3. LS-DYNA solver basics for crashworthiness

Crashworthiness simulation with Anthropomorphic Test Devices (ATDs) sits at the intersection of three solver pillars: the explicit time integration scheme that advances the equations of motion, the contact algorithms that transmit impact loads between the dummy, restraint systems, and vehicle structure, and the material models that govern how each deformable component responds. A model can be geometrically perfect and still produce meaningless injury values if any one of these pillars is misconfigured. This section builds the working knowledge needed to set up, diagnose, and trust an LS-DYNA ATD impact model.

Explicit Time Integration: The Central Difference Engine

LS-DYNA's explicit solver advances the solution using the central difference method. At each time step, nodal accelerations are computed from the assembled force vector, then integrated to velocity and displacement. The scheme is conditionally stable: the time step must not exceed the Courant–Friedrichs–Lewy limit, approximated for a solid element as

dt_crit = L_c / c
c = sqrt(E / rho)          (elastic bar wave speed)
dt = TSSFAC * dt_crit      (TSSFAC default 0.9)

Here L_c is the characteristic element length, c the sound speed in the material, E the Young's modulus, and rho the density. For a typical ATD model, the smallest elements (often in the face, neck, or lumbar spine) dictate the global time step. A 2 mm element in polyurethane foam with E = 50 MPa and rho = 500 kg/m³ yields c ≈ 316 m/s and dt_crit ≈ 6.3 µs. A 100 ms simulation therefore requires roughly 16,000 steps — this is why mass scaling and element quality control matter so much.

Mass scaling is the standard remedy. Adding mass to small elements increases dt_crit without changing the physics of the dominant response, provided the added mass stays below a few percent of the total model mass. In LS-DYNA this is controlled by *CONTROL_TIMESTEP with DT2MS set to a negative value (e.g., -1.0e-6 for a 1 µs target). Always check the added-mass report in d3hsp; if the percentage exceeds 1–2%, the inertial loading on the ATD may be artificially altered.

Contact Algorithms: Where the Dummy Meets the World

Contact in LS-DYNA is penalty-based by default. When a slave node penetrates a master segment, a restoring force proportional to the penetration depth and the segment stiffness is applied. The two most relevant formulations for ATD work are *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE (STS) and *CONTACT_AUTOMATIC_SINGLE_SURFACE (SS).

STS is used when the dummy contacts a well-defined structure — the steering wheel, airbag, seat belt, or instrument panel. It requires careful definition of slave and master sides; the mesh on the slave side should be finer. SS is used for self-contact within the dummy (e.g., the arm folding against the torso) or for complex assemblies where the contact direction is not known a priori. For belt-to-dummy interaction, *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE with the belt as slave and the dummy as master is standard, combined with *MAT_SEATBELT or a shell-based belt model.

Key parameters to control:

• SOFT — set to 1 or 2 for soft materials (foam, flesh) to avoid excessive penetration; SOFT=2 is segment-based and generally more robust for ATD skin.
• FS and FD — static and dynamic friction coefficients. For dummy skin against fabric, typical values are FS = 0.3–0.5, FD = 0.2–0.4. For metal-to-metal, FS = 0.1–0.2.
• SST / MST — optional thickness offsets for shell contact; important when the dummy's shell elements represent a physical thickness.
• DEPTH — maximum penetration depth for penalty force scaling; leave default unless debugging.

Contact energy is a diagnostic gold mine. In the glstat file, the "contact energy" should remain a small fraction of the total energy. A sudden spike usually indicates a contact instability — often caused by initial penetration, missing segments, or an overly stiff penalty. Check the d3hsp file for "initial penetration" warnings and resolve them with *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE's IGNORE parameter or by adjusting the geometry.

Material Models for ATD Components

An ATD is a multi-material assembly. Each region demands a different constitutive law. The table below summarizes the models most commonly used in LS-DYNA dummy models and the parameters that dominate their response.

For the rib cage, *MAT_PLASTIC_KINEMATIC with a yield stress around 30–50 MPa (depending on rib bone properties) and a tangent modulus of 1–2 GPa is a reasonable starting point for a 50th percentile male ATD. The hardening parameter β = 0 gives isotropic hardening, β = 1 gives kinematic; for rib deflection under belt loading, β = 0.5–1.0 is often used to capture the Bauschinger effect.

Foam materials deserve special attention. *MAT_LOW_DENSITY_FOAM requires a uniaxial stress–strain curve that must be defined in compression only; LS-DYNA extrapolates for tension. The curve should be smooth and monotonic — sharp corners cause numerical noise. A typical polyurethane foam for an ATD chest pad might show 0.1 MPa at 10% strain, 0.5 MPa at 30%, and 2.0 MPa at 60%, with densification beyond 70%.

Putting It Together: A Minimal ATD Impact Setup

Consider a simplified sled test: a 50th percentile male ATD seated on a rigid seat, restrained by a three-point belt, subjected to a 50 km/h frontal deceleration pulse. The LS-DYNA deck would include:

*CONTROL_TIMESTEP
$  DTINIT   TSSFAC   DT2MS
   0.0      0.9      -1.0e-6
*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE
$  slave    master   SST      MST      FS       FD
   1        2        0.0      0.0      0.3      0.2
*MAT_PLASTIC_KINEMATIC
$  mid      rho      E        PR       SIGY     ETAN     BETA
   10       7.8e-9   210000   0.3      350.0    1200.0   0.5
*MAT_LOW_DENSITY_FOAM
$  mid      rho      E        PR
   20       5.0e-10  50.0     0.0
$  stress-strain curve follows

After the run, verify three things before trusting any injury number. First, check the energy balance in glstat: total energy should be conserved, hourglass energy below 5% of internal energy, and contact energy stable. Second, inspect the d3hsp file for warnings about initial penetration, negative volumes, or mass scaling. Third, plot the ATD's chest deflection and head acceleration against the physical test corridor if available. A model that matches the corridor within 10–15% is generally considered validated for that loading condition.

Common failure symptoms and their fixes: if the dummy "explodes" at the first contact, check for initial penetration or missing contact definitions. If the time step collapses mid-run, look for distorted elements in the foam or belt; consider *MAT_ADD_EROSION or mesh refinement. If injury values are unrealistically high, verify that the material curves are not too stiff and that the contact friction is not excessive.

The diagram above traces the data flow through an explicit ATD simulation. Inputs feed the central difference engine, which advances the solution while contact algorithms and material models update forces at each step. The feedback loop — energy balance and diagnostic checks — is what separates a run that merely completes from one whose injury numbers can be defended.

Practical Checklist Before Submitting an ATD Run

• Confirm the smallest element size and the resulting dt_crit; set DT2MS accordingly and verify added mass in d3hsp.
• Verify that every contact pair has a defined slave/master and that SOFT is set appropriately for foam and flesh.
• Check friction coefficients against physical test data or literature; do not leave defaults at zero.
• Ensure material curves are smooth, monotonic, and defined over the full strain range expected in the impact.
• Run a short (5–10 ms) initialization check to catch initial penetration and negative volumes before committing to a full 100 ms run.
• After the full run, plot energy histories and confirm hourglass and contact energy are within acceptable bounds.

These solver fundamentals — time step control, contact definition, and material selection — form the foundation on which every ATD injury prediction rests. Master them, and the rest of the modeling workflow becomes a matter of refinement rather than rescue.