2. MADYMO model architecture for occupants
Before any calibration activity can be planned, the analyst must understand what kind of numerical object is actually being calibrated. MADYMO occupant models are not a single homogeneous entity: they combine rigid multibody (MB) chains, finite element (FE) deformable structures, and contact definitions in one solver. The formulation chosen for each subsystem determines which parameters are physically meaningful, which are numerically sensitive, and which validation metrics can legitimately be compared against test data. This section establishes that mapping.
2.1 Two Model Families: Dummy and Human Body Models
MADYMO distinguishes between dummy models and human body models (HBM), and the distinction is not cosmetic.
Dummy models (e.g., Hybrid III 50th percentile male, ES-2re, SID-IIs, Q-series child dummies) are numerical representations of physical Anthropomorphic Test Devices. Their geometry, mass distribution, joint stiffness, and instrumentation locations are defined by regulation (FMVSS 208, ECE R94/R95, Euro NCAP protocols). Because the physical dummy is a calibrated artifact, the numerical dummy is calibrated to the dummy, not to human tissue. Typical calibration targets are:
- Head drop test: peak resultant acceleration and HIC window from a 376 mm drop onto a rigid plate.
- Neck pendulum test: flexion/extension moment–angle corridors at specified pendulum speeds.
- Chest deflection: sternum-to-spine displacement under a 23.6 kg chest impactor.
- Knee slider and femur/tibia force response under axial impact.
Human body models (e.g., THUMS, GHBMC, and MADYMO-compatible HBM variants) represent human anatomy. Their calibration targets are cadaveric and volunteer test data: rib cage force–deflection from belt loading, pelvic fracture tolerance, brain strain from cadaver head impact, and so on. The consequence for calibration is fundamental: a dummy model can be tuned to match a well-defined certification corridor, whereas an HBM must be tuned against scattered, specimen-dependent biological data with substantial inter-individual variation. HBM calibration therefore reports distributions and corridors rather than single curves.
2.2 Multibody and Finite Element Formulations
MADYMO's MB formulation treats bodies as rigid bodies connected by kinematic joints (revolute, translational, spherical, universal, bracket) with prescribed stiffness and damping characteristics. Degrees of freedom are small — typically 6 per body — and contact is handled through ellipsoid or plane contact models with penalty stiffness. The FE formulation discretizes deformable structures into shell, solid, beam, and membrane elements with a material model, and solves the resulting system with explicit time integration.
The two formulations are usually combined in one occupant model. A typical frontal-impact Hybrid III model uses:
| Subsystem | Formulation | Typical Calibration Parameters |
|---|---|---|
| Head | Rigid MB body + ellipsoid contact | Mass, inertia, contact stiffness, friction |
| Neck | MB chain (3–5 revolute joints) | Joint stiffness curves, damping, bump stops |
| Thorax | FE shell + solid (deformable) | Rib shell thickness, Young's modulus, yield stress, damping |
| Pelvis / femur | Rigid MB + force transducer | Joint stiffness, contact friction |
| Belt / airbag interaction | FE membrane + MB contact | Belt stiffness, airbag pressure–volume, permeability |
The calibration implication is that MB parameters are lumped and can often be tuned by direct curve matching, while FE parameters are distributed and interact through the mesh. Changing a single FE material modulus alters the global force–deflection path in a way that is not analytically separable from geometry and boundary conditions. This is why FE-dominated subsystems require design-of-experiments or optimization-based calibration rather than manual iteration.
2.3 Architecture Map and Calibration Coupling
The following diagram shows how the two formulations coexist in a single occupant model and where calibration effort concentrates.
2.4 Why Formulation Determines Calibration Strategy
The formulation choice propagates directly into how calibration is executed.
Parameter identifiability. In an MB neck model, the flexion moment–angle curve is governed by a small number of joint stiffness and damping coefficients. Each coefficient has a distinguishable effect on the response shape, so a least-squares fit over the corridor is well-posed. In an FE thorax model, chest deflection depends on rib geometry, cortical bone modulus, trabecular bone modulus, cartilage stiffness, and contact friction simultaneously. Several parameter combinations can produce nearly identical force–deflection curves, which is the classic non-identifiability problem. The practical remedy is to fix parameters that have strong literature backing (cortical bone modulus, for example) and calibrate only the parameters with genuine uncertainty.
Computational cost. An MB-only model runs in seconds to minutes. An FE-dominated model with a 5 mm rib mesh and 1 ms time step may run for hours. This changes the calibration workflow: MB models can be tuned interactively, while FE models require a surrogate model or a batch DOE. A common approach is to build a response surface over 20–50 FE runs, then optimize on the surrogate and verify the optimum with a full FE run.
Validation metric selection. MB models naturally output joint angles, accelerations, and contact forces — quantities directly comparable to dummy instrumentation. FE models output element stresses, strains, and section forces, which must be post-processed into comparable metrics (for example, integrating rib element forces into a chest deflection at the sternum). If the validation metric is not defined consistently with the formulation, the calibration will converge to a numerically good but physically meaningless solution.
2.5 A Practical Calibration Sequence
For a combined MB–FE occupant model, the following sequence avoids the most common failure mode: tuning FE parameters to compensate for an incorrectly calibrated MB chain.
- Isolate and calibrate MB subsystems first. Run the head drop, neck pendulum, and knee impact simulations as standalone models. Match peak acceleration, moment–angle corridors, and force peaks within the tolerance defined by the relevant regulation or protocol.
- Calibrate FE subsystems against component tests. For the thorax, use a rigid impactor against the isolated chest model. Adjust material parameters to match force–deflection and deflection–time histories. Record the parameter set and the residual error.
- Assemble and check the coupling. Verify that MB–FE constraints do not introduce artificial stiffness. A useful check is to run the assembled model with the FE part replaced by a rigid body of equivalent mass and confirm that the MB response is unchanged.
- Validate against full-system sled or vehicle tests. Only at this stage compare occupant kinematics and injury criteria against the full-scale test. If the full-system response deviates, diagnose whether the error originates in the MB chain, the FE subsystem, or the coupling — do not re-tune everything at once.
2.6 Key Takeaways
- Dummy models are calibrated to certification corridors; human body models are calibrated to biomechanical response distributions. The validation target dictates the model family.
- MB parameters are lumped and directly tunable; FE parameters are distributed and require DOE or optimization.
- The coupling layer between MB and FE domains is itself a calibration-relevant interface — verify it before tuning subsystem parameters.
- Calibrate in order: MB joints, then FE materials, then coupling, then full-system validation. Reversing this order produces non-physical parameter sets that do not transfer to new load cases.