MATERIALS IN FINITE ELEMENT ANALYSIS

MATERIALS IN FINITE ELEMENT ANALYSIS

Part Two

The Technical Modeling Guide

Using the Abacus INP Comprehensive Analyzer and other FEA tools

Developed in collaboration with Claude (Anthropic)

BEFORE WE BEGIN.

This is Part Two — the technical guide. It covers how to define materials correctly in Abacus and in any finite element tool. What properties are required and why. The most consequential errors analysts make — wrong units, missing rate dependency, static data in impact models — and how the Abacus INP Analyzer catches them before the solver does.

This guide stands on its own. If you have a drop test model to review and a deadline tomorrow, everything you need is here. But if you have not yet read Part One — the nature of materials, the character behind the numbers — I would encourage you to go there when you can. Part One is tool-agnostic. It covers what materials actually are, not just how to enter them into a solver. When you return to this guide after Part One, the density requirement will mean something different. The rate-dependent plasticity flag will mean something different. The three questions at the heart of this guide will mean something different. The technical content does not change. Your relationship to it does.

THE MATERIAL CARD IS NOT THE MATERIAL.

In drop and impact analysis, materials are where simulations fail silently. A perfect mesh with perfect contact can still give you completely wrong results if the material model is wrong. And many of these errors look plausible right up until the physical test.

Here is what that looks like. A design team runs a drop test simulation on a polymer housing. Clean model, solid mesh, correct boundary conditions, properly defined contact, material card from the supplier datasheet. The simulation shows a safety factor of two-point-five. Physical drop testing: the part fractures on the first drop. Cleanly. At the screw boss. The analyst did not know where the injection mould weld line was. The actual strength at that location was forty percent of the datasheet value. No amount of mesh refinement recovers from that.

Three questions to run through before accepting any material card. Where did this property come from? What process created the part? And what environment will the material see? If you cannot answer all three with confidence, document your assumptions explicitly before submission. A simulation with clearly documented material assumptions is honest engineering. A simulation with unchecked defaults is mind blindness.

THE FOUNDATION. DENSITY, ELASTICITY, AND UNITS.

In explicit structural dynamics, deformable materials require at minimum two things: density and a stiffness definition. Without density there is no mass, no inertia, no gravity effects, and the explicit solver cannot compute dynamics. Without elastic properties, the solver cannot compute wave speed, which governs the stable timestep. Static analyses, thermal models, and rigid body definitions have different requirements — these rules apply specifically to deformable components in dynamic impact models.

The unit system trap on density is the most destructive single error in production drop models. In the tonne-millimetre-second system, steel density is 7.85 times 10 to the negative 9 tonnes per cubic millimetre. Not 7850. Not 7.85. Put the SI value in a tonne-millimetre-second model and you have declared steel a trillion times denser than it is. The dangerous version is a mixed model — some materials entered in SI, some in tonne-millimetre-second — where the errors partially compensate and the results are wrong but not obviously so. The unit system detector in the Analyzer cross-references every material's modulus and density against a library of known engineering materials in both unit systems. Use it on every model.

Poisson's ratio: keep it in the range 0.15 to 0.45 for most structural materials. Values of 0.49 or even 0.499 are physically valid for near-incompressible materials and are acceptable when used with appropriate hybrid element formulations. Only exactly 0.5 produces a mathematically singular bulk modulus and must never be used. For elastomers and foam, use hyperelastic formulations rather than elastic with Poisson's ratio approaching 0.5 — not as a workaround, but because hyperelastic theory is the physically correct constitutive framework for those materials.

METALS. PLASTICITY DATA AND THE MONOTONIC REQUIREMENT.

The property on the mill certificate and the property in your finished part are often not the same number. Alloy temper is the single most important designator. Aluminium 6061: O-temper yield stress approximately 55 megapascals, T4 approximately 145, T6 approximately 276. A five-to-one range from the same alloy depending entirely on heat treatment. Die-cast metals carry porosity — ADC-12 die-cast aluminium yield stress approximately 145 megapascals, not 6061-T6 wrought. Welded aluminium carries a heat-affected zone with a five-times local yield reduction invisible in a model with uniform T6 properties.

Plasticity data must be in true stress and true plastic strain — not the engineering stress-strain curve from the datasheet. True stress equals engineering stress times one plus engineering strain. True total strain equals the natural log of one plus engineering strain. True plastic strain is then true total strain minus the elastic component — for small elastic strains, that is true stress divided by Young's modulus. These conversions are valid up to necking. Beyond necking the simple formula breaks down, and the true stress and strain at the neck must be measured or inferred.

