FEA Best Practices Vol 4

FEA Best Practices

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Volume 4: Keeping the Simulation Honest

Joe McFadden

McFaddenCAE.com

FEA Learning Center • Audiobook Script

We have covered a lot of ground in this series. In Volume 1, we built the foundation -- consistent units, correct materials, appropriate elements, and a converged mesh. In Volume 2, we explored the perturbation family -- modal analysis, harmonic response, random vibration, and shock response spectrum -- where linearity is both the constraint and the power. In Volume 3, we crossed into the explicit world -- shock analysis, contact formulations, drop test workflows, jerk and fragility assessment, and bulk viscosity -- where nonlinearity rules and the physics gets messy.

Now comes the question that should follow every simulation you ever run: how do I know the answer is right?

This is the trust volume. Not trust in the software -- the math is correct. Not trust in the hardware -- the computer calculated exactly what you asked it to. Trust in the model. Trust that the numbers on your screen represent something real. Trust that you can put those numbers in a report, present them to a customer or a program manager, and stand behind them.

Three topics give you the tools to build that trust. Energy balance is the master diagnostic -- the single most important quality check for any explicit dynamic simulation. Hourglassing is a silent numerical pathology that can corrupt your results without any warning message. And mass scaling is the most powerful and most dangerous shortcut in explicit dynamics, capable of saving enormous computation time or completely destroying your answer.

Each one answers the same fundamental question: is the physics being conserved, or is something artificial contaminating the results?

Energy Balance -- the Master Diagnostic

If you run explicit dynamic simulations -- crash, drop test, impact, forming -- energy balance checking is not optional. It is the single most important quality check for your results. Period. Everything else you look at -- stresses, displacements, accelerations -- is only meaningful if the energy balance is clean.

Here is the concept. In any physical system, energy is conserved. Energy in must equal energy out plus energy stored. That is not an approximation. It is a law. In an explicit finite element simulation, several types of energy exist simultaneously: kinetic energy from moving parts, internal strain energy stored in deformed elements, energy dissipated by friction and plasticity, energy dissipated by damping, and energy from external work done on the system. If you add them all up, the total should remain constant -- or change only by the amount of external work applied.

Abacus tracks all of these automatically. The key energy output variables are: ALLKE for total kinetic energy. ALLIE for total internal energy, which includes elastic strain energy plus plastic dissipation. ALLVD for viscous dissipation -- energy absorbed by damping and bulk viscosity. ALLFD for frictional dissipation. ALLEE for total external work. ALLAE for artificial strain energy -- this is the energy associated with hourglass control, and it is the one that should set off alarm bells if it gets too large. And ETOTAL, which is the total energy balance -- ideally zero or constant throughout the simulation.

Two critical checks.

First: the artificial energy ratio. ALLAE divided by ALLIE should be less than 5 percent. If this ratio exceeds 5 to 10 percent, hourglassing is corrupting your results. The deformation patterns are partially artificial, and your stress values are unreliable.

Second: ETOTAL should remain approximately constant throughout the simulation. If total energy is growing, something is adding non-physical energy to your system -- often contact instabilities, mass scaling artifacts, or overconstrained boundary conditions pumping energy in. If total energy is decreasing unexpectedly, energy is being artificially removed, usually from excessive bulk viscosity or damping. A drift of more than 1 to 2 percent of the peak energy is a warning sign that needs investigation.

Let me walk through a concrete example so you can visualize the energy story.

Consider a drop test. At the start, the product is falling. All the energy is kinetic -- ALLKE is at its peak, ALLIE is zero. The instant the product hits the floor, kinetic energy begins converting to internal energy as the material deforms. If the material is elastic, the energy bounces back -- internal converts back to kinetic as the product rebounds. If the material yields plastically, some energy is permanently dissipated and never returns. Friction at the contact interface dissipates more energy as the product slides or rotates on the floor.

At any point during this process, ALLKE plus ALLIE plus ALLVD plus ALLFD should equal the initial kinetic energy. ETOTAL should be flat -- a horizontal line on your plot. If ETOTAL drifts upward, energy is being created from nothing. If it drifts downward beyond what dissipation mechanisms account for, energy is being destroyed. Neither is physical. Both mean something is wrong.

The workflow for energy checking.

First, make sure you request energy output. This sounds obvious, but it is the most common omission. Without energy history output, you cannot check anything.

Second, after the analysis completes, plot ALLAE divided by ALLIE versus time. If it stays below 5 percent throughout, you are in good shape. If it exceeds 10 percent at any point, take action before trusting any other result.

Third, plot ETOTAL versus time. It should be flat. If it is not, identify when the drift starts and what event corresponds to that time.

