2. LS-DYNA fundamentals for crash simulation

Vehicle crash simulation in LS-DYNA is built on three tightly coupled pillars: an explicit time-integration solver that advances the equations of motion at very small time steps, a contact engine that prevents structures from passing through one another, and a library of material models that reproduce how metals, plastics, and foams deform and fail. Understanding how these three interact is what separates a model that merely runs from one that predicts realistic occupant and structural response.

Explicit Time Integration and the Critical Time Step

LS-DYNA's core solver uses the central-difference explicit method. Instead of solving a global stiffness matrix at every step, it computes nodal accelerations directly from the internal and external forces acting on each node:

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 matrix inversion is required, which makes each step extremely cheap. The trade-off is conditional stability: the time step must satisfy the Courant-Friedrichs-Lewy condition, and for a shell or solid element the critical step is approximately

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

where L_c is the characteristic element length, c is the speed of sound in the material, E is Young's modulus, and rho is density. A typical steel with E = 210 GPa and rho = 7.85e-9 tonne/mm^3 gives c ≈ 5170 mm/ms. For a 5 mm shell element, dt_crit ≈ 0.97 µs. A 100 ms frontal impact therefore needs on the order of 100,000 steps — this is why element size directly controls cost, and why a single tiny element can stall an entire job.

Mass scaling is the standard remedy. Adding mass to small elements raises dt_crit without changing geometry. The rule of thumb is to keep added mass below 1–2% of the total model mass; beyond that, inertia effects contaminate the physics. Selective mass scaling, invoked with *CONTROL_TIMESTEP and DT2MS negative, scales only elements below the target step.

Contact Algorithms

Crash models are dominated by self-contact: sheet metal folds onto itself, suspension parts collide, and occupants interact with restraints. LS-DYNA offers several contact formulations, and choosing the wrong one is a common source of penetration or instability.

Penalty-based contact is the default. A spring is placed between a slave node and the master segment; the force is proportional to penetration depth and a stiffness k derived from the segment's bulk modulus and area. If k is too soft, nodes tunnel through; if too stiff, the contact force drives the time step down or causes high-frequency noise. LS-DYNA scales k automatically, but you can tune it with SLSFAC and SOFT on the optional card.

Friction is defined by a coefficient of friction mu and, for rate-dependent surfaces, a static and dynamic pair. For steel-on-steel crash contact, mu = 0.1–0.15 is a reasonable starting point; for tire-to-road, mu = 0.8–0.9. The friction force is capped by the normal contact force, so a poorly converged normal force also corrupts friction.

Material Models for Vehicle Structures

Vehicle structures are predominantly mild steel, high-strength steel, aluminum, and engineering plastics. Each requires a model that captures yielding, hardening, strain-rate sensitivity, and failure.

*MAT_PLASTIC_KINEMATIC (MAT_003) is the workhorse for ductile metals. It combines isotropic and kinematic hardening via the parameter beta (0 = kinematic, 1 = isotropic) and includes Cowper-Symonds strain-rate scaling:

sigma_y = [1 + (eps_dot / C)^(1/p)] * (sigma_0 + beta * E_p * eps_p)

For a typical DP590 high-strength steel, representative values are sigma_0 = 380 MPa, E = 210 GPa, E_p = 1.2 GPa, C = 40 s^-1, p = 5. The strain-rate term can raise yield strength by 20–40% at the strain rates seen in a 50 km/h impact, which is why rate sensitivity cannot be ignored.

For aluminum extrusions and castings, *MAT_PLASTIC_KINEMATIC still works, but *MAT_JOHNSON_COOK (MAT_015) is preferred when temperature and large plastic strain matter. Its flow stress is

sigma = (A + B * eps_p^n) * (1 + C * ln(eps_dot*)) * (1 - T*^m)

with A the initial yield, B and n the hardening constants, and C the rate coefficient. For AA6061-T6, A = 324 MPa, B = 114 MPa, n = 0.42, C = 0.002.

Foams and honeycombs used in energy absorbers are modeled with *MAT_CRUSHABLE_FOAM (MAT_063) or *MAT_HONEYCOMB (MAT_026), which define a stress-versus-volumetric-strain curve. The plateau stress and densification strain determine how much energy the absorber can take before it bottoms out.

Failure is handled either by a plastic strain limit in the material card or by *MAT_ADD_EROSION, which deletes elements when a criterion such as equivalent plastic strain or pressure reaches a threshold. Deleting elements too early removes load paths and under-predicts intrusion; too late and elements distort into negative volume, aborting the run.

Putting the Three Pillars Together

A practical frontal-impact model illustrates the coupling. The bumper beam is meshed with 5 mm shells and assigned *MAT_PLASTIC_KINEMATIC with DP590 properties. The barrier is a rigid wall with *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE, SOFT = 1, and mu = 0.15. The crash box uses *MAT_ADD_EROSION with a plastic strain limit of 0.25 so that it can fold and then tear.

During the run, watch three quantities. First, the time step in d3hsp should stay near the target; a sudden drop means a contact penalty or a collapsing element. Second, the contact energy in glstat should be a small fraction of internal energy — large contact energy indicates over-stiff penalty or penetration. Third, the hourglass energy should stay below 5% of internal energy; if it grows, the shell formulation or mesh quality needs attention.

If the model terminates with a negative-volume error, the usual cause is an element that has compressed past its failure strain without being deleted. Reduce the erosion threshold, refine the mesh in the fold region, or switch to a fully integrated shell formulation. If the barrier shows penetration, verify that the slave side is the finer mesh and that SLSFAC is not set too low.