The monotonic condition: the plasticity framework in every major FEA solver assumes the tangent modulus of the true stress-true strain curve remains positive throughout the plastic region — the material hardens as it deforms, spreading deformation rather than concentrating it. For structural metals, the true stress-strain curve is genuinely monotonically increasing even through necking. The engineering curve descends after the ultimate tensile strength because you are dividing by the original area rather than the shrinking current area. The material at the neck is still hardening — the geometry is softening, but the material is not. Entering the engineering curve directly gives a descending post-ultimate branch that violates the monotonic condition. For polymers with a pronounced upper yield drop — nylon, polypropylene, polyethylene — the true stress-strain curve genuinely descends from upper yield to lower yield plateau. Regularise the data: replace the descending branch with a horizontal step directly from upper yield point to lower yield plateau. Apply this regularisation independently at each strain rate in your rate-dependent tables. Check the maximum plastic strain in your results against the maximum strain in your input data. If elements are operating beyond your data range, the extrapolated response is an assumption. Document it.

Rate-dependent plasticity: local strain rates in drop test contact zones reach 10 to 1000 per second. Many structural metals show yield strength increases at impact rates — 20 to 50 percent is common for some grades, but the actual magnitude must come from material-specific data or calibrated rate constants. Using only quasi-static data underpredicts peak contact forces and overpredicts deformation. The Analyzer flags every plasticity material in an explicit dynamic model that lacks a rate-dependent definition.

Johnson-Cook combines strain hardening, rate strengthening, and thermal softening in one expression. Three multiplicative terms: A plus B times equivalent plastic strain to the power n — strain hardening. Times one plus C times the log of the normalised strain rate — rate strengthening. Times one minus homologous temperature to the power m — thermal softening. Representative parameters for common structural steels: A 350 to 550, B 400 to 800 megapascals, n 0.2 to 0.4, C 0.01 to 0.04, m 0.5 to 1.0. For 6061-T6 aluminium: A 270 to 324, B 150 to 500, n 0.3 to 0.45, C 0.002 to 0.015, m 0.8 to 1.34. Do not pair Johnson-Cook with a separate rate-dependent definition — the rate term is already inside Johnson-Cook. The Analyzer flags this double-counting.

PLASTICS. THE STATIC MODULUS COMPROMISE AND WHAT IT MEANS.

Plastics are rate-dependent, temperature-dependent, moisture-dependent, viscoelastic, anisotropic after moulding, and history-dependent. Steel shares some of these characteristics — it is rate-dependent and temperature-dependent, and it carries its manufacturing history — and we have covered those effects in depth. But in plastics these effects are fundamentally different in both magnitude and nature. Steel does not absorb moisture in ways that halve its modulus. Steel is not normally modelled as viscoelastic at room-temperature structural engineering conditions. And while steel’s rate sensitivity raises yield strength by 20 to 50 percent at impact rates, it does not switch the failure mode from ductile to brittle the way temperature and rate can in polycarbonate. The combination — moisture, viscoelasticity, moulding-induced anisotropy, weld lines, and large shifts in both strength and failure mode with rate and temperature — is what makes plastics uniquely demanding to model correctly.

Here is something important to understand about how we typically model polymers in drop simulations, and what that approach does and does not capture. The most common approach is a fixed elastic modulus taken from quasi-static test data, combined with rate-dependent plastic stress-strain curves at multiple strain rates. This approach captures the significant increase in yield strength with strain rate — which is the dominant effect — and the change in post-yield behaviour and energy absorption capacity. But it does not capture the rate-dependent stiffness below the yield point. In reality, the initial modulus of most engineering polymers increases noticeably at the high strain rates encountered during drop impacts — the polymer chains have less time to relax, the material feels stiffer even before yielding. That increase in pre-yield stiffness is invisible to a fixed elastic modulus definition. To capture rate-dependent stiffness fully — in both the elastic region and at yield — you need a viscoelastic model using the Prony series, covered in the next section.

