2. MADYMO fundamentals

MADYMO is a hybrid solver: within a single simulation it couples a multibody (MB) system with an explicit finite element (FE) solver. Understanding which parts of an occupant-safety model belong to which solver — and how the two exchange data every time step — is the prerequisite for integrating MADYMO results with crash FE data. This chapter establishes that foundation: the two solver formulations, the dummy and restraint model families, and the output channels that later chapters will map, align, and fuse with LS-DYNA or PAM-CRASH results.

Two Solvers, One Time Loop

The multibody solver represents bodies as rigid bodies with mass and inertia, connected by kinematic joints (revolute, translational, spherical, universal, bracket, etc.) and force elements (springs, dampers, contact interactions, belts). Its state vector is small — typically a few dozen to a few hundred degrees of freedom — so it is fast and numerically robust. The FE solver uses the same explicit central-difference scheme as crash codes: nodal accelerations are computed from internal and external forces, then integrated to velocity and displacement. Its state vector can reach millions of DOF.

Coupling happens through support and contact interfaces. A multibody body can be attached to an FE node or node set via a SUPPORT definition, so the MB body inherits the FE motion; conversely, MB contact forces can be applied to FE surfaces through CONTACT_MB_FE. Both solvers advance with the same time step, which is governed by the smallest FE element and by the stiffest MB contact stiffness. A typical occupant model runs at 1–5 µs for FE-dominated cases and 10–50 µs for MB-dominated cases.

Dummy Models

MADYMO ships validated dummy model families that are themselves hybrid MB/FE assemblies. The most common in crash integration work are:

• Hybrid III 50th percentile male — the regulatory baseline for frontal impact (FMVSS 208, ECE R94). The MB version uses rigid segments with joints; the FE version refines the thorax, abdomen, and neck for belt-loading and rib-deflection studies.
• THOR 50th percentile — advanced frontal dummy with a more biofidelic thorax and abdomen, used for research and Euro NCAP front-row assessment.
• WorldSID 50th percentile male — side-impact dummy, typically positioned with the POSITION tool and coupled to door trim and side airbag FE meshes.
• Q-series (Q0, Q1, Q1.5, Q3, Q6, Q10) — child dummies for ECE R44/R129 and FMVSS 213.

Each dummy model exposes standard measurement channels at defined anatomical locations. For integration, the critical point is that these channels are defined in the dummy's local coordinate system, which is oriented by the initial positioning. If the crash FE model uses a different global origin or a different vehicle attitude, the dummy channels must be transformed before comparison — a topic developed in Chapter 6.

Restraint Systems

Restraint modeling in MADYMO spans both solvers:

• Seat belts — modeled with BELT definitions: a sequence of belt segments (MB) or membrane/1D FE elements, running through sliprings and retractors. The retractor can include a load limiter (force-limiting torsion bar) and a pretensioner. Belt-to-dummy contact uses CONTACT_BELT with a defined friction coefficient (typically 0.3–0.5).
• Airbags — modeled with the GASFLOW or AIRBAG (uniform-pressure) module. A gasflow airbag divides the bag into chambers connected by fabric porosity and vent holes; the uniform-pressure model is adequate for simple driver bags but insufficient for side bags or curtain bags with multiple chambers.
• Steering column and knee bolster — usually FE, with a defined collapse force or a full mesh.
• Seat and head restraint — MB for the frame, FE for the foam and trim where deformation matters.

Restraint timing is controlled by TIME_FUNC definitions: pretensioner firing, retractor lock, and airbag inflator mass-flow rate are all time functions. These must be synchronized with the crash pulse and with the FE vehicle model's event timing.

Output Channels Relevant to Integration

MADYMO writes results to *.xml (kinematics, forces, accelerations) and optionally to *.kn3 or *.ps for post-processing. The channels that matter for integration with crash FE data fall into four groups:

All channels are sampled at a user-defined output interval. For integration with crash FE data, the output interval must match or be resampled to the FE output interval (commonly 0.1–1 ms). Mismatched sampling is a frequent source of apparent phase error when comparing MADYMO and LS-DYNA curves.

Worked Example: A Frontal Sled Model

Consider a driver-side frontal sled model. The vehicle body is represented by a prescribed acceleration pulse applied to an FE floor and to the seat frame. The Hybrid III 50th MB dummy is positioned with the POSITION tool, a three-point belt with a 4 kN load limiter and 60 mm pretensioner is defined, and a driver airbag with a 150 kPa inflator is modeled with GASFLOW.

# Simplified MADYMO input structure (illustrative)
SYSTEM {
  FE_MODEL floor  { ... }
  MB_MODEL  dummy { ... }
  BELT      belt  { retractor: load_limit=4.0kN, pretension=60mm }
  AIRBAG    dab   { type=GASFLOW, inflator: mass_flow=TIME_FUNC }
}
CONTACT_MB_FE { dummy.surface, floor.surface, friction=0.4 }
SUPPORT { dummy.pelvis, floor.node_set }
OUTPUT { interval=0.5ms, channels=[head.acc, chest.def, belt.force] }

After the run, check three things before using the results: (1) hourglass energy below 5% of internal energy; (2) belt force at the retractor rises within 10–15 ms of the pretensioner firing; (3) head acceleration peak occurs after airbag contact, not before. If the head peaks before airbag contact, the dummy is too close to the steering wheel or the airbag timing is late. If belt force spikes without a pretensioner event, the retractor lock time is mis-set.

Practical Checks Before Integration

Before exporting MADYMO results for fusion with crash FE data, verify the following. First, confirm the dummy model version and its channel definitions match the test or the FE model's dummy. Second, confirm the output interval and the time origin — MADYMO time zero is the start of the simulation, which may not coincide with the FE model's time zero if the FE model includes a pre-crash phase. Third, confirm the coordinate system: MADYMO's default is a right-handed system with the vehicle forward direction along +X, but the FE model may use a different convention. Fourth, check that the support nodes and contact surfaces in the MADYMO model correspond to the same physical locations as the FE model's interface nodes. A mismatch here produces a constant offset in every integrated channel.

With these fundamentals in place — solver roles, dummy and restraint model families, output channel groups, and the pre-integration checks — the next step is to examine how crash FE data is structured and what it provides at the interface.