Fourth, plot ALLKE and ALLIE together versus time. Watch the energy conversion. Does it make physical sense? In a drop test, you should see kinetic energy drop as internal energy rises at the moment of impact. In a quasi-static forming simulation, kinetic energy should remain small compared to internal energy throughout.

Common causes of energy balance problems.

Hourglassing -- the most frequent cause. Reduced integration elements develop zero-energy deformation modes that create artificial strain energy. The fix involves enhanced hourglass control, mesh refinement, or switching element types.

Excessive mass scaling -- artificially heavy elements carry more kinetic energy than they should. Check that added mass does not exceed 1 to 2 percent of the physical total.

Contact instabilities -- nodes oscillating through surfaces inject energy with each pass-through. Fix with refined contact parameters or mesh refinement at the contact interface.

Initial penetrations -- parts overlapping at the start create enormous artificial forces as the solver pushes them apart. Always resolve overclosures before running.

A useful diagnostic trick: if the hourglass ratio is too high, plot artificial energy by part or by region. This tells you exactly where the problem lives, so you know where to focus your mesh refinement rather than refining the entire model.

One more thing. Document your energy balance check in every analysis report. A plot of ETOTAL and the hourglass ratio should be standard content. If someone asks how do you know these results are valid -- your energy balance plots are the first answer.

Now, that artificial energy ratio -- ALLAE over ALLIE -- keeps coming up. Let us talk about what creates it.

Hourglassing -- the Silent Corruption

Hourglassing is one of the most important numerical pathologies in finite element analysis. If you use reduced integration elements -- and most explicit analysts do, because C3D8R is the workhorse of explicit dynamics -- you need to understand this.

Here is what is happening. A C3D8R hexahedral element has eight nodes but only one integration point, right at the center. That single point is where the element evaluates strain, computes stress, and generates internal forces. One point instead of eight makes it fast. One point also avoids shear locking, which plagues full-integration elements in bending. Those are real advantages.

But here is the trade-off. Certain deformation patterns produce zero strain at that single center point. The element changes shape -- sometimes dramatically -- but the integration point sees nothing. No strain means no stress. No stress means no internal resisting force. And with no resisting force, the deformation grows unchecked.

Visualize it. Imagine a cube where opposite corners move in opposite directions while the center stays put. The element distorts into an hourglass shape -- hence the name -- but the center point does not move and registers zero strain. The element thinks nothing is happening while it is actually deforming wildly.

These zero-energy deformation modes are called hourglass modes, and when they propagate through a mesh, the result is a wavy, zigzag pattern of alternating displacements -- a checkerboard of nodes moving up and down that has nothing to do with the physical response. The stresses in those regions are meaningless. The displacements are non-physical. And the energy associated with that artificial deformation shows up as ALLAE -- the artificial strain energy we check in the energy balance.

How do you detect it?

The primary diagnostic is the ratio we just discussed: ALLAE divided by ALLIE. Above 5 percent is significant. Above 10 percent, your results are unreliable.

Visually, look for checkerboard stress patterns -- alternating high and low stress in adjacent elements that should show a smooth gradient. Look for wavy or rippled deformation in regions that should be smooth. And watch the animation carefully -- hourglass modes often appear as a high-frequency oscillation superimposed on the physical response, like static on a TV signal.

Abacus provides several hourglass control methods, and choosing the right one matters.

Relax stiffness is the default for most elements. It adds a small artificial stiffness that resists hourglass deformation modes. It works for many problems but can be too soft for severe loading or coarse meshes.

Enhanced hourglass control is more robust and generally recommended for production work. Instead of using an arbitrary artificial parameter, it calculates hourglass resistance based on the actual element stiffness. This gives better accuracy, especially for coarse meshes and bending-dominated problems. I recommend using enhanced control as your default for every explicit analysis.

Viscous hourglass control adds damping rather than stiffness to resist hourglass modes. Useful for high-speed dynamic problems where adding stiffness might reduce the stable time increment.

Combined stiffness and viscosity uses both mechanisms. Broadest control but adds the most artificial energy.

When controls alone are not enough -- and sometimes they are not -- you have other options.

Refine the mesh. Hourglassing is worse with coarse meshes because each element spans a larger portion of the stress gradient.

Switch element types. C3D10M modified tets have no hourglass problem. C3D8I incompatible-modes hexes use internal degrees of freedom that eliminate the zero-energy modes. Either is a valid alternative when C3D8R hourglassing cannot be controlled.

Check your loading. Concentrated point loads on a single node of a C3D8R mesh are notorious hourglass triggers. Distribute loads over an area.

A common pattern in drop tests: the impacting corner hourglasses due to extreme compression. The fix is mesh refinement at the impact corner combined with enhanced hourglass control. Sometimes switching to C3D10M tets at the impact zone is the most practical solution.

For shell elements, S4R can also hourglass in membrane mode. Enhanced control is recommended. S4 full integration shells avoid hourglassing but may exhibit shear locking in bending, so it is a trade-off.

