3. LS-DYNA explicit dynamics fundamentals for crash simulation

Vehicle body-in-white (BIW) crashworthiness simulation is dominated by LS-DYNA's explicit dynamics solver, and understanding why explicit integration is used—and what it demands of the model—is the foundation for every subsequent optimization decision. This section covers the four pillars that determine whether a crash model runs stably and produces trustworthy results: time integration, contact algorithms, hourglass control, and stability (time step).

3.1 Why Explicit Time Integration

A frontal impact event lasts roughly 80–150 ms, but the physical response contains high-frequency content driven by shell buckling, spot-weld rupture, and contact chatter. The semi-discrete equation of motion is:

M·a + C·v + F_int(u) = F_ext

In the explicit central-difference scheme, the mass matrix M is lumped (diagonal), so no matrix inversion or factorization is required. Velocities and displacements are advanced as:

v_(n+1/2) = v_(n-1/2) + a_n · Δt
u_(n+1)   = u_n + v_(n+1/2) · Δt

This is conditionally stable: the time step must not exceed the Courant limit. The trade-off is that the step size is tiny (typically 0.5–1.5 µs for BIW meshes), but each step is extremely cheap. For a 100 ms event, that means 10⁵–10⁶ steps—acceptable because no global stiffness matrix is ever assembled or solved.

3.2 Contact Algorithms

Contact is the single largest source of both realism and instability in crash models. LS-DYNA offers penalty-based, kinematic, and tied formulations. For BIW self-contact during folding, *CONTACT_AUTOMATIC_SINGLE_SURFACE is the workhorse: it detects penetration of any segment against any other segment in the same part set, which is essential when a rail folds onto itself and the contact pair is not known a priori.

Key parameters and their practical meaning:

• SOFT — penalty stiffness formulation. SOFT = 1 (soft constraint) is recommended for shell-to-shell contact because it scales stiffness with nodal mass and time step, reducing spurious high-frequency noise.
• FS / FD — static and dynamic friction coefficients. For lubricated steel-on-steel sliding, FS = 0.1–0.15; for painted BIW surfaces, FS = 0.2–0.3 is a reasonable starting point.
• SST / MST — optional thickness offsets for shell contact. Set SST = MST = 1 when shell mid-surfaces are offset from the physical surface, otherwise the effective gap is wrong by half the thickness.
• DEPTH — search depth for initial penetration. A value of 2–5 is typical; too small misses deep initial penetrations, too large wastes CPU.

For spot welds, *CONTACT_SPOTWELD or tied contact with a failure criterion (e.g., NFLF, SFLF for normal and shear force limits) governs when the joint releases. A common mistake is to leave the weld tied indefinitely, which artificially stiffens the joint and under-predicts separation.

3.3 Hourglass Control

Reduced-integration shell and solid elements are used for speed, but they have zero-energy deformation modes called hourglass modes. If uncontrolled, these modes grow and pollute the solution with a characteristic checkerboard pattern. LS-DYNA provides several hourglass control types via *HOURGLASS or the IHQ parameter on the part/control card:

The hourglass energy should be monitored in glstat. A widely used acceptance criterion is that hourglass energy must remain below 5% of the total internal energy; above 10% the result is suspect. If hourglass energy is excessive, refine the mesh locally, switch to type 4 or 6, or increase the hourglass coefficient QM (default 0.1 for shells).

3.4 Stability and Time Step Control

The critical time step for a shell element is approximately:

Δt_crit = L_s / c,   c = sqrt(E / (ρ · (1 - ν²)))

where L_s is the characteristic element length and c is the wave speed. For steel with E = 210 GPa, ρ = 7.85e-9 t/mm³, ν = 0.3, the wave speed is about 5.0 mm/µs. A 5 mm element therefore gives Δt_crit ≈ 1.0 µs.

Two mechanisms control the actual step:

1. Mass scaling (*CONTROL_TIMESTEP, DT2MS): adds mass to small elements to raise their critical step. Use it sparingly—added mass changes inertia and can mask real behavior. A target of 1–5% added mass is acceptable; check glstat for the "added mass" percentage.
2. Selective mass scaling (*CONTROL_TIMESTEP with DT2MS < 0): applies scaling only to elements below the target step, preserving the rest of the model. This is the preferred approach for BIW models with a few tiny elements around holes and flanges.

3.5 Putting It Together: A Minimal Stable BIW Setup

Consider a 200 mm long, 1.2 mm thick steel rail modeled with 5 mm shells. The natural step is ~1.0 µs. If a 0.8 mm flange element exists, its step drops to ~0.16 µs, forcing the whole model to that step. Applying selective mass scaling with DT2MS = -1.0e-6 raises the flange element's step to 1.0 µs while adding negligible mass elsewhere. The result is a 6× speedup with no measurable change in the force-displacement curve.

After the run, verify three things in glstat: (1) added mass < 5%, (2) hourglass energy < 5% of internal energy, and (3) no "out-of-range" or "negative volume" messages in d3hsp. If any fails, revisit the contact definition, hourglass type, or mass scaling before trusting the result.

The diagram above summarizes the closed loop: explicit integration advances the solution, contact and hourglass control shape the internal forces, the time step is governed by the smallest element, and the post-run energy checks tell you whether the result is trustworthy. In practice, a BIW crash model with 1–2 million elements will run 100 ms of physical time in 4–12 hours on 32–64 cores, provided the stability and contact settings are correct. The next section builds on this foundation by examining material models and failure criteria that define how BIW components absorb energy.