2. LS-DYNA solver fundamentals for crashworthiness

Rear impact and whiplash simulation is a transient, highly nonlinear dynamic problem. The seat, head restraint, seat belt, and occupant interact over a time window of roughly 100–300 ms, with large rigid-body motion, rapid load transfer, and localized deformation in the seatback and recliner. LS-DYNA is built around exactly this class of problem, and three solver fundamentals determine whether a rear-impact model is trustworthy: the explicit time-integration scheme, the contact algorithms that transmit load between occupant and seat, and hourglass control for the reduced-integration shell and solid elements that dominate a seat model. This section explains what each mechanism does, how to configure it, and how to judge whether the result is physically meaningful.

Explicit Time Integration and the Stable Time Step

LS-DYNA's default explicit solver advances the solution with the central-difference method. For each node, acceleration is obtained from the assembled force balance, then velocity and displacement are updated:

a_n = M^-1 (F_ext - F_int)
v_(n+1/2) = v_(n-1/2) + a_n * dt
d_(n+1)   = d_n + v_(n+1/2) * dt

Because the mass matrix M is lumped (diagonal), no system of equations is solved and no global stiffness matrix is factorized. Each cycle is cheap, which is why explicit LS-DYNA scales well on many cores. The price is conditional stability: the time step must satisfy the Courant condition, and LS-DYNA computes a per-element limit

dt_e = L_c / c,   c = sqrt(E / rho)

where L_c is a characteristic element length and c is the acoustic wave speed. The global step is the minimum over all elements, scaled by a safety factor (default TSSFAC = 0.9 for solids and shells). A single small or badly distorted element therefore controls the cost of the entire run. In a seat model, typical offenders are thin trim shells, small recliner bracket solids, and foam elements compressed to near zero thickness.

Practical controls follow directly from this. First, check the initial step in the d3hsp file and identify the elements that set it; a step below about 0.5 µs usually indicates a modeling defect rather than a genuine requirement. Second, use *CONTROL_TIMESTEP with DTINIT only when you understand the consequence, and prefer mass scaling (DT2MS) over simply forcing a larger step. Mass scaling adds nonphysical mass to small elements; keep the added mass below roughly 1–2 % of the total model mass and verify it in the mass-scaling summary. Third, terminate the run with *CONTROL_TERMINATION set to the physical event duration plus a small margin, for example ENDTIM = 0.25 s for a 250 ms rear-impact pulse.

Contact Algorithms for Occupant–Seat Interaction

In a rear-impact model, load paths are almost entirely contact-driven: head-to-head-restraint, torso-to-seatback, pelvis-to-cushion, and belt-to-occupant. LS-DYNA offers several contact formulations, and choosing the wrong one is a common source of either penetration or spurious stiffness.

Three parameters deserve attention. SOFT (or SOFT = 1 on the optional card) activates a penalty formulation that is far more robust when materials have very different stiffnesses, such as rigid head form against soft foam. FS and FD are static and dynamic friction coefficients; for occupant–seat interfaces, values around FS = 0.3 and FD = 0.2 are a reasonable starting point, but they must be consistent with the trim material. DEPTH controls the search depth for surface-to-surface contact and should be increased when the mesh is coarse relative to the sliding distance.

Penetration is the most common contact failure. Check it with *DATABASE_BINARY_D3PLOT output and the contact penetration summary in glstat and sleout. If the head passes through the head restraint, the usual causes are an insufficient contact thickness on the shell, a slave surface that is too coarse, or a missing contact definition between the two parts. Increasing SST/MST thickness or refining the head-restraint surface is normally more effective than raising the penalty stiffness.

Hourglass Control

Seat structures are modeled predominantly with fully integrated shells or with reduced-integration (one-point) shells and solids. Reduced integration is fast but has zero-energy deformation modes called hourglass modes: the element distorts without storing strain energy, producing a characteristic checkerboard pattern. If uncontrolled, these modes grow and corrupt the response.

LS-DYNA provides several hourglass formulations through *HOURGLASS and the IHQ parameter on *CONTROL_HOURGLASS. Type 1 (standard viscous) is the default and is adequate for most crash models. Type 4 (stiffness-based, Flanagan–Belytschko) is often preferred for seat frames because it resists hourglassing more firmly at large deformation. Type 6 is a stiffness form with a physical basis and is a good choice when the model must also be accurate in low-speed or quasi-static loading.

Two coefficients matter. QM scales the hourglass viscosity or stiffness; the default is 0.1 for solids and 0.05 for shells. Raising QM suppresses hourglassing but adds artificial stiffness, which can make the seat appear stronger than it is. The correct workflow is to monitor the hourglass energy reported in glstat and matsum: it should stay below roughly 5 % of the internal energy. If it exceeds that, refine the mesh or switch to a stiffness-based formulation before increasing QM.

Putting the Three Fundamentals Together

The three mechanisms are coupled. A small time step often originates from an element that is also hourglassing; a contact that penetrates may be caused by a shell whose thickness was reduced to fix a time-step problem; excessive mass scaling changes the inertia of the head and therefore the whiplash response. A defensible rear-impact model is one in which the time step is set by genuine geometry, contact penetrations are within the allowed tolerance, and hourglass and added mass remain small. The diagram below summarizes how these checks relate to one another during a run.

In practice, a rear-impact analyst should establish these three checks as a routine before interpreting any occupant response. If the time step is stable, contact penetration is negligible, and hourglass and added mass are small, the kinematic output—head rotation, neck moment, and the resulting whiplash metrics—can be treated as a solver-consistent result. If any of the three checks fails, the occupant response is not yet a physical prediction, and the model must be corrected before the results are used for seat design or restraint tuning.