3. Why is this useful?

This video shows how an elastic–plastic analysis can support sound design decisions on a simple, familiar problem: a thin S235 steel plate with a small central hole, fixed at one end and pulled by a remote nominal stress at the other.

A basic linear-elastic calculation highlights the stress concentration around the hole, with von Mises stresses above the yield strength. That finding is common and expected, but by itself it does not tell us whether the part will fail in static service. Linear results ignore plastic redistribution, so peak elastic stresses can look alarming even when the actual load path is safe. If you must stay with an elastic assessment, you would need a recognised method such as stress categorisation in pressure-vessel codes (eg. [1]) or the plastic-notch-factor approach in the FKM Guideline [2]to interpret those peaks correctly.

Switching the material to a simple bilinear elastic–plastic law makes the picture clearer. For monotonic loading, isotropic and kinematic hardening give practically the same response, so either is fine. The analysis now reveals a small plastic zone around the hole while the rest of the section remains elastic. This is a useful, direct check: if only a small fraction of the net section is plastic at the design load, you have healthy margin against immediate plastic collapse.

Strain outputs become more informative once plasticity is modelled. Looking at elastic, plastic and total strain separately helps you judge local behaviour at the hotspot and the broader structural response. As a rough sense-check, you can compare the computed total strain with the yield strain and with the material’s elongation at fracture from a tensile test. Treat this comparison with care: tensile test elongation is measured over a gauge length and is not a pass/fail limit for local strains at a notch, but it does provide useful context for how severe the local deformation is likely to be.

A simple "load, unload, reload" cyclic elastic–plastic run adds value when you lack detailed cyclic data. Using a kinematic hardening model with a modest tangent modulus is a sensible default for steels, because it captures the Bauschinger effect and quickly shows whether the hotspot exhibits elastic shakedown or ratcheting. In our example the hotspot shakes down: after a small amount of first-cycle plasticity the subsequent cycles are effectively elastic at the chosen load range. That behaviour indicates safety against incremental plastic collapse and supports the static strength of the component.

With a bilinear, kinematic model, the local strain amplitude typically stabilises within a couple of cycles, which means you can take that stabilised amplitude forward into a simplified low-cycle fatigue check using a Strain–Life approach, applying a suitable mean-stress correction if needed. Keep in mind that reliable fatigue predictions still depend on having appropriate strain–life data for the material.

1. R. Rennert, E. Kullig, M. Vormwald, A. Esderts, and M. Luke, Analytical Strength Assessment for Machine Components, 7th ed., FKM-Guidelines, Forschungskuratorium Maschinenbau e.V., 2020. ISBN: 978-3-8163-0745-7.
2. CEN, EN 13445-3:2021 - Unfired pressure vessels - Part 3: Design, 12-May-2021, ICS 23.020.30 - Pressure vessels, gas cylinders. Directive 2014/68/EU, Mandate M/071, CEN/TC 54.