2. Contact mechanics fundamentals for LS-DYNA

Contact in LS-DYNA is not a single algorithm but a family of penalty-, constraint-, and projection-based methods that decide, at every time step, whether two surfaces are touching, how hard they push apart, and how much tangential resistance they offer. Getting a high-fidelity impact model right depends far less on the solver's default settings than on understanding four coupled mechanisms: normal contact force generation, friction transfer, penetration control, and the energy bookkeeping that tells you whether the contact treatment is physically consistent. This section builds that understanding from the mechanics up, then connects each concept to concrete LS-DYNA keywords and diagnostics.

Normal contact: penalty stiffness and the force–penetration relation

LS-DYNA's default penalty contact treats penetration as a spring compression. When a slave node passes a master segment, the solver computes the penetration depth δ along the segment normal and applies a restoring force

F_n = k · δ        (linear penalty)
k   = SFS · K_master · A_master / V_master   (solid elements)
k   = SFS · K · A / l                        (shell segments)

Here SFS is the scale factor for the penalty stiffness (default 0.10 for *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE), K is the bulk modulus of the master material, A is the segment area, and l is a characteristic length. The key engineering consequence is that penetration is not zero in penalty contact — it is inversely proportional to stiffness. Doubling SFS halves the penetration but also halves the stable time step, because the contact spring adds to the system's highest frequency. A practical starting point is SFS = 0.1 for metal-on-metal impact and SFS = 1.0 for soft materials such as foam or rubber, where the master stiffness is low and larger penetrations are tolerable.

Two normal-direction quantities must be distinguished. The contact normal force is what the solver applies; the contact pressure is that force divided by the contributing segment area. For a rigid impactor striking a deformable plate, the peak pressure typically occurs within the first few microseconds and is strongly mesh-dependent — refining the master surface concentrates the same force onto smaller segments and raises the reported pressure. This is why pressure-based failure criteria must be paired with a mesh convergence study, not read from a single run.

Friction: Coulomb transfer and the role of the normal force

LS-DYNA implements Coulomb friction through a tangential penalty spring. The trial tangential force is F_t^trial = k_t · Δs, where Δs is the incremental tangential slip. If |F_t^trial| ≤ μ · F_n, the contact sticks and the spring force is applied. If the trial force exceeds the friction cap, the node slips and the tangential force is limited to μ · F_n. This coupling is critical: friction force scales with normal force, so any error in penalty stiffness propagates directly into the friction response.

For *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE, friction is activated with FS (static) and FD (dynamic) coefficients on the optional card. A common mistake is setting FS = FD = 0.3 and assuming the model is "frictional." In practice, the friction coefficient should reflect the interface condition: lubricated steel-on-steel is 0.05–0.10, dry steel-on-steel is 0.15–0.30, and rubber-on-concrete can exceed 0.8. The viscous friction coefficient DC adds a velocity-dependent term μ_eff = FD + DC · |v_rel|, which is useful for suppressing high-frequency tangential chatter but must be kept small (typically DC < 0.01) to avoid nonphysical damping.

Penetration: detection, control, and the cost of getting it wrong

Penetration in LS-DYNA arises from three sources: (1) the inherent compliance of penalty contact, (2) insufficient contact thickness for shell elements, and (3) nodes passing entirely through a master segment between time steps — the classic "tunneling" failure. The first is physical and acceptable; the second and third are numerical defects.

Shell contact thickness is controlled by SST and MST (slave and master thickness scale factors) plus the optional THKOPT flag. For thin shells under impact, setting SST = MST = 1.0 with THKOPT = 1 uses the actual element thickness, which is usually correct. For rigid walls, the geometric thickness may be zero, so a nonzero MST is required. Tunneling is mitigated by *CONTROL_TIMESTEP with DTMIN and by the automatic contact's internal segment-based sorting, but the most reliable fix is to keep the time step below the time for a slave node to traverse a master segment:

Δt_crit ≈ l_segment / (2 · c)   where c = sqrt(E/ρ)

If the computed stable time step exceeds this, reduce TSSFAC or refine the master mesh. A useful diagnostic is the rcforc file, which reports contact force history per interface; a sudden spike followed by zero force often indicates a node has tunneled and the interface has lost contact.

Energy balance: the audit that validates the whole model

LS-DYNA's glstat file provides the energy audit. For a closed system, the sum of kinetic, internal, and contact energies should equal the initial energy plus external work, minus any hourglass and damping losses. The critical ratios to monitor are:

Contact energy in LS-DYNA is the work done by penalty springs, both normal and tangential. It is not a physical energy sink — it is stored and released as the surfaces separate. A model that shows contact energy growing monotonically without recovery is usually over-penetrated or has an excessively stiff penalty. The recommended workflow is to run a short 10–20 μs initialization, confirm that hourglass and sliding energy are below the thresholds above, then extend to the full event duration.

Putting the four mechanisms together

The four mechanisms are not independent. Penalty stiffness sets the normal force; normal force caps the friction force; penetration depth is the visible symptom of penalty stiffness; and contact energy is the integral of both normal and tangential work. A change in SFS therefore propagates through all four. The diagram below shows this coupling as a signal chain from geometric detection through force generation to the energy audit, with the key LS-DYNA controls annotated at each stage.

The feedback loop in the diagram is the part most analysts miss. When the energy audit shows excessive sliding energy, the instinct is to reduce friction. But sliding energy is also proportional to penalty stiffness, so the correct first action is often to lower SFS and re-check penetration, not to change FS. Conversely, if penetration is unacceptably large but energy is clean, raising SFS is appropriate — provided the time step is reduced accordingly. Treating the four mechanisms as a coupled system, rather than four independent knobs, is what separates a converged impact model from one that merely runs to termination.