected in a series of experiments) are used as
boundary or loading conditions in the transient non-
linear dynamics analysis of mine blast effect on the
targeted vehicle: While this approach makes the
computational analyses simpler and manageable, it
fails to include fully the interaction effects between
the air blast, detonation products, mine fragments,
and soil ejecta with the target as well as the effect of
the target’s kinematic response (e.g. targets undergo
large motions or deformations while the prescribed
loads are defined for fixed spatial locations).
Furthermore, extrapolation from the finite set of
experimental data to the specific mine-burial geo-
metrical and explosive-type conditions are fre-
quently required, which introduce additional
sources of errors. As will be demonstrated in the
present section, the use of the loading-function
approach as opposed to simultaneously modelling
Fig. 6 A schematic diagram of the side view showing
the interaction between a wheel and sand
during straight-line roll

the mine detonation process and the interactions
between the detonation products, mine fragments,
and sand ejecta with the targeted vehicle may
seriously misrepresent the kinematic and ballistic
response of the vehicle.
(a) CONWEP loading function [31]. The CONWEP
loading function [31] was originally designed for use
with a free-air or a ground-laid mine detonation.
Neither of these two conditions accurately repre-
sents the situation encountered in the case of anti-
vehicular mines which are typically buried in the soil
to a depth of 0–30 cm. Since the depth of burial of a
mine can have a significant effect in directing the
energy on to the target by funnelling the force of the
mine blast upwards and the soil ejecta play a major
role in the momentum transfer to the target, the use
of the CONWEP loading function in the analysis of
the structural response of the vehicle to the mine
blast is expected to have a limited value. To
prescribe the CONWEP loading function, only the
following details have to be provided for the
explosive charge [24]: its mass, position and the
trinitrotoluene TNT equivalent (the mass of TNT
that would give the same blast performance as the
unit mass of the explosive in question). This
information is then used to compute the blast-
loading pressure as a function of the radial distance
from the charge centre as
P~Prcos2
hzPin 1zcos2
h{2cosh
À Á
ð1Þ
where Pr denotes the reflected (normal incident)
pressure, Pin denotes the incident (side-on inci-
dence) pressure, and h is the angle of incidence. The
mathematical expressions for Pr and Pin (tenth-order
polynomials of the logarithm of the scaled radial
distance, i.e. the radial distance divided by the TNT-
equivalent charge weight) can be found in reference
[31].
(b) The westine et al. [32] loading function. The
loading function proposed by Westine et al. [32] was
developed empirically by measuring the total im-
pulse resulting from the explosion of a shallow-
buried mine on a rigid plate with plugs. By
measuring the initial velocity of the plugs, Westine
et al. [32] developed the following relationship for
the specific impulse iz, which is given by
iz~0:1352
tanh 0:9589Psð Þ
Ps
3:25
r
1=2
soilW1=2
1z7d=9sð Þ
s1=2
ð2Þ
where
Ps~
rd
s5=4A
3=8
mine tanh 2:2d=sð Þ3=2
ð3Þ
and r is the radial distance of a point on the target
from the vertical line passing through the centre of
the mine, d is the depth of burial, Amine is the area of
the mine, s is the stand-off distance, W is the energy
released by the mine, and rsoil is the density of soil. It
should be noted that s and d in equation (3) are
measured with respect to the centre of the mine. It is
important also to note that the loading function was
originally developed using 0.27 kg shallow-buried
mines. Thus, when the loading function of Westine
et al. [32] is used to quantify the blast-loading results
from the detonation of anti-vehicle mines (1–10 kg in
mass), it is assumed that the specific impulse scales
linearly with the mass of the mine. Some justifica-
tion for this assumption was given by Morris [33].
Morris [33] further extended the loading function of
Westine et al. [32] to include the effect of target
inclination. The specific impulse relation proposed
by Morris contains equation (2) multiplied by a
factor cosh/cosb, where h is the angle between the
target-plate normal and the line connecting the
mine centre with the point on the target, while b is
the angle between the vertical axis passing through
the mine centre and the line connecting the mine
centre to the same point on the target.
(c) Loading functions versus explicit mine detonation
modelling. To demonstrate that the two aforemen-
tioned loading functions cannot accurately account
for the blast loading resulting from the detonation of
a mine shallow buried in sand, the case of the up-
armoured HMMWV targeted by the previously
described landmine (buried in dry sand at a depth
of burial (equal to 15 cm)), is considered.
To reveal differences in the blast loading pre-
scribed by the two loading functions and by the
explicit modelling of the landmine detonation more
clearly, all the materials in the HMMWV are
considered as elastic or hyperelastic, in this portion
of the work. Consequently, the initial response of the
vehicle was forced to be dominated by its (more
rigid-body motion) kinematic component. It is
otherwise normally observed (see, for example,
reference [10]) that the initial response of the vehicle
is dominated by its deformation and failure and only
at later post detonation times do the kinematic
effects become more significant.
An example of the results obtained in this portion
of the work is displayed in Figs 7(a) and (b). In

