Implicit vs Explicit Methods in Finite Element Analysis (FEA)
When running impact or collision simulations in FEA, one of the first questions is: Which solver should I use — implicit or explicit?
From my experience, explicit solvers are best for impacts and collisions. Here’s why.
Static vs Dynamic Analysis
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Static analysis uses an implicit solver (e.g., in LS-DYNA). Mass (inertia) and damping have no effect.
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Dynamic analysis includes nodal forces from mass, inertia, and damping. Here, you can use either explicit or implicit solvers.
Implicit Solvers
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Nonlinear implicit analysis requires iterations at each time step.
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Each step must reach equilibrium within a defined tolerance.
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The solver inverts the stiffness matrix repeatedly, which is computationally expensive for large models.
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Advantage: Can use large time steps, since there’s no stability limit tied to wave speed.
Explicit Solvers
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No iterations — nodal accelerations are solved directly.
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Time step size must be smaller than the critical time step (time for a sound wave to cross an element).
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Handles contact and material nonlinearities more easily than implicit.
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Often faster for short-duration, highly nonlinear events (impacts, crashes, explosions).
How it works
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Solve nodal accelerations at time n using the diagonal mass matrix and force vector.
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Update velocities at n+½ and displacements at n+1.
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Calculate strain from displacement, then stress from strain.
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Repeat the cycle for each time step.
Personal Experience: Forced to Use Implicit
I once analyzed a spring-loaded switch that slammed against a steel shock absorber. The company’s FEA package lacked an explicit solver, so I was forced to use implicit.
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The model took weeks to stabilize.
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Substep convergence was a major challenge (unique to implicit methods).
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An explicit solver would have solved the problem more efficiently — and likely more cheaply than the lost time caused by using the implicit solver.
In the end, I achieved a match between FEA and physical test results. But for impact problems, I’ll always reach for an explicit solver first.
Key Takeaways
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Use implicit solvers for static problems or long-duration dynamic problems.
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Use explicit solvers for short, highly nonlinear events like impacts and crashes.
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Explicit avoids convergence issues but requires very small time steps.
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Implicit allows large time steps but struggles with complex contact and nonlinearity.
Norman Neher
Analytical Engineering Services, Inc.
Elko New Market, MN
www.aesmn.org