Implicit vs Explicit Methods

What’s the difference between Implicit and explicit in FEA?

One question in impact and collision analysis is which solver to use. From my experience, the explicit solver is best for impacts and collisions. Here’s why.

In static analysis, mass (inertia) and damping don’t have an effect. In dynamic analysis, we include nodal forces from mass/inertia and damping.

Static vs Dynamic analysis

Static analysis uses an implicit solver in LS-DYNA. For dynamic analysis, you can use either the explicit or implicit solver.

In nonlinear implicit analysis, each step needs many trial solutions or iterations. We do this to achieve equilibrium within a set tolerance. But in explicit analysis, there are no iterations. Nodal accelerations provide a direct solution.

Time step size

The time step in explicit analysis needs to be less than the currant time step. This is the time it takes for a sound wave to move across an element. Implicit transient analysis does not have a limit on time step size. So, implicit time steps are usually much larger than explicit ones.

Explicit provides faster solutions in some cases

Implicit analysis needs a numerical solver to invert the stiffness matrix many times during a load/time step. This matrix inversion is costly, especially for large models. Explicit analysis skips this step.

Explicit analysis manages nonlinearities with greater ease than implicit analysis. This includes contact and material nonlinearities.

In explicit dynamic analysis, we solve nodal accelerations through a direct approach. This calculation uses the diagonal mass matrix and the net nodal force vector. Once we know accelerations at time n, we calculate velocities at time n+1/2 and displacements at time n+1. From displacements, we find strain, and from strain, we find stress. Then we repeat the cycle.

Forced Implicit analysis

I recently did an impact analysis on a complex mechanical assembly. I focused on the differences between the two solvers.

The assembly was a spring-loaded switch that came to an immediate stop against a steel shock absorber. The company’s FEA code lacked the explicit solver, so I had to use the implicit solver.

Substep convergence  required in Implicit only

The program required weeks to achieve proper functionality. A key issue was achieving convergence at each substep. In contrast, explicit methods have very small time steps, so convergence is not a problem. It wold have been cheaper to purchase the explicit solver!

After some time, I got it to work, and the physical test results matched the finite element analysis results. Getting a good solution with the explicit solver can be tough too. But for impact problems, I will always prefer the explicit solver first.

Norman Neher
Analytical Engineering Services, Inc.
Elko New Market, MN
www.aesmn.org