Fig. 7(a), the deformed configuration of the HMMWV
when subjected to the CONWEP loading function
[31] is displayed, while the corresponding config-
uration obtained in the analysis in which buried-
mine detonation (under the front right wheel) is
considered explicitly is displayed in Fig. 7(b). In both
cases, the post-detonation time is 10 ms. A simple
examination of the results displayed in Figs 7(a) and
(b), clearly reveals that serious differences exist
between the spatial distribution and the extent of
dynamic loading brought about by the CONWEP
loading function and by the direct mine-blast
modelling. Similar differences were observed in the
case of the loading function proposed by Westine et
al. [32].
While the results displayed in Figs 7(a) and (b)
pertain to one post-detonation time, similar discre-
pancies were also observed at other times. Also, when
Fig. 7 A comparison in the kinematic response of the HMMWV when subjected to (a) the
CONWEP loading function and (b) blast loads generated during buried-mine detonation

the plasticity of materials and the damage initiation
and evolution were restored, major differences were
observed relative to the extent and spatial distribution
of failure and fracture in the vehicle. These results are
not shown here for brevity. In summary, the results
presented (and those generated but not shown) in
this section clearly revealed that the utility of the two
loading functions in analysing vehicle response to
buried-mine detonation under the vehicle’s right
front wheel is quite limited.
3.1.2 Vehicle survivability to mine detonation
In this section, selected results are presented for the
spatial distribution and the extent of damage of the
HMMWV upon detonation of the previously de-
scribed landmine. Towards that end the plasticity
and damage initiation and evolution properties of
the materials have been restored. Because of the
shortcomings of the loading functions described in
the previous section, only the results obtained in the
analyses in which mine detonation was modelled
explicitly are presented. Also, owing to the sensitive
nature of the subject matter, mainly qualitative
results will be shown.
Temporal evolution of the materials deformation
and damage in the HMMWV is displayed in Figs 8(a)
to (c). Clearly, the damage is extensive and more
pronounced at the front right side of the vehicle. The
components such as tyres, wheel rims, and hubs,
which were closest to the mine have been either
completely disintegrated or heavily damaged. The
presence of underbody armour and up-armoured
doors did not as expected provide any additional
protection to the aforementioned components.
However, the extent of damage in the underbody,
vehicle frame, and the doors was measurably lower
in the up-armoured HMMWV than in that lacking
additional armour (the results pertaining to the latter
configuration of the vehicle are not shown for
brevity).
It should be pointed out that the results presented
in Figs 8(a) to (c) show a typical initial response of the
vehicle to buried-mine detonation. That is, the initial
(less than about 10–20 ms) stage of the response is
dominated by extensive deformation and failure of
the components of the vehicle directly above the
buried mine. At this stage, very little vertical move-
ment of the vehicle’s centre of gravity is observed.
Conversely, at longer times (longer than about 50 ms)
the response of the vehicle is dominated by its
upward translation and the rotations about the
vehicle’s centre of gravity. Owing to space limitations,
only the first stage of the vehicle’s kinematic response
(with the inclusion of plasticity and failure initiation
and evolution of the materials) was analysed in the
present paper.
Temporal evolution of the total acceleration at the
location of the gas and brake pedals for the case of the
up-armoured and standard HMMWV configurations
are displayed in Fig. 9(a). Because of previously
mentioned concerns regarding the misuse of the
present results, arbitrary units are used along the y
axis in Fig. 9(a). Also, the two curves in Fig. 9(a) are
shifted in the positive and negative y directions
respectively to improve clarity of the figure. The results
such as those displayed in Fig. 9(a) can be used to
assess and predict the type and extent of injuries
suffered by the vehicle occupants. In such assessments
and predictions, various mine-blast injury-occurrence
criteria can be used. An example of these criteria is
displayed in Table 2 [34]. The results displayed in
Fig. 9(a) clearly show that added armour reduces the
level of acceleration and, hence, reduces the possibility
or extent of trauma to the driver’s ankles and feet.
Temporal evolution of the pressure in one of the
elements of the seat cushion for the two configura-
tion of HMMWV is displayed in Fig. 9(b). Again, the
two curves in Fig. 9(b) are shifted in the positive and
negative y directions respectively to improve clarity
of the figure. It is well established that exposure to
high values of the peak overpressure (pressure in
excess of the atmospheric pressure) can have serious
consequences to humans. The results shown in
Table 3 [35] reveal the type of injuries associated
with different levels of peak overpressure. While the
results displayed in Table 3 were obtained using pigs
as test objects, similarities of the body masses and
tissue structures in pigs and humans tend to suggest
that these results may be relevant to humans too.
The results displayed in Fig. 9(b) show that the
added armour does not significantly alter the value
of the peak overpressure at the location of the
driver’s seat. Thus additional measures are required
to protect the driver from mine-detonation-induced
high levels of overpressure.
The results presented and discussed in the present
section are all of a computational nature. To validate
fully the HMMWV finite-element model, the inter-
actions between the detonation products, sand
ejecta, and the vehicle, and the resulting kinematic,
structural, and failure responses of the vehicle, these
results should be compared with their experimental
and field-test counterparts. However, while limited
and mainly qualitative comparison between the
present computational results and the respective