For most production drop simulations of handheld devices, the static modulus plus rate-dependent plasticity compromise is acceptable and widely used. The reason: the highest strain rates in a drop event are localised — concentrated in the immediate contact zone, sharp corners, ribs, and screw bosses. The majority of the part experiences much lower strain rates where the fixed elastic modulus is a reasonable approximation. The biggest errors from ignoring rate effects entirely are in the post-yield regime — underpredicted peak forces and overpredicted deformation — and those are captured by the rate-dependent plasticity tables. Use the static modulus plus rate-dependent plasticity as your baseline. Add a Prony series viscoelastic definition when you need better correlation with measured acceleration traces or force-time histories, or when large areas of the part are experiencing moderate-to-high strain rates simultaneously.

The monotonic condition for polymer plasticity is more demanding than for metals. Regularise the upper yield drop for nylon, polypropylene, and polyethylene — replace the descending branch with a horizontal step at the lower yield plateau. Apply this at every strain rate independently. The Analyzer flags engineering polymers — modulus 50 to 5000 megapascals — missing rate-dependent definitions in explicit dynamic steps, with a message tailored specifically to polymers. Thermoplastics are often more rate-sensitive in terms of failure mode change than metals.

For moisture: nylon at 50 percent relative humidity has Young's modulus approximately 1600 megapascals and yield near 55 megapascals — a factor of two lower than dry-as-moulded. Weld lines reduce strength 30 to 70 percent at the weld location. Create separate element sets at weld line locations with reduced failure thresholds. For failure criteria: maximum equivalent plastic strain for ductile behaviour, maximum principal stress for brittle. Check both and use the lower safety margin as governing.

THE PRONY SERIES. CAPTURING RATE-DEPENDENT STIFFNESS.

The Prony series is one of the most common and widely supported ways to represent time-dependent stiffness in FEA — it tells the solver that the stiffness of a material is not fixed, but depends on how fast you load it. This is the heart of viscoelastic behaviour. When you load a polymer slowly, the molecular chains have time to uncoil, slide past each other, and relax. The material feels softer. When you load it very quickly — as in a drop impact — the chains do not have time to relax. The material responds with higher stiffness. The standard fixed elastic modulus plus rate-dependent plasticity approach cannot capture this pre-yield stiffening. The Prony series does.

The Prony series represents the time-dependent relaxation behaviour using a sum of exponential decay terms. Each term has three parameters: a relative shear modulus fraction, a relative bulk modulus fraction, and a relaxation time tau. The relaxation time controls which loading rates that term governs. A short relaxation time — a small tau — activates at high loading rates, corresponding to the fast dynamics of a drop impact. A long relaxation time activates at slow loading rates, corresponding to quasi-static bending or sustained loads. Multiple terms covering a wide range of relaxation times together describe the full viscoelastic character of the material across the entire rate spectrum from creep to impact.

To calibrate Prony series parameters from physical testing, the most direct method is a stress relaxation test: apply a fixed strain to a specimen and record the decaying force over time. Convert force to stress using the specimen geometry, normalise by the initial stress to get the relaxation modulus as a function of time, and fit the Prony terms to that curve. Most FEA solvers — including Abacus — have built-in curve fitting tools that take relaxation test data directly and output the Prony series constants. Recording data at 0.1 second intervals may be adequate for capturing slower relaxation terms, but impact-rate calibration requires sufficiently dense early-time data to resolve the short-time relaxation response. Longer test durations are beneficial, not a limitation — they capture the longer relaxation times that govern quasi-static and creep behaviour and allow the complete relaxation spectrum to be characterised.

A key practical point on test coverage: the early data in a stress relaxation test — the first few seconds — captures the fast relaxation terms that govern impact-rate behaviour. The later data captures the slow terms that govern creep and sustained loading. Know which regime drives your application and make sure your test covers it.

Testing at multiple strain levels is important for polymers because they are often nonlinear viscoelastic — the relaxation behaviour changes with the strain level. Test at the strain levels that represent the actual loading in your simulation, not just at a single convenient amplitude. For chemical exposure effects, applying the chemical to the specimen face that is in tension during the relaxation test is far more discriminating than testing unstressed specimens — the chemical reaches the most vulnerable molecular locations and the effect is detected much sooner. This is particularly valuable for evaluating cleaning fluid compatibility and chemical stress cracking risk.

When implementing Prony series in Abacus, use the Star Viscoelastic, Time equals Prony keyword. Combine it with a Star Elastic definition as the base modulus — the Prony terms are fractional relative to that base. For elastomers and large-strain polymer components, combine with a hyperelastic base instead. The Analyzer flags viscoelastic materials without a Prony series definition as incomplete, and flags adhesive-type materials in explicit dynamic steps that appear to use only static properties.

