4. Contact and impact modeling in MADYMO

In a multibody crash model, contacts are what turn a collection of rigid bodies into a physically meaningful collision. MADYMO offers several distinct contact formulations, and choosing the wrong one — or leaving the default penetration function in place where a measured stiffness curve is required — is one of the most common sources of non-physical results. This section explains the contact types available, how penetration-based force generation works, how friction is applied, and how energy absorption is controlled and verified.

Contact Types and When to Use Them

MADYMO distinguishes between multibody contacts (between rigid bodies or ellipsoids) and FE contacts (between finite element surfaces, or between an FE surface and a multibody ellipsoid/plane). The principal multibody contact types are:

• Ellipsoid–ellipsoid — the workhorse for occupant-to-interior contacts (head-to-instrument panel, knee-to-knee bolster). Each body is represented by one or more ellipsoids; the contact is evaluated between the closest points on the two surfaces.
• Ellipsoid–plane — used for ground contact, seat cushion planes, or any large flat surface. The plane is defined by a point and a normal vector.
• Ellipsoid–mesh (FE surface) — couples a multibody ellipsoid to a deformable FE structure, common when a dummy interacts with a detailed airbag or a deformable barrier.
• FE–FE — surface-to-surface contact between two finite element meshes, used for structural crush and self-contact.

The choice is driven by the geometry you actually need to resolve. If the contacting surface is essentially rigid and its shape can be approximated by an ellipsoid, a multibody contact is far cheaper and more stable. If the surface deforms significantly — an airbag, a crushable bumper — an FE contact is required because the contact pressure distribution depends on the deformation.

Penetration Functions: From Overlap to Force

All penetration-based contacts in MADYMO generate a force as a function of the penetration depth δ, defined as the overlap between the two contacting surfaces along the contact normal. The sign convention used throughout this course is: δ is positive when the surfaces overlap, and the resulting contact force acts along the contact normal to push the surfaces apart. The contact normal points from the master surface toward the slave surface.

The force–penetration relationship is defined by a penetration function. MADYMO supports several forms:

• Linear: F = k·δ, where k is a contact stiffness. Simple but rarely physical for occupant contacts.
• Nonlinear (power law): F = k·δⁿ, with n typically between 1.5 and 2.5. This captures the stiffening behavior of foam and sheet metal.
• Tabulated (piecewise linear): F is read from a user-supplied curve of force versus penetration. This is the most accurate option when you have measured or simulated stiffness data.
• Hysteresis / unloading: a separate unloading curve can be defined so that the contact dissipates energy on rebound, rather than returning all stored elastic energy.

For a head-to-instrument-panel contact, a typical tabulated curve might start at F = 0 N at δ = 0 mm, rise to 2.5 kN at δ = 15 mm, and reach 8 kN at δ = 40 mm. These values are illustrative and must be replaced with data from a component test or a validated FE submodel. The key point is that the curve shape — not just the peak force — governs the occupant deceleration pulse.

Two parameters deserve attention. First, contact thickness (or surface offset) defines the gap at which contact is detected; setting it too small causes the solver to miss the initial contact, while setting it too large produces a premature force. Second, the maximum penetration should be checked after every run: if the peak δ exceeds roughly 10–15% of the characteristic body dimension, the contact geometry is no longer valid and the force is likely overestimated.

Friction Modeling

Friction acts tangentially at the contact point and opposes relative sliding. MADYMO applies a Coulomb-type friction model, where the friction force is bounded by μ·F_n, with F_n the normal contact force and μ the friction coefficient. The tangential force is computed from the tangential relative velocity and a stick–slip formulation: below a small velocity threshold the surfaces stick, and above it they slide with force μ·F_n.

Friction coefficients are contact-pair specific. Representative values used in occupant simulations include:

These are starting estimates for a baseline model, not validated constants. Friction is often the least well-characterized input in a crash model, so a sensitivity study on μ is strongly recommended for any contact that controls occupant kinematics — particularly the pelvis-to-seat interface.

Energy Absorption and Verification

Energy absorption in a contact is governed by two mechanisms: plastic/structural deformation of the counter-surface (captured by the penetration function and, for FE, by material plasticity) and friction dissipation. In MADYMO the global energy balance is reported in the .rep or .kn3 output, and the contact energy is available as a separate term.

A useful verification workflow is:

1. Run the model and extract the contact force–penetration history for each critical contact.
2. Integrate the force over penetration to obtain the absorbed energy: E = ∫F dδ.
3. Compare the absorbed energy against the kinetic energy that must be dissipated by that contact. For a head impact at 25 km/h with a 4.5 kg head, the initial kinetic energy is approximately ½·4.5·(6.94)² ≈ 108 J. If the contact absorbs only 40 J before the head rebounds, the remaining energy is being stored elastically and returned — check whether the unloading curve is realistic.
4. Inspect the energy balance for negative or growing contact energy, which indicates penetration is not returning to zero or the contact is chattering.

The figure below summarizes how the contact type, penetration function, friction, and energy terms relate within a single contact evaluation.

The chain is evaluated at every time step: the contact type determines which geometric pair is tested, the penetration function converts overlap into normal force, friction adds the tangential component, and the resulting work appears in the energy balance. When a model produces an unexpectedly high head acceleration or a dummy that slides forward under the belt, the cause is usually traceable to one of these four elements — most often an over-stiff penetration function or an unrealistically low friction coefficient.

Practical Checklist for Contact Setup

• Define the contact normal direction explicitly and confirm it points from master to slave.
• Set contact thickness to a small positive value (e.g., 1–2 mm) rather than zero.
• Use tabulated penetration functions wherever measured stiffness data exist; document the source.
• Define an unloading curve for any contact expected to dissipate significant energy.
• Assign friction coefficients per contact pair and run a sensitivity study on the critical ones.
• After each run, check peak penetration, contact energy, and the global energy balance before accepting the result.

With the contact definitions in place, the next step is to validate that the forces and kinematics they produce match physical expectations — which is the subject of the validation workflow that follows in later chapters.