📚 Course ContentsChapter 4 Mass scaling in LS-DYNA

4. Mass scaling in LS-DYNA

Mass scaling is the most widely used—and most frequently misused—technique for controlling the critical time step in an explicit LS-DYNA analysis. The idea is deceptively simple: since the stable time step of a solid element scales with the square root of density, artificially increasing the density of the smallest, stiffest elements raises their stable step and lets the whole model advance with a larger Δt. The engineering question is never "can I scale mass?" but "how much mass can I add before the inertia I have fabricated corrupts the physics I am trying to capture?" This chapter develops the mechanics behind that trade-off, contrasts global and selective scaling, and shows how to read the added-mass ratio as a quantitative accuracy gate.

Why the time step is governed by the smallest element

For a one-point-integrated solid element, the Courant condition gives the stable step as

Δt_crit = L_e / c,   c = sqrt(E / ρ)

where L_e is a characteristic element length and c is the dilatational wave speed. Because c depends on ρ through a square root, doubling the density of an element increases its stable step by only a factor of √2 ≈ 1.414. Conversely, a single sliver element with L_e one-tenth of the nominal mesh size drags the global step down by an order of magnitude, forcing every other element in the model to march at that crippled rate. This is the classic "one bad element ruins the run" scenario, and it is precisely what mass scaling is designed to neutralize.

LS-DYNA computes the time step from the minimum over all elements (and, for shells, from the in-plane and transverse wave speeds). The *CONTROL_TIMESTEP card exposes the key switches: DTINIT (initial step), TSSFAC (time-step safety factor, default 0.9 for solids), and DT2MS, the mass-scaling time step. When DT2MS is negative, LS-DYNA performs selective mass scaling: only elements whose stable step is below |DT2MS| receive added mass, and only enough to bring them up to that target. When DT2MS is positive, the code applies global scaling, adding mass to every element so that the entire model reaches the target step.

Selective versus global scaling

Selective scaling is almost always the correct default. It confines the artificial inertia to the small fraction of elements that actually limit the step, leaving the bulk of the mesh—where most of the kinetic energy and deformation reside—untouched. In a typical automotive crash model, perhaps 0.5–2% of elements fall below the target step; scaling only those elements adds a negligible amount of mass to the system while recovering most of the step. Global scaling, by contrast, inflates the density of every element, including the large, well-shaped elements in the occupant compartment or the rigid barrier, and can add tens of percent of spurious mass to the model.

The practical consequence is that global scaling is appropriate only when the mesh is uniformly fine and the target step is close to the natural step—for example, a fine-mesh metal forming simulation where every element is roughly the same size. In crashworthiness, blast, and impact work, selective scaling with a negative DT2MS is the standard practice. A representative card looks like this:

*CONTROL_TIMESTEP
$#  dtinit    tssfac      isdo    tslimt     dt2ms      lctm     erode     ms1st
         0       0.9         0         0    -1.0E-6         0         0         0

Here DT2MS = -1.0E-6 s tells LS-DYNA to scale only those elements whose stable step is below 1 µs, bringing them up to 1 µs. The MS1ST flag controls whether scaling is recomputed as the mesh deforms; setting MS1ST = 1 freezes the scaling at the initial configuration, which is often preferable because it avoids the step changing mid-run as elements compress.

The added-mass ratio as an accuracy gate

Every mass-scaling run must be audited with the added-mass ratio, reported in the d3hsp file and in the ASCII glstat output as added mass and % added mass. The ratio is the total artificial mass divided by the original model mass. The widely used engineering rule of thumb is to keep the added mass below 5% for crash and impact problems, and below 1–2% when the response is dominated by high-frequency content or when the model contains thin, compliant structures whose natural frequencies are close to the scaled step. These thresholds are not arbitrary: added mass lowers the model's natural frequencies by roughly sqrt(1 + r), where r is the local added-mass ratio, so a 5% mass increase shifts frequencies by about 2.5%—usually acceptable, but enough to matter in modal or vibration-sensitive work.

A low global added-mass ratio does not guarantee accuracy. Selective scaling can concentrate 30–50% added mass in a handful of tiny elements at a contact interface or a fillet, producing locally wrong inertia and contact forces while the global ratio reads a comfortable 1%. Always inspect the per-part or per-element mass distribution, not just the model total.

The figure below traces how a target step propagates through selective scaling: elements below the threshold are lifted to the target, the global step rises to the target, and the added-mass ratio is the feedback signal that tells you whether the target was too aggressive.

Reading the added-mass ratio in practice

In the glstat file, the added-mass line appears once per output interval. A healthy selective-scaling run shows a small, roughly constant percentage that does not grow as the simulation proceeds. If the percentage climbs steadily, it usually means elements are compressing under load and their stable step is falling below the frozen target—LS-DYNA then adds more mass to keep them at |DT2MS|. That growth is a warning that the target step is too aggressive for the deformation the model is experiencing. The remedy is to lower |DT2MS| (a smaller target means less added mass), refine the offending geometry, or switch to MS1ST = 1 to freeze scaling at t = 0.

A second diagnostic is the energy ratio. Added mass does not create energy, but it changes the partition between kinetic and internal energy. If the scaled model's internal energy at a given crush distance differs from an unscaled reference by more than a few percent, the added inertia is doing mechanical work that the real structure would not do. Running a short unscaled or lightly scaled reference case on a coarse mesh is the cheapest way to calibrate how much scaling the problem tolerates.

Choosing a target step

A defensible workflow is: first run with no scaling and record the natural minimum step and the element count below a candidate target; then set |DT2MS| to roughly 0.5–1.0 µs for typical automotive steel meshes (element size 5–10 mm, wave speed ~5000 m/s gives natural steps of 1–2 µs, so a 1 µs target is mild); then inspect the added-mass ratio and the per-part distribution. If the ratio exceeds 5%, reduce the target or fix the mesh. The target should never be set so high that the scaled step exceeds the natural step of the bulk mesh—at that point global scaling has effectively taken over and the selective benefit is lost.

For models with a few pathological slivers, it is often faster and more accurate to delete or remesh those elements than to scale them. A 0.2 mm sliver scaled to a 1 µs step carries an added-mass ratio of (1/0.2)² ≈ 25× its original mass—enough to dominate local contact behavior even though the global ratio looks benign.

Mass scaling is a lever, not a free lunch. Used selectively, with a target step chosen from the natural step distribution and validated against the added-mass ratio and an energy comparison, it can cut wall-clock time by an order of magnitude while preserving the crash pulse and the deformation pattern. Used globally or pushed past the 5% gate, it silently rewrites the inertia of the model and produces results that look plausible but are physically wrong. The discipline is to treat the added-mass ratio as a first-class output, inspect it per part, and never accept a scaled run without a reference comparison.