Jerk & Fragility Analysis

FEA LEARNING CENTER

Jerk & Fragility Assessment

Beyond Peak G

By Joseph P. McFadden Sr.

McFaddenCAE.com

Companion document to the FEA Learning Center

in the Abaqus INP Comprehensive Analyzer

A device passes a 2,500 G face drop.

Engineering signs off. The test report says "pass." Everyone moves on.

Two weeks later, the same device fails a 1,400 G corner drop.

How is that possible? How does something survive a severe shock and then break under a seemingly milder one?

The answer is that peak G alone is a terrible predictor of damage. It's one number. And one number cannot describe an event that varies in duration, frequency content, energy distribution, and — crucially — how sharply the force arrives.

The field has known this for decades. And yet, peak G remains the most commonly reported metric in shock testing. It's the number in the spec. It's the number in the report. And it's the number that gives engineers a false sense of security — right up until something fails that shouldn't have.

This discussion is about the other parameters. The ones that actually correlate with failure. And the one most engineers have never heard of — jerk.

The Why — What Peak G Misses

Let me walk through a concrete example that makes the problem visceral.

Pulse A is a half-sine, 3,000 G peak, 0.8 milliseconds duration. Pulse B is a half-sine, 1,500 G peak, 3 milliseconds duration.

Peak G says Pulse A is twice as severe. But let's look at the other numbers.

Velocity change — the integral of acceleration over the pulse duration — tells you the total momentum change. Pulse A delivers about 15.3 meters per second of velocity change. Pulse B delivers about 28.6 meters per second. Nearly double. That velocity change is the total energy that the structure must absorb. Pulse B, at half the peak G, is pumping almost twice the energy into the system.

The shock response spectrum tells you where that energy lands in frequency. Pulse A, being shorter, has its energy concentrated at higher frequencies. Pulse B, being longer, pushes energy down into the lower frequency range — the range where circuit board bending modes live, where component leads flex, where solder joints strain. If your critical failure modes are in the 200 to 800 Hertz range, Pulse B is the one that targets them.

And jerk — the rate of change of acceleration — tells you how suddenly the force arrives. A short, sharp pulse rises to peak extremely quickly, creating a steep acceleration front. That steep front is a stress wave with a sharp leading edge. When that wave encounters a stiffness mismatch — the interface between a ceramic component and a PCB, the bond line of a rigid adhesive, the edge of a glass display — the sharp front loads the brittle material faster than it can distribute the stress. Cracking initiates before the surrounding material can help carry the load.

Peak G didn't predict any of that. It took four parameters — peak acceleration, velocity change, SRS, and jerk — to see the full picture.

The What — Jerk And The Four-parameter Framework

Let me define jerk precisely, because it's the parameter that gets the least attention and may be the most revealing for certain failure modes.

Jerk is the time derivative of acceleration. Acceleration is the rate of change of velocity. Jerk is the rate of change of acceleration. It's the third derivative of position with respect to time. Its units are meters per second cubed, or G per second.

When you feel an elevator start to move, you don't feel the steady acceleration — that just feels like slightly heavier gravity. What you feel is the onset — the moment the acceleration changes. That sensation is jerk. Your inner ear detects not just acceleration but the rate at which acceleration is changing.

In a shock event, high jerk means the acceleration rises or falls very steeply. The stress wave front is sharp. The force arrives suddenly. Materials and interfaces that are brittle or rigid cannot deform fast enough to redistribute the load, and they crack or fracture at stress levels well below their static strength.

Low jerk means the acceleration changes gradually. The stress wave front is smooth. The force builds up slowly enough that the material can distribute it through elastic deformation. Even if the peak acceleration is high, the gradual onset gives the structure time to respond.

Here's the practical insight that ties this to the drop test mystery I opened with.

A face drop distributes the impact force across a large, flat contact area. The deceleration pulse is relatively smooth — the compliance of the product casing and the contact surface blends the event into a broad, rounded pulse. Peak g may be high, but jerk is moderate.

A corner drop concentrates the initial contact into a tiny area. The deceleration onset is extremely abrupt — from zero to peak in a fraction of a millisecond. The peak G may be lower because the corner yields and absorbs energy, but the jerk is much higher. That sharp stress wave front races through the structure and hits every brittle interface and rigid adhesive bond at full severity.

The device failed the corner drop not because of the G level, but because of the jerk.

Jerk-dominated Failure Modes

Not every failure mode is jerk-sensitive. Heavy component retention — a battery, a metal shield, a heatsink — is primarily driven by peak acceleration, because the inertial force is mass times acceleration and these components are massive relative to their attachment.

But several critical failure modes correlate strongly with jerk.

Display glass fracture. Glass is strong in compression but brittle in tension. A sharp stress wave front creates localized tensile stress at the glass edges and at points of constraint before the surrounding structure can absorb the load. The faster the onset, the more localized the stress concentration, the lower the effective strength.

Ceramic capacitor cracking. Multilayer ceramic capacitors — MLCCs — are the single most common component failure in drop and shock testing of electronic assemblies. They're stiff, brittle, and mounted on a flexible PCB. The jerk of the board's bending pulse determines how sharply the capacitor body is loaded relative to the board curvature. High jerk means the board curves faster than the capacitor can follow, and it cracks.

Solder mask cracking and pad cratering. These are interface failures where a rigid body — the component — meets a less rigid substrate — the PCB laminate. The sharpness of the stress wave determines whether the load transfers smoothly or creates a stress concentration that initiates a fracture at the interface.

