15.01.2026 – The Neuber Correction
Imagine this scenario: we have built a huge model, that has contacts and even some parts that can undergo plasticity and we have therefore also used a non linear material model for those parts.
The calculation took few hours, so we have run it over night, we got the results, we checked them and then, disaster (!), in one of the parts that we did not expect to have plasticization, actually the yield limit of the material is widely overcome, maybe even by three times!
What could we do in such a case? Well, the first thing that jumps in mind is to apply a non linear material model also to the parts that have exceeded the elastic limit and then to re-run the model; but now it might take even longer, due to the additional complexity we have just introduced (another “non linearity”) and it might show that, even with the stress mitigation effect given by plasticization, the part has to be anyway redesigned.
Therefore, before acting without thinking, we could use the “Neuber Correction”, or Neuber Plastic Strain Method, using the results already obtained from our model; this way we can at least have a first idea if the part has some hopes to survive into its plastic range or if even the elongation at failure is overcome and therefore a redesign is required.
The method has some limitations:
- The finite element mesh should be fine enough to accurately predict the actual peak stress at the features
- The material should be ductile enough to allow for local redistribution
- There must be enough local material at a lower stress level to allow for local redistribution
- The stress field should be largely linear, or uniaxial in nature.
Even if all those hypotheses are not respected, it is anyway worth trying to apply it at our “desperate” case and then evaluate weather to proceed with the new calculation accounting for a non linear material model or to go directly into the redesign process.
The method is applied as follows:
a) the linear peak stress has to be evaluated (this is the result of our model, so it is already available) and with this value the strain energy is calculated (this is the area of the read triangle in the graph):
E = ½ · σel · εel
b) the constant strain energy curve is plotted (this is an hyperbole – blue line in the graph)
c) the actual stress-strain curve of the material is plotted (green line in the graph); here we have considered a bi-linear material, but the Ramberg-Osgood model can be also used
d) the intersection between the material curve and the constant strain energy curve is identified: the yellow triangle has the same area as the red triangle (for obvious reasons) and therefore the stress/strain at the intersection point would generate the same strain energy as if the material was again linear, but with a much smaller Young’s modulus
e) the values at the intersection point can be taken as a first approximation of what we could expect if we re-run the FE model using the same bi-linear material behavior.
Because in reality the area below the bi-linear stress-strain curve is bigger that the area of the yellow triangle, this method is deemed to be conservative.