field-test results pertaining to the spatial distribution
and the extent of damage of various components of
the vehicle were carried out by the present authors,
details of this comparison could not be presented
here because of the sensitive nature of the subject
matter. Nevertheless, based on the results of this
comparison, it was concluded that the present finite
element model and simulations of the mine-blast
vehicle survivability are fairly reasonable.
3.2 Simple off-road and on-road straight-line
brake manoeuvres of the HMMWV
In this section, the effect of the tyre–sand model,
presented in section 2.2, on the vehicle performance
during a simple straight-line brake manoeuvre, is
presented and discussed. For comparison, the on-
road performance of the same up-armoured
HMMWV under the same braking condition is also
presented. To reveal better the effect of the new tyre–
Fig. 8 Temporal evolution of the material deformation and damage in the up-armoured HMMWV following mine
detonation for post-detonation times of (a) 0.2 ms, (b) 0.85 ms, (c) 1.5 ms, and (d) 2.1 ms

sand model on the vehicle performance, two levels
of off-road tyre–sand interfacial friction, at the same
nominal inflation pressure of 207 kPa, are consid-
ered: firstly, a high level (equal to 1.0), typical of the
on-road tyre–road interactions; secondly, a lower
level (equal to 0.4), more typical of the tyre–
deformable-road interactions. For the same reason,
two levels (207 kPa and 138 kPa) of tyre inflation
pressure at the same low friction coefficient are also
considered.
The straight-line brake test is simulated as follows.
1. The vehicle is first driven at a constant velocity of
80 km/h for 1 s by prescribing the corresponding
rotational speed to all four wheels.
2. Within the next 3 s, the braking torque has been
linearly increased to 50 per cent and 30 per cent
of its wheel-locking critical value for the high and
low off-road tyre–road friction coefficients re-
spectively.
While it is questionable whether the vehicle can
acquire a speed of 80 km/h on off-road sandy terrain, it
Fig. 8 (Continued)

