📚 Course ContentsChapter 4 Model initialization and boundary conditions

4. Model initialization and boundary conditions

In MADYMO occupant simulations, the quality of a result is decided long before the solver integrates the first time step. Positioning, initial velocities, gravity, and contact definitions form the initialization state of the model, and any inconsistency in these inputs propagates through the entire event. This chapter examines how each initialization parameter is defined, how it interacts with the rest of the model, and why disciplined boundary-condition management is the foundation of repeatable occupant simulations.

Positioning: The Reference State of the Occupant

Positioning defines the occupant's spatial relationship to the vehicle interior at time zero. In MADYMO, this is expressed through the initial position and orientation of the multibody or facet occupant relative to the vehicle reference frame. The standard convention is a right-handed coordinate system with the origin typically at the vehicle centerline, X forward, Y lateral, and Z upward. All joint angles, belt routing, and contact gaps are measured from this reference state, so a positioning error shifts every downstream result.

For a Hybrid III 50th percentile male occupant, a typical driver position places the H-point at a defined seat reference point with the torso reclined approximately 22–25° from vertical and the knees flexed near 90°. These values are not arbitrary; they follow the seating posture defined by the vehicle geometry and the restraint system layout. When positioning a MADYMO occupant, the practical sequence is:

Place the occupant pelvis at the seat reference point using the seat cushion and backrest surfaces as geometric constraints.
Adjust torso and neck angles so the head rests in a natural posture relative to the head restraint.
Set limb joint angles to match the target posture, then verify that no body segment penetrates the seat, floor, or trim surfaces.
Route the seat belt across the occupant and confirm the belt-to-body gap is within the intended tolerance.

Penetration at initialization is a common and damaging error. If the occupant's back penetrates the seat backrest by even a few millimeters, the contact solver will apply a large corrective force in the first time step, producing a spurious acceleration spike that contaminates the entire response. The same applies to belt routing: a belt that starts embedded in the chest will generate an artificial load path. Always run a zero-velocity, gravity-only settling simulation before the full event to confirm the model is in equilibrium.

Initial Velocities and Gravity

Initial velocity defines the occupant's motion state at time zero. In a frontal impact simulation, the occupant and vehicle are typically given an initial velocity equal to the impact speed, or the occupant is held stationary while the vehicle decelerates through a prescribed pulse. The choice depends on the reference frame: an inertial (fixed) frame requires the occupant to carry the initial velocity, while a vehicle-fixed frame applies the crash pulse as a boundary acceleration.

Gravity is defined as a constant acceleration vector, conventionally −9.81 m/s² along the Z axis. Gravity matters most during the pre-impact settling phase and for low-speed or rollover scenarios. In a high-severity frontal impact, gravity is negligible compared to the crash pulse, but it still influences the initial contact state between the occupant and the seat. A model that ignores gravity during settling may show the occupant floating slightly above the cushion, creating an artificial gap that closes abruptly once the pulse begins.

Define gravity and initial velocity in the same reference frame. Mixing an inertial-frame velocity with a vehicle-fixed gravity vector is a frequent source of non-physical initial motion.

Contact Definitions and Their Role in Repeatability

Contact definitions determine how the occupant interacts with the seat, belt, airbag, steering wheel, and floor. In MADYMO, contacts are defined between contact bodies (facets or ellipsoids) with a specified contact characteristic: a force-penetration curve, a friction coefficient, and a contact thickness. The contact stiffness and friction coefficient directly control how load is transferred, so they must be consistent across every run of a validation matrix.

Repeatability is the ability to reproduce the same result from the same input. It is not the same as accuracy, but without repeatability, accuracy cannot be assessed. The initialization parameters that most strongly affect repeatability are:

Parameter	Typical Sensitivity	Repeatability Risk
Occupant position (H-point)	High — shifts belt and contact geometry	Manual repositioning between runs
Joint angles	Medium — affects limb contact timing	Inconsistent posture targets
Initial velocity	High — scales entire response	Frame mismatch or unit errors
Gravity vector	Low in high-severity, high in settling	Omitted or misdirected
Contact stiffness	High — controls force-penetration slope	Different curves per run
Friction coefficient	Medium — affects belt slip and sliding	Unspecified or defaulted

The practical discipline is to freeze all initialization parameters in a single input deck or parameter file, and to change only the variable under study between runs. If positioning is adjusted manually for each run, the resulting scatter will be indistinguishable from the physical effect being investigated.

Worked Example: Settling Check for a Driver Model

Consider a MADYMO driver model with a Hybrid III 50th percentile occupant, a belt system, and a driver airbag. Before running the 50 km/h frontal impact, perform a settling simulation with the following setup:

# Settling phase configuration (example values)
gravity        = (0, 0, -9.81)   # m/s^2, vehicle-fixed frame
initial_velocity = (0, 0, 0)     # m/s, occupant at rest
duration       = 0.050           # s, settling only
time_step      = 1.0e-5          # s
contact_damping = 0.1            # critical damping fraction
belt_preload   = 50              # N, initial belt tension

Run the settling phase and inspect three outputs: the occupant's pelvis Z displacement, the maximum contact penetration, and the belt tension. A well-initialized model shows the pelvis settling by less than 2 mm, contact penetration below 1 mm, and belt tension stabilizing near the preload value. If the pelvis oscillates or the penetration exceeds a few millimeters, the initial position is inconsistent with the contact geometry and must be corrected before the impact run.

Do not skip the settling phase. A model that is not in equilibrium at time zero will produce an initial transient that can be mistaken for a physical response, especially in low-severity or out-of-position studies.

Effect on Repeatability

Repeatability in occupant simulation is achieved when the same input produces the same output within numerical tolerance. The initialization parameters are the largest controllable source of run-to-run variation. Three practices make the difference:

Parameterize everything. Store position, velocity, gravity, and contact properties in a single parameter file so that no value is hard-coded in multiple places.
Verify equilibrium before the event. Always run a settling phase and confirm that the model is stable before applying the crash pulse.
Document the reference frame. State explicitly whether the model is inertial or vehicle-fixed, and confirm that velocity, gravity, and contact definitions all use that frame.

When these practices are followed, the scatter between repeated runs of the same configuration typically falls within a few percent for peak occupant accelerations and displacements. When they are ignored, scatter can exceed 20%, making it impossible to distinguish a genuine design change from initialization noise. The next chapter builds on this foundation by examining how the validated initialization state is used to construct the loading and restraint boundary conditions of the full event.