Shock Analysis

FEA LEARNING CENTER

Shock Analysis

The Moment of Truth

By Joseph P. McFadden Sr.

McFaddenCAE.com

Companion document to the FEA Learning Center

in the Abaqus INP Comprehensive Analyzer

Drop your phone on a tile floor and in the span of two or three milliseconds, the entire event is over.

In that sliver of time, peak decelerations can reach hundreds or even thousands of G's. Stress waves travel through the structure at the speed of sound in the material. Display glass flexes. Solder joints strain. Adhesive bonds absorb energy. And either everything survives, or something fails.

You don't get a second chance to study that event in real time. It's too fast. By the time you realize something broke, the physics are long over.

That's what shock analysis does. It lets you replay that event — millisecond by millisecond — in a simulation. It lets you see the stress wave propagate, watch the board flex, identify where the strain concentrates. And it lets you do that before you build a prototype, before you run a physical test, before you find out the hard way that the corner drop is the one that kills you.

The Why — What Makes Shock Different

Shock is fundamentally different from steady-state vibration. In a vibration analysis — harmonic response, random vibration — you're looking at how a system responds to a sustained excitation over time. The system reaches a steady state where the response at each frequency is predictable and repeatable.

Shock is a transient event. It starts suddenly, ends quickly, and the entire response happens during the transition. There is no steady state. The structure is absorbing energy, converting kinetic energy to strain energy and back, propagating waves, and dissipating energy through material damping and contact friction — all in a few milliseconds.

This means shock analysis requires solving the equations of motion at every tiny time step throughout the event. Force equals mass times acceleration — but the force, the deformation, and the contact state are all changing continuously. The solver marches forward in time, computing the state of every node at each increment. For explicit dynamics, those increments can be sub-microsecond.

That's computationally expensive. A modal analysis might take seconds. A shock simulation might take hours. But it captures physics that a modal analysis never can — contact, material yielding, large deformation, wave propagation. The real world of impact.

The What — Types Of Shock And What They Demand

Not all shocks are the same, and the type of shock determines how you model it.

A drop test is the most common. A product falls from a defined height, impacts a surface, and you want to know what happens to the internals. The impact velocity is straightforward — the square root of two times gravity times height. A one-meter drop gives you about 4.43 meters per second. What happens after impact — the deceleration profile, the duration, the energy absorption — depends on the structure, the contact surface, and the geometry of the impact.

A classical shock pulse is a different approach. Instead of modeling the full drop with contact, you apply a predefined acceleration pulse directly to the model. Half-sine, terminal peak sawtooth, or square wave. This is the approach used in MIL-STD-810 and most qualification standards. It's simpler to set up than a full contact simulation, and it produces conservative results when done correctly.

The half-sine is the most common — a smooth rise to peak, then a smooth return to zero. The terminal peak sawtooth ramps linearly to peak and then drops abruptly — that abrupt termination generates high-frequency content that makes it more severe than a half-sine at the same peak G. The square wave is the most conservative — constant acceleration for the full duration, delivering the maximum impulse for a given peak and duration.

Pyroshock is at the extreme end. Explosive bolts, stage separation events, deployment mechanisms. Peak accelerations of thousands or tens of thousands of G's, durations under a millisecond, dominant frequency content above a thousand Hertz. This is where SRS analysis becomes essential because the energy distribution across frequency matters more than the peak value.

And seismic events are at the other extreme — low frequency, long duration, moderate acceleration. A building in an earthquake sees one to two G's for tens of seconds. The physics are the same — transient dynamic response — but the frequencies and time scales are completely different from a product drop test.

The Insight — Peak G Is Misleading

This is the single most important thing I can tell you about shock analysis, and it's the thing most engineers get wrong.

Peak acceleration does not determine damage severity.

I know that sounds counterintuitive. Higher G means more force. More force means more stress. More stress means more damage. Right?

Not necessarily.

Consider two shock pulses. Pulse A hits 3,000 G with a duration of 0.8 milliseconds. Pulse B hits only 1,500 G but lasts 3 milliseconds. Most engineers would call Pulse A more severe — it's double the peak G. But Pulse B might cause far more damage, because its longer duration means a larger velocity change and more energy content at lower frequencies that align with the bending modes of circuit boards and component leads. The board flexes more, the solder joints strain more, and components fail — at half the peak acceleration.

This is why real fragility assessment requires multiple parameters working together. Peak acceleration tells you the instantaneous force. Velocity change tells you the total energy that must be absorbed. The shock response spectrum tells you how that energy is distributed across frequency. And jerk — the rate of change of acceleration — tells you how suddenly the force arrives.

