4. Multibody occupant modeling

In MADYMO, a restrained occupant is not modeled as a deformable finite element mesh but as a multibody system: a set of rigid bodies connected by kinematic joints, wrapped in contact surfaces, and driven by the restraint system. This approach is computationally cheap, numerically stable, and well suited to the large rigid-body rotations that dominate occupant kinematics during a crash. The four building blocks — ellipsoids, joints, contact definitions, and kinematic chains — determine whether the model produces physically meaningful belt loading and body motion or degenerates into an articulated dummy that slides through its own seat belt.

Ellipsoids as the Occupant's Contact Geometry

Each body segment (head, thorax, pelvis, upper and lower extremities) is represented by one or more ellipsoids. An ellipsoid is defined by a semi-axis vector and a local coordinate system, and it serves two purposes: it defines the outer surface used for contact detection, and it carries the inertial properties (mass, center of gravity, moment of inertia) of the segment. Typical MADYMO ellipsoid definitions for a 50th-percentile male Hybrid III-like occupant are shown below. These values are illustrative and should be replaced with the actual dummy database values for production work.

BODY  Thorax
  MASS      17.2
  ELLIPSOID 1
    SEMIAXES   0.155  0.130  0.115
    POSITION   0.000  0.000  0.000
    ORIENTATION 0.0  0.0  0.0
  END
END

The semi-axes control how the belt wraps the torso. If the thorax ellipsoid is too narrow in the lateral direction, the shoulder belt will slide off the shoulder; if it is too wide, the belt will contact prematurely and generate unrealistically high chest deflection. A practical check is to compare the ellipsoid envelope against the dummy's published external dimensions and against the belt path observed in a sled test.

Joints: Constraining Relative Motion

Joints connect adjacent bodies and remove degrees of freedom. MADYMO supports revolute, spherical, translational, universal, and free joints, among others. For a restrained occupant, the most important joints are:

• Neck joint — typically a spherical or universal joint between head and thorax, with optional stiffness to represent neck bending resistance.
• Spine joints — revolute or spherical joints between thorax, abdomen, and pelvis, allowing controlled torso flexion.
• Shoulder and hip joints — spherical joints that let the arms and legs articulate independently of the torso.
• Knee and elbow joints — revolute joints with stops to prevent hyperextension.

Joint placement is critical. A neck joint positioned too far forward relative to the head center of gravity will produce excessive head rotation under belt loading. The joint location should be taken from the dummy's geometric database, not estimated visually.

Contact Definitions: Belt, Seat, and Body Interaction

Contacts in MADYMO are defined between ellipsoids and other surfaces (belt segments, seat cushion, airbag, steering wheel). Each contact requires a contact model (e.g., CONTACT_MB for multibody-to-multibody, CONTACT_MB_FE for multibody-to-FE) and a force-penetration characteristic. The characteristic is usually a loading/unloading curve that defines the normal force as a function of penetration depth.

CONTACT_MB  Belt_to_Thorax
  BODY1      Thorax
  BODY2      Belt_Segment_3
  CHARACTERISTIC  Belt_Thorax_Char
  FRICTION    0.3
END

Friction is not optional. A belt with zero friction will slide freely over the thorax and fail to engage the shoulder; a belt with excessive friction will lock in place and produce unrealistic chest compression. A coefficient of 0.3 is a common starting point for belt-to-clothing interaction, but it should be calibrated against sled test data.

Kinematic Chains for Restrained Occupants

A kinematic chain is the ordered sequence of bodies and joints from a fixed reference (usually the vehicle floor or seat frame) to the most distal segment. For a restrained occupant, the chain typically runs:

Vehicle floor → seat frame → pelvis → lumbar spine → thorax → neck → head, with branches to the upper extremities (shoulder → upper arm → elbow → forearm) and lower extremities (hip → thigh → knee → shank → foot).

The chain determines how forces propagate. When the belt loads the thorax, the force travels through the spine joints to the pelvis, which is anchored by the seat. If the pelvis is not properly constrained (e.g., the hip joint is too free or the seat contact is too soft), the occupant will submarine — sliding forward under the lap belt — and the thorax will rotate excessively. This is a kinematic chain problem, not a contact problem.

Building a Working Model: A Step-by-Step Example

Consider a frontal impact simulation with a belted 50th-percentile male occupant. The following sequence produces a stable, physically plausible model:

1. Define the kinematic chain from the seat frame to the head, using the dummy database for body masses, centers of gravity, and joint locations. Verify that the chain has no redundant degrees of freedom that would allow the torso to rotate freely about the vertical axis.
2. Assign ellipsoids to each body segment. Check that the ellipsoid semi-axes match the dummy's external dimensions and that adjacent ellipsoids do not overlap excessively, which would create artificial contact forces.
3. Define belt segments as a series of multibody elements or as an FE belt. For a multibody belt, each segment is a rigid body connected by revolute or spherical joints, with contact characteristics against the thorax, pelvis, and shoulder.
4. Set contact characteristics for belt-to-body, body-to-seat, and body-to-airbag (if present). Use loading/unloading curves with a slope that prevents penetration but does not introduce numerical stiffness.
5. Apply the crash pulse to the seat frame and run the simulation. Monitor belt forces, chest deflection, and head acceleration.

Verification and Troubleshooting

After the simulation, compare the model's response against physical test data or published corridors. Key indicators include:

If the model exhibits excessive penetration, reduce the time step or increase the contact characteristic slope. If the belt slides off the shoulder, adjust the shoulder belt anchor position or increase the friction coefficient. If the occupant rotates about the vertical axis, add a torsional stiffness to the lumbar joint or constrain the pelvis with a seat back contact.

The multibody approach in MADYMO is powerful precisely because it separates geometry (ellipsoids), constraints (joints), interaction (contacts), and topology (kinematic chains). When these four elements are correctly defined, the model captures the essential physics of a restrained occupant without the computational cost of a full FE dummy. The next step is to integrate this occupant model with the vehicle environment and the restraint system actuation.