DISPLAY GLASS, ADHESIVES, ELASTOMERS, AND FOAM.

Glass is linear elastic until fracture. No yield. Failure metric is maximum principal stress — not Von Mises. Young's modulus approximately 70 gigapascals, Poisson's ratio approximately 0.22. Fracture strength varies from 50 megapascals for annealed glass to 700 to 800 megapascals for pristine chemically strengthened cover glass, with a surface scratch potentially reducing that to 150 to 200 megapascals. Calibrate the failure criterion from biaxial flexure tests on production panels in the fielded surface condition — not pristine laboratory specimens. Model residual biaxial compression as an initial condition for tempered and chemically strengthened glass — omitting it can significantly underestimate the effective tensile strength the glass can sustain before the surface goes into net tension.

Pressure-sensitive adhesives like VHB are viscoelastic — significantly stiffer under impact than under static loading. Using static properties overpredicts deflection of bonded components and underpredicts load transmitted through the bond. Both errors are unconservative. Use Star Viscoelastic Time equals Prony with coefficients fitted to dynamic mechanical analysis data at impact-relevant frequencies, combined with a hyperelastic base.

Elastomers require hyperelastic formulations — not Young's modulus. Neo-Hookean for strains to about 50 percent. Mooney-Rivlin to about 150 percent — the most widely used industrial model. Yeoh for carbon-black-filled rubbers. Ogden and Arruda-Boyce for large-strain applications. Constants must be fitted to test data spanning the actual deformation modes — uniaxial alone is insufficient. Use hybrid elements — C3D8H, C3D10H — to prevent volumetric locking.

Foam requires a foam-specific constitutive model — Hyperfoam for recoverable cellular foam, Crushable Foam for permanently crushing foam — not low-stiffness linear elastic. Linear elastic captures only the initial cell-bending regime and misses the energy-absorbing plateau and densification entirely. Fit constants to dynamic compression test data — quasi-static datasheets underestimate foam stiffness during a drop event.

RATE DEPENDENCY, TEMPERATURE, AND WHAT THE ANALYZER CHECKS.

For impact, drop, and crash simulations, any material expected to enter plasticity should be evaluated for strain-rate sensitivity. If rate effects are not modelled, that assumption should be justified and documented — not left as an unchecked default. Many structural steels show significant yield strength increases at impact rates — the magnitude varies with grade, strain-rate range, and temperature, but increases of 20 to 50 percent are common for typical structural grades, and can be higher. Engineering polymers shift failure mode as well as magnitude. Good test correlation using static properties is often accidental — two errors compensating each other — not physically correct modelling. That kind of correlation does not transfer when the design changes.

Temperature: polycarbonate at minus 40 degrees is approximately 55 percent of room-temperature strength with failure mode shifted toward brittle fracture. Nylon with combined temperature and moisture effects can lose a factor of 4 to 6 in stiffness versus dry-as-moulded room-temperature data. If the qualification range includes cold or hot environments, temperature-dependent property tables are required.

The Analyzer Recommendations tab checks: missing density on any material — always flagged as error. Density magnitude inconsistent with detected unit system — cross-checked against material library. Rate-dependent plasticity absent in explicit dynamic steps — flagged for metals and engineering polymers separately. Viscoelastic without Prony series definition — flagged as incomplete. User material UMAT or VUMAT — flagged as cannot-validate. Johnson-Cook with redundant separate rate-dependent definition — double-counting flagged. Damage initiation criteria inconsistent with the material type.

The Materials tab total assembly mass computed from mesh volumes times densities is one of the most powerful quality checks available. Compare it to the physical product weight. A discrepancy greater than 10 percent demands investigation before submission. Missing part, wrong density, unit system error, section assignment problem. Find it before the solver does.

CLOSING.

When materials are right, everything else has a fighting chance of being right too. When they are wrong, no mesh density, no contact formulation, no solver sophistication recovers from it.

When someone asks you in a design review why you believe the simulation correctly predicts drop survival, the strongest answers start with: let me show you the energy balance, and: let me walk you through the material models we used. When you can answer both of those with confidence, the simulation has earned its safety factor.

And if you have not yet read Part One — the nature of materials — it is there waiting. It will not change the keywords. It will change how you hear them.