2. Restraint system architecture

A MADYMO occupant model is only as credible as the restraint hardware it represents. Before any sled run or design-of-experiments sweep, the analyst must translate the physical restraint system — belts, retractors, pretensioners, load limiters, airbags, and the surrounding occupant packaging — into a consistent set of FE/multibody definitions. This section describes how those components are structured in MADYMO, how they interact, and which packaging constraints govern their placement.

Belt System Topology

In MADYMO, a seat belt is built from a BELT system containing one or more BELT_SEGMENT definitions. Each segment is a chain of belt elements connected to a retractor, an anchor, or a buckle. The three-point belt is normally split into a shoulder (diagonal) segment and a lap segment, joined at the buckle point. The belt is defined in the FE domain using membrane elements with a user-supplied force–strain curve, or in the multibody domain using discrete belt elements with a stiffness function. For occupant safety work, the FE belt is preferred because it captures belt-to-occupant contact pressure and slip.

Key inputs for each belt segment include the initial routing (node coordinates), the retractor type, the pretensioner stroke, and the load limiter force level. The belt must be routed so that it lies on the occupant surface with a small initial penetration or gap; excessive initial slack produces a delayed belt engagement and unrealistic chest deflection.

Pretensioners and Load Limiters

A pretensioner is modeled as a retractor with a prescribed pull-in stroke, typically 40–80 mm for a buckle pretensioner and 60–120 mm for a retractor pretensioner. In MADYMO this is implemented through a RETRACTOR with a time-dependent belt length function or a PRETENSIONER element that removes slack over a defined time window (commonly 10–20 ms). The pretensioner reduces belt slack and couples the occupant to the restraint earlier, lowering chest deflection and reducing submarining risk.

The load limiter is a force-limiting element in the retractor or belt path. It is defined by a force–displacement curve, for example a plateau at 3.5–4.5 kN for a front passenger. In MADYMO the load limiter is represented as a FORCE_LIMITER or as a belt element with a plastic plateau in its force–strain characteristic. The interaction between pretensioner timing and load limiter level is critical: a pretensioner that fires too late, or a load limiter set too high, will produce excessive chest deflection; too low a limit allows excessive forward excursion and possible contact with the instrument panel.

Airbag Modeling

Airbags in MADYMO are modeled with the AIRBAG module, which uses a control-volume (CV) or finite-volume (FV) approach. The CV method computes internal pressure from the ideal gas law using the inflator mass flow rate and the bag volume; the FV method divides the bag into chambers for more accurate pressure distribution. For passenger frontal airbags, the CV approach is usually sufficient and computationally cheaper.

Required inputs include the inflator mass flow curve (from tank tests), the bag geometry (unfolded and folded), vent hole area, and fabric permeability. The bag must be positioned relative to the instrument panel and the occupant's head and chest. A common error is an airbag that is too far from the occupant, which delays head contact and increases neck injury metrics; too close, and the bag may not fully deploy before contact, causing high head acceleration.

Occupant Packaging Constraints

Packaging defines the geometric relationship between the occupant, the seat, the belt anchors, and the airbag. In MADYMO, the occupant is positioned using the OCCUPANT module with a specified H-point, torso angle, and limb positions. The belt anchors and airbag module are then placed relative to this occupant. Critical packaging parameters include:

• Seat belt anchor positions: The shoulder anchor should be at or above shoulder height to avoid neck loading; the buckle anchor should be low and inboard to keep the lap belt on the pelvis.
• Airbag module location: Typically in the instrument panel, with the bag centerline aimed at the occupant's chest.
• Steering wheel and column: For driver models, the column angle and wheel position affect bag deployment and belt routing.
• Seat back angle: A reclined seat changes belt geometry and increases submarining risk.

These constraints are not independent. Moving the seat rearward changes the belt anchor distance, the airbag standoff, and the occupant's interaction with the knee bolster. MADYMO allows parametric studies where these positions are varied to find a robust configuration.

Coupling and Initialization

Once the components are defined, they must be coupled. The belt is connected to the occupant via contact; the airbag is connected to the occupant via contact and to the vehicle via a prescribed motion or fixed position. MADYMO requires an initialization step where the belt is pre-stressed to remove slack and the airbag is folded. The INITIAL keyword or the BELT_INITIALIZATION option is used to settle the belt onto the occupant before the simulation starts. Skipping this step often leads to an initial pressure spike or belt slip that corrupts the early response.

Time step and contact stiffness also matter. A belt modeled with too high a contact stiffness can cause numerical instability; too low, and the belt penetrates the occupant. Typical belt contact stiffness is 50–100 N/mm per element, with a friction coefficient of 0.3–0.5 between belt and clothing.

Verification Checks

Before trusting any result, verify the following in the MADYMO output:

• Belt force–time history: should show a rapid rise during pretensioning, then a plateau at the load limiter level.
• Airbag pressure–time history: should peak within 30–50 ms and then decay through vents.
• Occupant kinematics: head and chest should contact the bag, not the instrument panel; lap belt should remain on the pelvis.
• Energy balance: total energy should be conserved within 5%.

With the architecture correctly defined, the model becomes a reliable platform for parametric studies — varying pretensioner timing, load limiter level, and airbag standoff to meet injury criteria such as HIC, chest deflection, and femur load. The next step is to populate the model with validated material data and run the baseline simulation.