2. LS-DYNA explicit dynamics workflow for crashworthiness

An LS-DYNA crashworthiness model is not a single file but a hierarchy of keyword files assembled by the solver at runtime. Understanding that hierarchy, the stability limit that governs the explicit time step, and the mass-scaling techniques used to keep runtimes practical is the foundation for every bumper and crash box study that follows. This section walks through the input structure, the derivation of the critical time step, and the practical application of mass scaling with verifiable diagnostics.

Keyword Input Structure

LS-DYNA reads a deck composed of keyword blocks, each beginning with an asterisk. The solver processes them in a defined order: initialization, model definition, contact, boundary and loading, then control and termination. A typical crash box deck is organized as follows:

*KEYWORD
*INCLUDE
crashbox_mesh.k
bumper_beam_mesh.k
*INCLUDE
material_cards.k
*CONTROL_TERMINATION
       0.120
*CONTROL_TIMESTEP
  0.000000  0.900000  0.000000  0.000000  0.000000
*CONTROL_ENERGY
         2         2         2         2
*DATABASE_BINARY_D3PLOT
  0.002000
*DATABASE_GLSTAT
  0.000500
*DATABASE_MATSUM
  0.000500
*END

The *INCLUDE mechanism lets mesh, material, and control data live in separate files, which is essential when the same material library is reused across bumper variants. The *CONTROL_TERMINATION card sets the physical end time; for a 50 km/h frontal impact on a 400 mm crash box, 0.120 s is a reasonable termination time because the box strokes fully within roughly 60–80 ms and the remaining time captures rebound and residual deformation.

Contact definition is where most crashworthiness decks fail. For a crash box welded to a bumper beam and impacting a rigid wall, the standard combination is:

*CONTACT_AUTOMATIC_SINGLE_SURFACE
*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE
*RIGIDWALL_PLANAR

*CONTACT_AUTOMATIC_SINGLE_SURFACE handles self-contact of the folding box walls, while *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE manages the box-to-wall interface. The rigid wall is defined with a normal vector and a friction coefficient; for a steel-on-steel impact, a static friction of 0.15 and a dynamic friction of 0.10 are typical starting values.

Time Step Control

The explicit solver advances with a central-difference scheme whose stability is bounded by the Courant condition. The critical time step for a solid element is:

Δt_crit = L_c / c
c = sqrt(E / ρ)
L_c = V_e / A_max

where L_c is the characteristic length (element volume divided by the largest face area), c is the acoustic wave speed, E is Young's modulus, and ρ is density. For steel with E = 210 GPa and ρ = 7.85e-9 tonne/mm³, the wave speed is approximately 5.17 mm/µs. A crash box meshed with 5 mm solid elements therefore has a critical time step near 0.97 µs. With a 0.9 scale factor applied by *CONTROL_TIMESTEP, the solver uses about 0.87 µs.

The practical consequence is severe: a 0.120 s termination time at 0.87 µs requires roughly 138,000 cycles. If the smallest element in the model is 1 mm, the step drops to 0.19 µs and the cycle count exceeds 630,000. This is why mesh quality directly controls cost, and why a single sliver element can dominate the entire run.

Always check the initial time step report in d3hsp. LS-DYNA prints the smallest element, its part ID, and the resulting time step. If the reported step is far below your expectation, locate that element before adding mass scaling.

Mass Scaling

Mass scaling increases the density of small or stiff elements so their critical time step rises to a target value. The time step scales with the square root of density:

Δt_new / Δt_old = sqrt(ρ_new / ρ_old)

To raise a 0.19 µs step to 0.87 µs, density must increase by a factor of (0.87/0.19)² ≈ 21. That is a large penalty. Selective mass scaling, invoked through *CONTROL_TIMESTEP with DT2MS negative, adds mass only to elements below the target step:

*CONTROL_TIMESTEP
  0.000000 -8.700e-07  0.000000  0.000000  0.000000
                                     1         0

A negative DT2MS of -8.7e-7 s sets the target step to 0.87 µs. The final flag controls whether scaling is recalculated as the model deforms; setting it to 1 recomputes at each cycle, which is more accurate but slightly more expensive. The added mass fraction is reported in glstat as added mass and percent added mass.

Keep the added mass below 5% of the total model mass for crashworthiness correlation. Above that threshold, the inertial response of the structure changes enough to shift peak force and intrusion results. For a bumper beam weighing 8 kg, 5% is 0.4 kg — a hard budget when scaling many small elements.

Worked Example: Crash Box Deck

Consider a 350 mm long, 80 mm × 80 mm square crash box with 2.0 mm wall thickness, meshed with 4 mm shell elements and 5 mm solid elements at the welded flange. The flange solids are 1.5 mm thick, giving a critical step of about 0.29 µs. The shell field runs at 1.2 µs. Without scaling, the flange dictates the step.

Applying DT2MS = -8.0e-7 raises the flange step to 0.80 µs. The added mass is concentrated in the flange solids, which represent a small fraction of the total mass, so the global penalty stays near 1.8%. The run completes 150,000 cycles in approximately 4 hours on 16 cores. The glstat file confirms the added mass fraction, and matsum shows the internal energy plateauing at the end of stroke, indicating the box has fully folded.

LS-DYNA Crashworthiness Workflow: Input, Time Step, and Mass Scaling Keyword Input Structure *KEYWORD *INCLUDE (mesh, material) *CONTACT_AUTOMATIC_SINGLE_SURFACE *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE *RIGIDWALL_PLANAR *CONTROL_TERMINATION (0.120 s) *CONTROL_TIMESTEP *DATABASE_GLSTAT / MATSUM Time Step Control Δt_crit = L_c / c c = sqrt(E / ρ) L_c = V_e / A_max Steel: c ≈ 5.17 mm/µs 5 mm element → Δt ≈ 0.97 µs 1 mm element → Δt ≈ 0.19 µs Sliver elements dominate cost Mass Scaling Δt_new / Δt_old = sqrt(ρ_new / ρ_old) DT2MS = -8.7e-7 s (target step) Selective scaling on small elements Added mass reported in glstat Keep added mass < 5% total Recompute flag = 1 for accuracy Execution and Verification Chain Build deck (mesh + cards) Check d3hsp initial Δt Apply DT2MS selective scaling Run solver monitor glstat Verify added mass < 5% If added mass exceeds 5%, refine mesh or reduce DT2MS target before accepting results Check matsum internal energy plateau to confirm full stroke

Diagnostics and Failure Symptoms

Three files drive verification. d3hsp reports the initial time step and the controlling element. glstat reports added mass, total energy, and the ratio of kinetic to internal energy. matsum reports internal energy per material, which should plateau when the crash box has fully folded. If glstat shows added mass above 5%, the standard remedies are local mesh refinement at the flange, switching from solid to shell elements where thickness permits, or reducing the target step and accepting a longer run.

A common failure symptom is a sudden drop in time step mid-run. This usually means an element has inverted or distorted severely, reducing its characteristic length. LS-DYNA prints the new controlling element in d3hsp; locating it in the deformed geometry usually reveals a contact penetration or an unconstrained node. Adding *CONTROL_TIMESTEP with DT2MS recomputation and tightening the contact stiffness through *CONTACT optional card A (penalty scale factor) typically resolves it.

With the input hierarchy, stability limit, and mass-scaling budget under control, the model is ready for the material and section definitions that determine how the crash box actually absorbs energy — the subject of the next stage of the workflow.

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