was chosen here to amplify the effect of the tyre–soil
model relative to the tyre–hard-road model on the
vehicle performance during braking.
3.2.1 High off-road-friction-coefficient case
A summary of the results obtained in the case of high
off-road tyre–road friction coefficient are displayed
in Figs 10(a) to (h). A simple examination of the
results displayed in Figs 10(a) to (h) reveals the
following.
1. At the same high value of the tyre–road friction
coefficient, a larger reduction in the vehicle
velocity is observed in the case of the off-road
travel (Fig. 10(a)). This is clearly caused by the
presence of the wheel-sinkage-induced motion
resistance in the case of the off-road vehicle travel.
2. Larger values of the pitch angle are observed in
the case of the off-road travel (Fig. 10(b)). This
finding can be linked with the fact that, at a same
level of the longitudinal slip, the tyre–sand model
yields a larger value of the longitudinal force
(Fig. 10(g)).
3. Owing to rear-to-front weight transfer, both
longitudinal slip and the longitudinal force take
on larger magnitudes in the case of front wheels
than in the case of rear wheels (Figs 10(c) and (d)
versus Figs 10(e) and (f)).
4. Because of the presence of wheel-sinkage-in-
duced motion resistance, for both front and rear
wheels, the longitudinal slip and the longitudinal
force take on larger magnitudes in the case of the
off-road travel (Figs 10(e) and (f)).
5. At the same level of longitudinal slip, the off-road
vehicle travel is associated with a larger value of
the longitudinal force (Fig. 10(g)).
6. Owing to the aforementioned rear-to-front weight
transfer, a difference in the wheel sinkage devel-
ops between the front wheels (larger sinkage) and
rear wheels (smaller sinkage) (Fig. 10(h)).
3.2.2 Low-off-road-friction-coefficient case
A summary of the results obtained in the case of low
off-road tyre–road friction coefficient are displayed
in Figs 11(a) to (h). A simple examination of the
results displayed in Figs 11(a) to (h) reveals that the
following.
Table 2. Mine-blast acceleration-induced Injury
assessment [34]
Part Acceleration Duration (ms) Injury type
Head 150 g 2 High risk of brain damage
Pelvis 40 g 7 High risk of spinal cord
damage
Feet v 5 3.5–5.0 m/s Apparition of lower leg
fracture
Table 3. Mine-blast over-pressure induced injury
assessment [35]
Injury Overpressure (kPa)
Barotrauma 56
Mild contusion 130
Moderate Injury 237
Heavy injury 371
Lethal injury 1074
Fig. 9 Temporal evolution of (a) the acceleration at
the location of the gas and brake pedals and (b)
the pressure in an element located at the centre
of the driver’s seat cushion (both quantities are
expressed in arbitrary units (a.u.)) for the cases
of an up-armoured and a standard configura-
tion HMMWV

Fig. 10 A comparison of various vehicle–road interaction parameters for the cases of off-road
and on-road vehicle travel. In both cases, the tyre–road friction coefficient was set to 1.0.
See the text for details

Fig. 11 A comparison of various vehicle–road interaction parameters for the cases of off-road
and on-road vehicle travel. The on-road tyre–road friction coefficient was set to 1.0 and
its off-road counterpart to 0.4