Each parameter correlates with different failure modes. Solder joint fatigue correlates with velocity change and SRS content at board resonant frequencies. Display glass cracking correlates with jerk — the sharp stress wave front that loads brittle materials before they can distribute the load. Heavy component retention — batteries, shields — correlates with peak G because the inertial force is directly proportional to acceleration.

If you evaluate shock severity by peak G alone, you will eventually be surprised by a failure. A device will survive a severe face drop at 2,500 G and then fail on a seemingly mild corner drop at 1,400 G. Peak G says the corner drop was less severe. Multi-parameter assessment reveals the corner drop had higher jerk and SRS content at critical frequencies. It was more damaging despite lower peak G.

For a deep dive into this framework, see the dedicated Learning Center discussion on jerk and fragility assessment.

The How — Setting Up Shock Analysis In Abaqus

There are two fundamental approaches: explicit and implicit.

Explicit dynamics — Dynamic, Explicit step — is the workhorse for short-duration, high-velocity impact events. It marches forward in time using a central difference integration scheme with no matrix inversions. Each time increment is tiny — governed by the Courant condition, which means the time step must be smaller than the time it takes a stress wave to cross the smallest element in your mesh. For a typical impact simulation, that means increments on the order of microseconds or less.

The advantage is that explicit handles contact beautifully. Surfaces come together, slide, separate — no convergence issues. Material nonlinearity, large deformation, element failure — all handled naturally. The disadvantage is that it can require millions of increments, and you must check energy balance to verify the results are valid.

Implicit dynamics — Dynamic step with automatic time stepping — is better for longer-duration, moderate-velocity events. Seismic analysis, for example. Implicit solves a system of equations at each increment and can take much larger time steps, but it requires convergence at each step and doesn't handle severe contact as robustly.

For drop test and impact simulation, explicit is almost always the right choice.

Whichever approach you use, output requests matter enormously. Request acceleration, velocity, and displacement history at your nodes of interest. Request energy variables — kinetic energy, internal energy, artificial energy, total energy — for the whole model. Set your history output time interval based on the Nyquist criterion — at least five to ten times the highest frequency of interest. For a drop test, an output interval of 1 times 10 to the minus 5 seconds gives you 100 kilohertz sampling, which is adequate for most component-level shock analysis.

And when you export that data for external post-processing — for SRS computation, jerk extraction, velocity change analysis — make sure you export all steps. I can't emphasize this enough. If your analysis has a gravity preload step followed by a drop step, you need the complete time history across both steps. Exporting only the active step gives you truncated data that produces wrong derived quantities. There's a dedicated Learning Center discussion on output requests and post-processing that covers this in detail.

Energy Balance — Your Trust Metric

For explicit shock analysis, the energy balance is the single most important quality check.

Total energy — ETOTAL in Abaqus — should remain flat throughout the analysis. Energy is not created or destroyed; it transforms between kinetic and internal forms and dissipates through damping and friction. If ETOTAL drifts significantly, something is wrong — energy is being artificially added or removed, and your results are not trustworthy.

Artificial energy — ALLAE — comes from hourglass control. It should remain below five percent of total internal energy. If it's higher, hourglassing is corrupting your results. Consider using full-integration elements or enhanced hourglass control.

Check the kinetic-to-internal energy transition. In a drop test, kinetic energy starts high as the product approaches the floor and converts to internal energy — strain energy — during impact. After rebound, some kinetic energy returns. The exchange should look physically reasonable. If kinetic energy suddenly spikes in the middle of the analysis, something is generating non-physical motion — possibly failed contact, unconstrained rigid body modes, or mass scaling artifacts.

Energy balance doesn't guarantee your answer is right, but an energy balance failure guarantees your answer is wrong. It's the minimum standard for a credible explicit analysis.

The Bigger Picture

Shock analysis is where simulation meets the real world most directly. Your model either predicts what happens when the product hits the floor, or it doesn't. There's no abstract correctness — there's a physical test that will tell you, definitively, whether your simulation was right.

That's what makes it both challenging and satisfying. And that's why the fundamentals matter — consistent units, appropriate material models, energy balance verification, and the discipline to evaluate severity with multiple parameters rather than a single peak G number.

The tools to extract and evaluate those parameters — SRS, jerk, velocity change, filtered acceleration — from both simulation output and physical test data are available at McFaddenCAE.com.

For the complete eight-step drop test workflow, see the FEA Best Practices audiobook Volume 3: When Things Collide. For energy balance and mass scaling guidance, see Volume 4: Keeping the Simulation Honest.

This has been a Learning Center discussion on shock analysis. 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.