3. LS-DYNA forming simulation fundamentals
Sheet metal forming simulation in LS-DYNA is fundamentally a transient structural problem: a blank is deformed by rigid tooling over a finite stroke, and the resulting thickness distribution, strain state, and residual stress field are carried forward into the crash model. The numerical machinery used to solve that forming step differs in important ways from the crash solver settings most analysts are familiar with. This chapter explains the two solver families available in LS-DYNA, why forming usually favors one of them, and how time scaling and mass scaling are used to make the simulation affordable without destroying the physics.
Explicit vs. implicit: two ways to advance the solution
LS-DYNA's explicit solver advances the solution with a central-difference time integration scheme. There is no global stiffness matrix assembly and no matrix inversion; the equations of motion are solved directly at each node using the diagonal (lumped) mass matrix. The stable time step is governed by the Courant condition, approximately the smallest element characteristic length divided by the wave speed in the material. For a typical steel blank with a 1 mm element and a sound speed near 5000 m/s, the stable step is on the order of 0.2 µs. A forming stroke of 50 mm at a punch speed of 5 m/s takes 10 ms of physical time, which is roughly 50,000 steps. That is manageable, but the cost scales with the number of steps, and a slow press stroke of 0.1 m/s would multiply the step count by fifty.
The implicit solver, by contrast, solves a system of nonlinear equilibrium equations at each load increment using Newton–Raphson iteration. It assembles and factorizes a global stiffness matrix, so each increment is far more expensive than an explicit step, but the increment size is limited by convergence and accuracy rather than by a stability condition. For quasi-static forming, implicit can take large increments and reach the solution in far fewer steps. The trade-off is robustness: contact, material nonlinearity, and large deformation can cause convergence difficulties, and a diverging implicit job can be harder to diagnose than an explicit job that simply runs.
In practice, LS-DYNA users often run forming with the explicit solver because it handles contact and large deformation robustly, then optionally use implicit for springback. The choice is not ideological; it depends on the geometry, the material model, and whether the goal is a quick formability check or a converged residual stress state.
Why forming is quasi-static, and what that means for the solver
A real press stroke is slow. Inertia is negligible compared with the forming forces. If you run an explicit simulation at the real punch speed, the simulation time becomes enormous. The standard remedy is time scaling: increase the punch velocity so the stroke completes in a shorter simulated time, while keeping the kinetic energy small relative to the internal energy. The rule of thumb is to keep kinetic energy below about 5–10% of internal energy throughout the stroke. If kinetic energy spikes, inertia is contaminating the solution and the results are no longer quasi-static.
Time scaling is a modeling decision, not a numerical trick to be applied blindly. Doubling the punch speed halves the simulated time and roughly halves the step count, but it also increases strain rates. For mild steel at room temperature, strain-rate sensitivity is modest, so a moderate speed-up is usually acceptable. For aluminum alloys or high-strength steels, or for warm/hot forming, strain-rate sensitivity is significant and aggressive time scaling will change the predicted flow stress and formability. The correct approach is to scale the speed only as much as the kinetic-energy criterion allows, and to verify that the force–displacement response is insensitive to further speed increases.
Mass scaling: buying time step without changing the stroke
Mass scaling increases the mass of selected elements, which lowers the wave speed and therefore increases the stable time step. In LS-DYNA this is controlled through *CONTROL_TIMESTEP with DT2MS (the target time step) and related options. A positive DT2MS adds mass only to elements whose step is below the target; a negative value adds mass to all elements and is generally avoided in forming because it distorts the inertia of the whole model.
The physics constraint is the same as for time scaling: added mass must not dominate the solution. The added mass should typically remain below 1–5% of the total model mass, and the kinetic energy check still applies. Mass scaling is most useful when a few small elements—often at fillets, draw beads, or trimmed edges—are forcing an unnecessarily small global time step. Selective mass scaling targeted at those elements is far better than scaling the entire blank.
Putting the controls together
The following snippet shows a representative explicit forming setup. The values are illustrative and must be tuned to the actual blank material, element size, and stroke.
*CONTROL_TERMINATION
$ endtim
0.010
*CONTROL_TIMESTEP
$ dtinit tssfac isdo tslimt dt2ms lctm erode ms1st
0.0 0.9 0 0.0 -1.0e-6 0 0 0
*CONTROL_ENERGY
$ hgen rwen slnten rylen
2 2 2 2
*DATABASE_GLSTAT
$ dt
1.0e-4
*DATABASE_MATSUM
$ dt
1.0e-4
Here DT2MS = -1.0e-6 requests a target step of 1 µs with mass added to all elements; for a production job you would normally use a positive value and inspect the added-mass report. GLSTAT and MATSUM provide the global energy and mass summaries used for the checks below.
Verification: reading the energy and mass reports
After the run, open glstat and check three quantities over time: internal energy, kinetic energy, and total mass. Kinetic energy should rise during the initial contact and then stay small relative to internal energy. If it exceeds roughly 10% of internal energy at any point, reduce the punch speed or the mass scaling. The added-mass ratio, reported in glstat as the percentage of mass added, should stay within a few percent. A sudden jump in added mass usually indicates that a small element has collapsed or that a contact penalty is generating spurious deformation.
For the forming result itself, inspect the thickness and plastic strain fields. A successful forming simulation shows a smooth thickness gradient, no element with thickness below the forming limit, and a punch force–displacement curve that rises smoothly and then plateaus or drops as the material yields. A jagged force curve, a kinetic-energy spike, or a localized thickness collapse are the classic symptoms of excessive scaling or a contact problem, and the fix is to reduce the scaling factor, refine the mesh locally, or adjust the contact penalty rather than to accept the result.
Practical guidance for the crash workflow
When the forming result feeds a crash model, the residual stress and thickness fields must be transferred accurately. This means the forming simulation should be run with a mesh that matches the crash mesh, or with a mapping step that preserves the through-thickness integration points. Time and mass scaling affect the residual stress state: excessive scaling can leave spurious dynamic oscillations in the stress field that then appear as artificial initial stresses in the crash model. A common practice is to run the forming step with moderate scaling, then perform a short implicit or dynamic relaxation step to settle the residual stresses before mapping.
In summary, the explicit solver is the workhorse for forming because it handles contact and large deformation robustly, but its cost is controlled by the stable time step. Time scaling and mass scaling are the two levers that make the simulation affordable, and both are constrained by energy and mass checks. The disciplined workflow is to choose the solver based on the physics, apply the minimum scaling that meets the runtime budget, and verify the result against the kinetic-energy, added-mass, and force–displacement criteria before trusting the predicted thickness and stress state.