1. Most of the results displayed in these figures can
be readily accounted for by recognizing that the
braking force was substantially lower in the case
of off-road vehicle travel. For example, the
residual vehicle velocity after 4 s is about 42 km/
h in Fig. 11(a) while its counterpart is only about
30 km/h in Fig. 10(a). Also, the pitch angle is
reduced (see Fig. 11(b) versus Fig. 10(b)).
2. Owing to the associated reduced extent of rear-to-
front weight transfer, the longitudinal force in the
off-road travel case becomes either smaller in
magnitude than (Fig. 11(d)) or nearly equal to
(Fig. 11(f)) that in the on-road vehicle travel case.
3. At the same time, because of the reduced tyre–
sand interfacial friction coefficient, the longitu-
dinal slip increases in magnitude (Fig. 11(c)).
4. Finally, while the Fx versus slip reduction shows a
constant increase in the on-road vehicle travel
case it does not change considerably in the off-
road case (Fig. 11(g)).
3.2.3 Low-inflation-pressure case
It is generally recommended that the tyre inflation
pressure be lowered to 75–50 per cent of the nominal
on-road value in order to improve the off-road
mobility and manoeuvrability. Decreased tyre pres-
sures result in larger tyre–sand contact patches,
lower contact pressures, and lower wheel sinkage
(i.e. higher flotation). These, in turn, yield lower
motion resistance levels and improved mobility and
manoeuvrability. A summary of the results revealing
the effect of lower tyre inflation pressure is displayed
in Figs 12(a) to (c). A simple examination of the
results displayed in Figs 12(a) to (c) reveals the
following.
1. At the same low value of the off-road tyre–sand
friction coefficient, a lower reduction in the
vehicle velocity is observed in the case of the
lower tyre inflation pressure (Fig. 12(a)). This
finding suggests that excessive lowering of the
tyre pressure can result in undesirably long
braking distances.
2. Lower values of the pitch angle are observed in
the case of low tyre inflation pressure (Fig. 12(b)).
This finding can be linked with the fact that, at a
same level of the longitudinal slip, the tyre–sand
model yields a lower value of the longitudinal
force for the case of lower tyre inflation pressure.
3. As expected, lower wheel sinkage values are seen
in the case of the lower tyre inflation pressure
(Fig. 12(c) versus Fig. 11(h)). In addition, owing to
the aforementioned lower pitch angle observed
for the low tyre inflation pressure, less difference
between the wheel sinkages for the front and rear
wheels develops. These findings clearly reveal
that lowering of the tyre inflation pressure can
reduce the likelihood of vehicle mobility loss due
to excessive tyre sinkage accompanying a braking
manoeuvre. Taking into account the previously
mentioned tyre-pressure-reduction-induced in-
crease in the braking distance, it appears that
there is an optimal level of tyre inflation pressure
which balances vehicle braking performance with
its mobility.
3.2.4 Effect of HMMWV up-armouring on the
vehicle braking performance
As discussed earlier, up-armouring can compromise
the off-road performance of the HMMWV in general,
and the vehicle’s off-road straight-line braking
behaviour in particular. When analysing off-road
straight-line vehicle braking, the following perfor-
mance criteria are generally considered:
(a) the ability of the vehicle to regain traction
following a hard braking manoeuvre to full stop;
(b) the low propensity for the vehicle to undergo a
full frontal (end-over-end) rollover during a
downhill braking;
(c) the ability of the vehicle to come to a full stop
over a shortest braking distance.
The three criteria described above were intro-
duced in order of their perceived importance. It is
well established that a single phenomenon, namely
the extent of front-wheel sinkage, affects all three
aforementioned performance criteria and controls
the trade-offs between them. For example, deeper
front wheel sinkage results in a shorter braking
distance but, in turn, increases the tendency for
frontal rollover and may result in total loss of vehicle
mobility (it may cause the vehicle to become stuck).
Owing to space limitations and since a comprehen-
sive investigation of the effect of up-armouring on
the off-road vehicle performance is the subject of
our ongoing investigation by one of the present
authors, M. Grujicic, only a couple of typical results
pertaining to straight-line flatland braking will be
presented and discussed in the remainder of this
section.
The effect of the average braking torque on the
straight-line flatland braking distance for the standard
configuration and the up-armoured configuration of

the HMMWV (at an 30 km/h vehicle velocity before
the onset of braking) is displayed in Fig. 13. The
average braking torque was controlled by properly
assigning the time interval over which the wheels
achieve the full-lock condition (i.e. the time over
which the rotational velocity of the wheel decreases
linearly form its prebraking value to zero). On average,
a 6 per cent increase in the braking distance is seen to
result from HMMWV up-armouring.
The effect of the average braking torque on the
propensity for vehicle frontal rollover following a 30u
downhill sharp braking manoeuvre for the standard
configuration and the up-armoured configuration of
the HMMWV (at a 30 km/h vehicle velocity before the
onset of braking) is displayed in Fig. 14. The frontal-
rollover propensity of the vehicle is quantified by the
minimal braking torque at which rear wheel vertical
force first reaches a zero value. Clearly, the zero-
vertical-force condition used corresponds to the
onset of the incipient rollover. As correctly pointed
out by one of the reviewers of the present manuscript,
incipient rollover does not necessary lead to complete
rollover, since the vehicle can recover from the state
of incipient rollover. Figure 14 clearly shows that
vehicle up-armouring increases its propensity for
frontal rollover during downhill braking. That is, at a
braking torque of about 17 kN m, the rear wheels of
the up-armoured configuration are no longer in
contact with the road (i.e. there is a zero force acting
on the rear wheels), while in the case of the standard
configuration a downward force of about 100 N is
acting on the rear wheels.
Fig. 12 A comparison of various off-road vehicle–sand interaction parameters for the cases of
138 kPa and 207 kPa tyre inflation pressures. The tyre–sand friction coefficient was set to 0.4

