4. Hourglass control formulations in LS-DYNA

Reduced-integration solid and shell elements are the workhorses of explicit LS-DYNA models because they evaluate stresses at a single in-plane integration point (shells) or one point per element (solids), which keeps the critical time step large and the cost per cycle low. The price of that efficiency is the existence of zero-energy deformation modes: hourglass patterns in which the element distorts while its single integration point records no strain change. Left uncontrolled, these modes propagate through the mesh, produce oscillatory, mesh-dependent deformation, and can corrupt the energy balance you are monitoring. LS-DYNA offers three families of hourglass control — viscous, stiffness, and combined — selected and tuned through the IHQ flag and the QH coefficient on *CONTROL_HOURGLASS (and, for shells, the *SECTION_SHELL card). This chapter explains what each formulation does mechanically, how the parameters interact, and how to choose values that suppress hourglassing without over-stiffening the response.

What the three formulations actually do

Viscous control (IHQ = 1, the default). Viscous hourglass control applies a damping force proportional to the hourglass velocity field. It resists the rate of hourglass deformation, not its magnitude. Because the force vanishes when the hourglass mode stops growing, viscous control adds no artificial stiffness to the converged static response and is generally the least intrusive choice for impact and crash problems dominated by inertia. Its weakness is that it cannot arrest a slowly growing hourglass mode under sustained quasi-static loading, and the damping forces can add spurious energy that shows up in the energy balance as negative or non-physical hourglass energy.

Stiffness control (IHQ = 4 for solids, IHQ = 5 for shells in current versions). Stiffness control adds an elastic restoring force proportional to the hourglass amplitude, effectively giving the element a small artificial stiffness against the hourglass mode. It is far more effective at suppressing hourglassing in quasi-static, springback, and forming analyses, and it produces a well-defined, recoverable hourglass energy that is easy to interpret. The trade-off is that it can stiffen the element artificially if QH is set too high, biasing bending and membrane response.

Combined / physical stabilization (IHQ = 6 for solids, IHQ = 8 for shells). The combined form blends a stiffness-type stabilization with a viscous component, and in the shell case the "physical" stabilization derives the hourglass stiffness from the actual element material and geometry rather than from a user-scaled coefficient. This makes the response less sensitive to QH and more physically consistent across materials and element sizes, which is why it is often recommended for shells undergoing large rotation and for solids with strongly nonlinear material behavior.

Reading IHQ and QH together

On *CONTROL_HOURGLASS, IHQ selects the formulation and QH sets the coefficient. For solids, the default QH is 0.1 with viscous control; typical stiffness-control values range from 0.03 to 0.1, and combined/physical stabilization often uses 0.05–0.1. For shells, the hourglass coefficient is also carried on *SECTION_SHELL (field HQ / NIP-dependent), and the shell default is 0.1. The table below summarizes the practical mapping; treat the numbers as starting points, not universal constants.

Two diagnostics tell you whether the choice is working. First, the hourglass energy reported in glstat and matsum: as a rule of thumb, hourglass energy should stay below roughly 5% of internal energy (some practitioners accept 10% for crash models). Second, the total energy ratio: total energy should remain nearly constant, and the sum of internal, kinetic, hourglass, and sliding energy should track the initial energy. A rising hourglass energy with a falling internal energy is the classic signature of uncontrolled hourglassing.

Worked example: choosing control for a thin-walled crash box

Consider a 1.2 mm thick steel crash box modeled with Belytschko-Tsay shells (5 through-thickness integration points) impacting a rigid wall at 10 m/s. Start with the default viscous control (IHQ = 1, QH = 0.1) and run 20 ms. Inspect glstat: if hourglass energy exceeds 5% of internal energy and the box shows a checkerboard wrinkle pattern, switch to stiffness control (IHQ = 4 or 5) with QH = 0.05 and re-run. If the force–displacement curve becomes noticeably stiffer than the viscous run, reduce QH to 0.03. For a forming simulation of the same geometry, start directly with stiffness or combined control, because viscous damping will not arrest the slow hourglass growth during the quasi-static punch stroke.

*CONTROL_HOURGLASS
$#   ihq        qh
         4      0.05
*SECTION_SHELL
$#  secid    elform      shrf       nip     propt   qr/irid     icomp
         1         2       1.0         5       1.0       0.0         0
$#    t1      t2      t3      t4      nloc     marea
     1.2     1.2     1.2     1.2       0.0       0.0

Note that the shell hourglass coefficient can be set either globally on *CONTROL_HOURGLASS or per-part on *SECTION_SHELL; the section value overrides the global default for that part. When different parts need different stabilization — for example, a stiff bracket alongside a soft gasket — set QH per section rather than forcing one global value.

Choosing between the formulations

The decision is driven by the loading regime and the failure mode you observe. Inertia-dominated events with short durations favor viscous control because it does not bias the converged response. Quasi-static and forming analyses favor stiffness or combined control because they must resist sustained hourglass growth. Shells under large rotation and solids with hyperelastic or foam materials favor the physical/combined forms because the stabilization scales with the material stiffness rather than a fixed coefficient. When in doubt, run a short sensitivity sweep over QH (e.g., 0.03, 0.05, 0.1) and compare hourglass energy fraction and the global force–displacement response; the correct value is the smallest one that keeps hourglass energy acceptably low without visibly stiffening the result.

Practical parameter guidance and pitfalls

Three habits keep hourglass control from becoming a source of error. First, always report hourglass energy in your results summary; a model that "looks fine" but carries 15% hourglass energy is not converged. Second, change one parameter at a time: switching IHQ and QH simultaneously makes it impossible to attribute a change in response. Third, check the shell section card: the HQ field on *SECTION_SHELL can silently override the global QH, so a part that still hourglasses after a global change may be reading a stale section value. For solids, remember that IHQ = 4 is stiffness and IHQ = 6 is combined; for shells the numbering differs, so verify against the version's keyword manual rather than assuming the solid mapping carries over. Finally, when using stiffness or combined control in a quasi-static analysis, confirm that the artificial stiffness has not shifted your global stiffness by comparing the initial slope of the force–displacement curve against a viscous-control reference run.

With the formulation selected and QH tuned against the energy diagnostics, the next step is to interpret the hourglass energy curve itself — whether it is growing, plateauing, or oscillating — and to connect it to the total energy balance that the rest of this course builds on.