Do not just check the hourglass ratio at the end of the simulation. Check it throughout. Hourglassing can start small, grow gradually, and then explode near the end.

So energy balance tells you if something is wrong, and hourglassing is often the culprit. Now let us talk about the third topic -- a tool that can create energy balance problems if used carelessly, but can also solve practical problems that would otherwise be intractable.

Mass Scaling -- Power and Danger

Mass scaling is one of the most powerful and most dangerous tools in explicit dynamic analysis. Used correctly, it can reduce computation time by orders of magnitude. Used incorrectly, it can completely invalidate your results.

In explicit dynamics, the stable time increment is determined by the smallest element in your mesh divided by the wave speed through the material. One tiny element dictates the time step for the entire simulation.

Mass scaling works by artificially increasing the density of those smallest elements. Heavier elements have a lower wave speed, allowing a larger time step.

The trade-off is fundamental: you are adding mass that does not physically exist. Accelerations change. Contact forces change. Dynamic response shifts.

When is mass scaling appropriate? Quasi-static processes modeled with explicit dynamics. Metal forming, stamping, deep drawing, slow crush tests. If inertia does not matter, adding a small amount of artificial mass does not change the physics meaningfully.

Also appropriate when a few small elements bottleneck the time step for an otherwise reasonable mesh.

When should you absolutely not use mass scaling? High-speed impact events where inertia matters. Drop tests, crash simulations, ballistic impact. The accelerations are the answer. Artificially changing the mass changes the accelerations directly. Your peak g-level is wrong. Your design decision is wrong.

Wave propagation problems, where the wave speed is the physics and scaling changes it by definition.

Two types exist.

Fixed mass scaling applies scaling at the beginning and keeps it constant. You specify a target time increment, and the solver adds mass only to elements below that target.

Variable mass scaling recalculates periodically during the analysis, adapting as the mesh deforms.

The quality checks are non-negotiable.

First: total added mass should not exceed 1 to 2 percent of the model physical mass.

Second: for quasi-static processes, kinetic energy should remain small compared to internal energy. If ALLKE exceeds 5 to 10 percent of ALLIE, the process is not quasi-static anymore. Ramp your loads more smoothly, reduce the scaling, or extend the time period.

Third: check ETOTAL for energy balance. Mass scaling can introduce energy artifacts.

The most dangerous mistake with mass scaling is applying it to a dynamic analysis -- like a drop test -- and not realizing the results are wrong. The simulation runs. The energy balance might even look reasonable. The stress contours look plausible. But the peak acceleration is 30 percent low because the impact zone is artificially heavy. That error goes straight into your report.

If someone hands you a model and says the results are good, check the mass scaling first. It is one of the fastest ways to catch a fundamental error.

The Complete Picture

Let me bring the entire series full circle.

In Volume 1, I said that when we poke something, it responds, and the quality of what we learn depends on how faithfully we have represented the system. That is the philosophy.

Unit consistency ensures that the numbers going into the simulation are physically meaningful. Material properties define the system nature. Element types determine how we discretize continuous reality. Mesh convergence proves that our discretization is fine enough.

Modal analysis reveals the system natural dynamic character. Harmonic response, random vibration, and SRS each poke that system in a different way. All within the linear perturbation framework, where contact is prohibited and nonlinearity is absent.

Shock analysis, contact formulations, and drop test workflows cross into the nonlinear world. Parts collide, materials yield, geometry deforms. Jerk and fragility assessment revealed that peak g alone misleads -- real damage prediction requires multiple parameters, and the digital signal processing and model evaluation tools at McFaddenCAE.com help you extract and validate those parameters. Bulk viscosity manages the numerical challenges of shock wave propagation.

And in this volume, energy balance, hourglassing, and mass scaling provide the quality assurance framework.

Here is what I want you to take away from this entire series.

Simulation is not about running software. Anyone can click buttons. Simulation is about understanding physical systems deeply enough to build faithful mathematical representations, poking those representations in meaningful ways, and critically evaluating whether the response tells you something true about reality.

Every topic we have covered is a link in that chain. Break any link and the chain fails. Use the wrong units, and every downstream result is fiction. Choose the wrong element, and the numerical approximation does not match the physics. Ignore the perturbation limitations, and your modal-based results are meaningless. Skip the energy balance check, and you might be reporting artificial numbers as engineering facts.

The engineer who checks the energy balance, who verifies the hourglass ratio, who validates mass scaling constraints, who understands why contact cannot appear in a perturbation step, who knows the difference between damp and dampen, who recognizes that mode shapes show relative patterns and not absolute displacements -- that engineer can stand behind their results with confidence. Not because the software said so. Because they understand why the answer is right.

That is what best practices are. Not a checklist. A way of thinking.