2. LS-DYNA explicit solver fundamentals for crash

Side impact simulation in LS-DYNA is built on the explicit central-difference method. Unlike implicit solvers that assemble and factorize a global stiffness matrix at every increment, the explicit solver advances the solution one small time step at a time using only nodal accelerations, velocities, and displacements. This makes each increment cheap and highly parallelizable, which is exactly what a full-vehicle side impact model with millions of elements requires. The trade-off is that the time step must remain below a stability limit, and controlling that limit — through mesh design, mass scaling, or both — is the central numerical discipline of crash modeling.

Explicit Time Integration in One Paragraph of Math

At the start of each cycle, LS-DYNA computes the internal and external nodal forces, subtracts them to obtain the residual force vector, and divides by the lumped nodal mass to get acceleration:

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

Here M is the diagonal (lumped) mass matrix, so no matrix inversion is needed — only element-wise division. The method is conditionally stable: the time step must satisfy the Courant–Friedrichs–Lewy condition, which for a one-dimensional bar reduces to dt ≤ L/c, where L is the element characteristic length and c is the wave speed. In three dimensions LS-DYNA applies a safety factor (default TSSFAC = 0.9) and computes the critical step from the smallest element in the model.

Stable Time Step and the Element That Controls It

For a shell element, the characteristic length is the shortest distance across the element, and the wave speed is c = sqrt(E / (ρ (1 - ν²))). A single 3 mm shell in mild steel (E = 210 GPa, ρ = 7.85e-9 t/mm³, ν = 0.3) gives c ≈ 5.2 mm/µs and a critical step near 0.9 × 3 / 5.2 ≈ 0.52 µs. A 1 mm element in the same material drops that to roughly 0.17 µs. Because the solver uses the global minimum, one tiny element anywhere in the model — a bolt hole, a spot-weld patch, a poorly meshed bracket — can force the entire simulation to run three times slower.

This is why mesh quality control matters more than almost any other modeling decision. Before running, check the minimum element size and the resulting time step in the LS-DYNA output:

d3hsp file:
  smallest time step = 1.73E-01 µs
  controlled by shell element 482913
  initial time step   = 1.56E-01 µs

If the reported step is far below what your mesh should produce, locate the controlling element and inspect it for sliver geometry, collapsed edges, or an unintended thin part.

Mass Scaling: When and How to Use It

Mass scaling increases the density of small elements so their stable time step rises to a target value. It is a legitimate and widely used technique, but it must be applied with discipline. The two common forms are:

• Fixed mass scaling (*CONTROL_TIMESTEP with DT2MS negative): scales only elements whose step is below the target, adding mass where needed.
• Selective mass scaling (*DATABASE_EXTENT_BINARY plus *CONTROL_TIMESTEP): applies scaling only to parts or materials that are not structurally critical, such as rigid fixtures or non-structural trim.

A practical target for a full-vehicle side impact model is a time step between 0.5 and 1.0 µs. If the natural step is 0.17 µs, scaling to 0.7 µs adds mass to the smallest elements. The added mass must be tracked: LS-DYNA reports the total added mass and the percentage of the original model mass. As a rule of thumb, keep added mass below 1–2% of the total model mass for a side impact, and never allow it to concentrate in the struck door or B-pillar, where it would artificially stiffen the structure and corrupt the intrusion prediction.

Energy Balance: The Primary Sanity Check

The explicit solver tracks kinetic energy, internal energy, hourglass energy, sliding interface energy, and external work. For a well-behaved crash model, the sum of these should remain close to the initial kinetic energy, with the difference attributable to numerical dissipation. The standard checks are:

In a side impact model, the moving deformable barrier (MDB) carries the initial kinetic energy. As it strikes the door, that energy transfers into internal energy of the door, B-pillar, rocker, and floor. If the kinetic energy does not drop as expected, or if internal energy plateaus early, the model may have a contact problem or an unconstrained part flying off. Plot the energy curves in LS-PrePost and look for a smooth, monotonic transfer.

Putting It Together: A Reproducible Check Sequence

Before committing to a long side impact run, execute this sequence on a coarse or sub-assembly model:

1. Run one cycle with *CONTROL_TERMINATION set to a small ENDTIM and inspect the d3hsp file for the initial time step and the controlling element.
2. If the step is below 0.5 µs, decide whether to refine the mesh locally, remove the offending element, or apply mass scaling. Document the choice.
3. Enable *DATABASE_BINARY_D3PLOT and *DATABASE_GLSTAT to capture energy history.
4. Run the full event and plot kinetic, internal, hourglass, and sliding energies in LS-PrePost.
5. If hourglass energy exceeds 5% of internal energy, switch the affected parts to fully integrated shells (ELFORM = 16) or refine the hourglass control.
6. If added mass exceeds 2%, reduce the mass scaling target or fix the underlying mesh problem.

Mastering these four fundamentals — explicit integration, stable time step, disciplined mass scaling, and energy balance verification — turns a side impact model from a black box into a predictable engineering tool. The next step is applying them to the specific contact and material definitions that govern how the door, B-pillar, and occupant interact.