Rigid adhesive bond failure. UV-cured adhesives, cyanoacrylates, and filled epoxies with minimal elongation are strong in static loading but vulnerable to sharp stress wave fronts. The adhesive can't deform fast enough to distribute the load, and it fails adhesively — peeling from the surface — at stress levels below its rated shear strength.

In every one of these cases, the failure correlates more strongly with jerk than with peak G. An engineer who evaluates shock severity by peak G alone will miss these failure modes entirely — until the test lab calls with a surprise.

The How — Extracting Jerk From Simulation And Test Data

Jerk is computed by differentiating the acceleration time history. That sounds simple. It's not.

Differentiation amplifies noise. Every small fluctuation in the acceleration signal — numerical noise from the solver, high-frequency ringing from contact algorithms, quantization noise from a physical accelerometer — gets amplified when you take the derivative. If you differentiate a raw acceleration signal, the jerk trace will be dominated by noise. It will be useless.

You must filter before you differentiate. This is non-negotiable.

For simulation data, apply a low-pass Butterworth filter — fourth order, zero-phase, using the filtfilt approach to avoid phase distortion. The cutoff frequency depends on your analysis intent. For general drop test assessment, a cutoff of 5,000 to 10,000 Hertz captures the structural response while suppressing solver noise. For pyroshock, you may need a higher cutoff. The key is to choose a cutoff that preserves the physical content you care about while removing the noise that would corrupt the derivative.

For physical test data, apply the same filter class that was used on the accelerometer data — typically a CFC filter per SAE J211. CFC 1000 gives a cutoff around 1,650 Hertz. CFC 600 gives about 1,000 Hertz. Use the same filter on both simulation and test data before computing jerk, or the comparison is meaningless.

Once the acceleration is filtered, compute the derivative numerically — a simple central difference or numpy's gradient function. The result is jerk in G per second or meters per second cubed.

The key metrics from the jerk trace are peak magnitude — the maximum absolute value — jerk duration — how long the jerk exceeds a threshold — and jerk impulse — the integral of jerk magnitude over time. Peak jerk correlates with the sharpness of the stress wave front. Jerk duration indicates how sustained the sharp onset is. And jerk impulse integrates both intensity and duration into a single severity measure.

DSP tools for computing jerk from both simulation output and test data — including automatic filtering, differentiation, and multi-parameter fragility assessment — are available at McFaddenCAE.com.

Putting It All Together — The Fragility Framework

The four-parameter framework doesn't replace peak G. It puts peak G in context.

Peak acceleration tells you the instantaneous inertial force. It's the right parameter for heavy component retention, mounting bolt loads, and housing stress in the direction of acceleration.

Velocity change tells you the total energy transferred to the structure. It's the right parameter for overall structural integrity, cushion compression, and energy-absorbing feature performance.

The shock response spectrum tells you the frequency distribution of the shock energy. It's the right parameter for board-level flex failures, resonant component stress, and frequency-specific qualification.

Jerk tells you how suddenly the force arrives. It's the right parameter for brittle material fracture, rigid interface debonding, and stress wave-dominated failure modes.

No single parameter is sufficient. Each one correlates with different failure mechanisms. A comprehensive fragility assessment evaluates all four and maps each parameter to the relevant failure modes for the specific product.

When you run a drop test simulation, don't just report peak G. Compute velocity change from the integral of acceleration. Compute the SRS using a validated algorithm — the Smallwood ramp-invariant method at Q of 10 is the standard. Compute jerk from the filtered acceleration derivative. Plot all four. Compare across orientations — face, edge, corner. Compare across drop heights. Build a fragility map that shows which parameter governs which failure mode at which severity level.

That's real fragility assessment. That's what peak G alone was never designed to do.

The Common Mistake

I'll close with the mistake that starts this entire discussion.

An engineer evaluates a drop test by peak G only. The device survives a severe face drop at 2,500 G. The engineer reports "pass at 2,500 G" and signs off. Then the device fails a corner drop at 1,400 G — lower peak G, different geometry, different jerk signature. The report says "unexpected failure at lower severity level."

It wasn't unexpected. It was undetected. The fragility was always there — in the jerk, in the velocity change, in the SRS content at the board's bending frequency. But because the assessment looked at only one parameter, the vulnerability was invisible.

Don't let one number do a job that requires four.

For the complete multi-parameter fragility methodology and its connection to the drop test workflow, see the FEA Best Practices audiobook Volume 3: When Things Collide at McFaddenCAE.com.

This has been a Learning Center discussion on jerk and fragility assessment. I'm Joe McFadden. Thanks for listening.

About the Author

Joseph P. McFadden Sr. is a CAE engineer specializing in finite element analysis, modal analysis, materials behavior, and injection mold tooling validation. With nearly four decades of experience in structural simulation, he brings a holistic perspective to engineering education — connecting how systems respond to how people think and learn.

His work at McFaddenCAE.com includes the Abaqus INP Comprehensive Analyzer — a desktop tool for analyzing, visualizing, and extracting sub-assemblies from large FEA models without requiring an Abaqus license — along with DSP tools for SRS computation, jerk extraction, velocity change analysis, and energy balance verification.

The FEA Learning Center is an integrated educational platform within the Analyzer, providing guided discussions on structural dynamics topics with working example INP files. This document series is the companion written reference for those discussions.

The four-volume FEA Best Practices audiobook series — Building the Model, The System's Natural Character, When Things Collide, and Keeping the Simulation Honest — is available at McFaddenCAE.com.