3. Element formulation selection

In LS-DYNA, ELFORM is the single most consequential keyword on *SECTION_SHELL and *SECTION_SOLID. It determines the kinematic assumptions, the number of integration points through the thickness or volume, the susceptibility to hourglassing and shear locking, and the stable time step. Choosing the wrong formulation is one of the most common root causes of a crash model that either runs too slowly, produces non-physical deformation, or diverges during contact. This section compares the five formulations most frequently used in crashworthiness work and explains how to pair each with appropriate hourglass control.

Shell formulations: ELFORM 1, 2, and 16

For thin-walled structures — front rails, B-pillars, door beams, roof panels — shell elements dominate. The three workhorse formulations differ mainly in how they integrate through the thickness and how they handle transverse shear.

ELFORM 1 (Hughes–Liu, 2 integration points through thickness) is the default and the most widely validated shell in LS-DYNA. It uses a four-node quadrilateral with reduced in-plane integration (one point at the element center) and two through-thickness points. Because in-plane integration is reduced, ELFORM 1 is not prone to shear locking, but it is prone to hourglassing. It is the correct choice for large-deformation crash panels where bending dominates and where you can afford robust hourglass control. Typical stable time step for a 5 mm aluminum panel (E ≈ 70 GPa, ρ ≈ 2.7e-9 tonne/mm³) is on the order of 0.5–1.0 µs.

ELFORM 2 (Belytschko–Tsay, 2 integration points) is the classic explicit shell. It is computationally cheaper than ELFORM 1 because it uses a co-rotational formulation with a single in-plane integration point and a simplified hourglass stabilization. It performs well in high-velocity impact and blast where membrane action dominates, but it is more sensitive to hourglassing in bending-dominated problems and can exhibit zero-energy modes if the mesh is coarse. Use ELFORM 2 when runtime is critical and the deformation is predominantly membrane-stretching.

ELFORM 16 (fully integrated shell, 2 through-thickness points) uses 2×2 in-plane integration. This eliminates hourglassing entirely — no hourglass control is needed — but it introduces shear locking in thin shells because the fully integrated element cannot represent pure bending without spurious transverse shear. ELFORM 16 is therefore best reserved for thick shells, or for thin shells where you can afford a fine mesh and where hourglassing in ELFORM 1/2 has proven intractable. It is also useful for validating hourglass-controlled results.

Solid formulations: ELFORM −1 and ELFORM 1 (solid)

For solid elements — used in castings, joints, thick sections, and foam cores — the two dominant choices are ELFORM −1 (constant stress, one integration point) and ELFORM 1 (fully integrated, 2×2×2 points).

ELFORM −1 (constant stress solid) is the default solid in LS-DYNA. It uses a single integration point at the element centroid, which makes it extremely efficient and robust in large deformation. Its weakness is hourglassing: the single integration point cannot resist zero-energy modes, so hourglass control is mandatory. For crash applications, Type 4 (stiffness-based) or Type 5 (viscous) hourglass control is typical. ELFORM −1 is the right choice for most solid crash models, especially where the solid is confined by surrounding structure and hourglass modes are suppressed by contact and adjacent elements.

ELFORM 1 (fully integrated solid) uses 2×2×2 integration. It is immune to hourglassing but suffers from volumetric and shear locking in nearly incompressible materials (rubber, foam, undrained soil) and is roughly 8× more expensive per element. It is appropriate for small-strain, bending-dominated solids, or as a verification reference. In crash work, ELFORM 1 solids are rarely used for the deformable structure itself; they appear more often in rigid tooling or in validation studies.

Hourglass control: the essential companion

Hourglassing is a zero-energy deformation mode that produces a characteristic checkerboard pattern in the mesh. It is not a physical instability — it is a numerical artifact of reduced integration. The standard diagnostic is the hourglass energy reported in glstat and matsum. A healthy crash model keeps hourglass energy below 5% of total internal energy; above 10% the results are suspect.

LS-DYNA offers several hourglass control types via *HOURGLASS or the IHQ field on the section card:

• Type 1 (standard viscous): default, cheap, but can add artificial stiffness in slow processes.
• Type 2 (Flanagan–Belytschko viscous): better for solids, scales with element volume.
• Type 4 (stiffness-based): recommended for crash; provides stiffness without excessive damping, but can cause instability if the hourglass coefficient QM is too high.
• Type 5 (viscous with stiffness): hybrid, useful for foams and rubbers.
• Type 6 (stiffness-based, updated): improved Type 4, often the best default for shells in crash.

The hourglass coefficient QM (default 0.05–0.10) controls the magnitude. Start at 0.05 for Type 4/6 and increase only if hourglass energy remains high. Excessive QM artificially stiffens the response and can mask real deformation.

Shear locking and when it matters

Shear locking occurs when a fully integrated element cannot represent bending without generating parasitic transverse shear strains. It manifests as an overly stiff response — the structure appears stronger and stiffer than it should. In shells, ELFORM 16 is susceptible; in solids, ELFORM 1 is susceptible when the element aspect ratio is poor (thin, flat elements). The mitigation is either to use reduced integration (ELFORM 1 or 2 for shells, ELFORM −1 for solids) or to refine the mesh so that the element aspect ratio approaches 1. For crash models, reduced integration plus hourglass control is almost always the better trade.

Worked example: selecting ELFORM for a front rail section

Consider a 1.5 mm thick DP780 steel front rail modeled with 5 mm shell elements. The element aspect ratio is 3:1, t/L = 0.3, and the deformation is bending-dominated during axial crush. The initial choice is ELFORM 1 with Type 6 hourglass control and QM = 0.05. After a 30 ms simulation, glstat reports hourglass energy at 8% of internal energy — above the 5% threshold. Two remedies are available: refine the mesh to 3 mm (reducing hourglass energy by roughly a factor of 2–3) or switch to ELFORM 16. If ELFORM 16 is chosen, the rail becomes noticeably stiffer in the elastic regime due to shear locking, and the peak force may be overpredicted by 10–15%. The recommended path is mesh refinement with ELFORM 1, because it preserves the correct bending kinematics. If refinement is not feasible, ELFORM 16 with a calibrated thickness offset can be used, but the result must be validated against a physical test or a finer reference model.

Summary of selection criteria

The governing principle is simple: reduced integration buys efficiency and avoids shear locking, but it demands hourglass control and careful monitoring. Fully integrated formulations eliminate hourglassing but introduce locking and cost. In crash engineering, the default should be reduced integration with stiffness-based hourglass control (Type 4 or 6), with hourglass energy tracked as a first-class quality metric alongside internal energy and kinetic energy. When hourglass energy exceeds 5% of internal energy, refine the mesh before changing the formulation — the mesh is almost always the real problem.