As discussed earlier, all the results generated
within the present work are of a computational
nature. Clearly, to validate fully the present compu-
tational model and procedure pertaining to the
effect of HMMWV up-armouring on its off-road
performance, a comparison should be carried out
between the present results and their experimental
counterparts. Such comparison although fairly lim-
ited and mainly semiquantitative was carried out by
the present authors. However, the details of the
outcome of this comparison cannot be revealed
because of the sensitive nature of the subject matter.
What could be revealed is that the overall agreement
between computation and experiment was found to
be reasonable. For example, in the case of straight-
line braking, the present computational results were
found to be within ¡10 per cent of their experi-
mental counterparts.
To offer at least some level of proof that the
present model and the approach are reasonable, the
model was used to carry out a simple steady state
cornering analysis in which the vehicle was driven at
a constant velocity over a circular track of a constant
radius. The results of this analysis are compared with
their counterparts for a Jeep sport utility vehicle,
reported in reference [36]. The results reported in
reference [36] showed that up-armouring causes a
decrease in critical lateral acceleration of about 20
per cent for the incipient frontal rollover (i.e. the
lowest lateral acceleration at which the vertical force
on the inner wheels become zero). A very similar up-
armouring-induced reduction in the critical lateral
acceleration was obtained in the present work for the
HMMWV under identical conditions of total armour
weight and geometrical parameters of the cornering
manoeuvre.
3.3 Blast survivability of a moving vehicle
Ideally, it would be helpful to be able to investigate
the effect of mine blast on a moving vehicle rather
than a stationary vehicle. The computational analy-
sis needed is, however, rather more expensive since
the finite element model has to be fully validated
with respect to its ability to account correctly for the
basic vehicle kinematics and dynamics. The pre-
liminary investigation using a simple vehicle model
revealed that the effect of vehicle velocity on its
ballistic and blast survivability is secondary, at least
up to the vehicle velocities of 30 km/h.
4 SUMMARY AND CONCLUSIONS
Based on the results obtained in the present work,
the following main summary remarks and conclu-
sions can be made.
1. A preliminary computational investigation is
carried out of the performance of an up-
armoured HMMWV, firstly when, subjected to
Fig. 14 The effect of HMMWV up-armouring on the
propensity of the vehicle to reach the condi-
tion for incipient frontal rollover (i.e. the zero
rear-wheel normal load condition) during 30u
downhill braking. The vehicle prebraking
velocity was 30 km/h
Fig. 13 The effect of HMMWV up-armouring on the
braking distance under different braking-tor-
que conditions. The prebraking vehicle velo-
city was 30 km/h

the dynamic and impact loads associated with
detonation of a landmine buried under the
vehicle’s front-right wheel and, secondly, during
an off-road straight-line brake manoeuvre.
2. The same sand model, the CU–ARL sand model, is
used to model both the interactions of mine
detonation products and vehicle with sand in the
case of mine detonation analysis and the inter-
actions between the tyres and sand in the case of
the off-road vehicle performance analysis.
3. The results of the mine detonation analysis clearly
reveal that frequently used dynamic loading
functions can have serious short comings when
used as a substitute for the direct detonation
products–sand ejecta–vehicle interactions.
4. The off-road vehicle dynamics analysis clearly
revealed the effect of wheel sinkage in sand (and
the associated motion resistance) on the balance
between performance and mobility of the
HMMWV during severe manoeuvres such as
straight-line braking.
ACKNOWLEDGEMENTS
The material presented in this paper is based on
work supported by a research contract with the
Automotive Research Center (ARC) at the University
of Michigan and the US Army Tank–Automotive
Research, Development and Engineering Center
(TARDEC). In the course of conducting the work
presented in this manuscript, only the public-
domain data and information were used. No pro-
prietary, confidential, or classified data or informa-
tion was shared with Clemson University by either
the ARC or the TARDEC. Consequently and in
accordance with the ARC–TARDEC subcontract to
Clemson University, the work presented in this
manuscript is cleared for publication submission.
The authors are indebted to Professor Georges Fadel
for the support and continuing interest in the
present work.
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