ESTIMATION OF NON-LINEAR STRESS FROM LINEAR ANALYSIS

[StressMan2506]

Fellow Stress Engineers:

Some time ago I saw (in a calc file) a method for estimating non-linear stress from linear finite element analysis. I remember the method but did not take note of any references, so I am reluctant to put it forward myself.

It is based on the assumption that the linearly calculated unit strain energy (1/2*f^2/E) can be equated to the non-linear value (the area under the non-linear curve). Considering the attachment, this condition is achieved by calculating a non-linear stress/strain pair such that the two hatched areas are equal.

Clearly, there would be differences in strain energy distribution between similar bodies stressed linearly and non-linearly, but I’ll go along with the assumption of equal strain energy levels at a given point in the absence of performing a non-linear analysis.

Can anyone supply a reference to this method?

Thanks in anticipation.

 

[rb1957]

i guess it's a scientific way of guessing ... sure there's some logic (equating strain energy) but there're holes enough to drive a bus through ... the plastic strin energy requires larger strains, how is this accounted for ?

to be really scientific, i think you could define a boundary and say that the effects of local plasticity are not felt by the strcuture remote to this boundary. then you could do a strain energy calc within the boundary (from the linear FEA) and then infer a plastic stress desitribution within the boundary that has the same strain energy.

sounds like doing NL FEA would be easier/quicker/"better" ...

 

[StressMan2506]

Thanks rb1957. The method inherently yields larger strains; to match areas, the non-linear strain is further along the axis than the linear one.

In the case I'm working with, I think a lower max. stress would be found with better modelling without going non-linear...

 

[rb1957]

yees, clearly plasticity reduces the maximum stress, which you can justify using the stress/strain curve, and develop larger strains.

my point (about accounting for these larger strains) was meant as i was picturing you looking at the strain energy at the edge (or at the peak stress) locally and justifying a reduced stress from teh stress/strain curve, but not accounting for how the surronding material accommodates these larger plastic strains.

thus i suggested looking at a larger volume of the part, where in reality the larger plastic strains are reacted by internal stresses ... much like the J-integral for crack tip stress intensity.

 

[Taz99]

What I think you are trying to do is account for the effect of either a stress concentration, or a stress gradient due to a bending moment to reduce a peak stress shown in your FE model.

However, I think you have to be careful with taking a single stress strain pair and using the approach you have proposed as it can be non conservative, consider the case of a single load path uniform cross section with a pure axial load applied. If you extract your stress strain pair and then do your calculations by equating the areas under the stress-strain curves to show the stress is 10% lower (for example) this is incorrect and unconservative.

I would think there would be a way to use a pair of stress-strain points to give you information about the stress gradient present in your area of interest and then compare total energy in the section to an allowable energy.

One way that I have used is to extract the free body forces and moments from the FE model at the centroid of a cross section and then followed Bruhn chapter C3 to calculate the ultimate strength in combined axial stresses and plastic bending.
This method also solves the problem of stress concentrations as they are ignored at ultimate in hand calculations.

 

[StressMan2506]

Thanks, Taz99. The problem has arisen from representing load input via a Nastran RBE.; we have a pair of unrealistic point moments. I am going to propose a simple re-modelling of the area.

 

[mcclain]

The method you are using is applicable in situations whereby your stress is a "secondary stress".
Per ASME "secondary stress: a normal stress or shear stress developed by the constraint of adjacent material or by self-constraint of the structure. Its basic characteristic is that it is self-limiting. Local yielding, minor distortions, and concrete cracking can satisfy the conditions that cause the stress to occur, and failure is not to be expected. Examples are general thermal stresses, bending stress at a gross structural discontinuity, and stresses induced by concrete shrinkage and creep."
Neuber and Glinka each have developed methodologies which accomplish what you are doing. Glinka's method is very similar to you method. These methods are termed "plasticity correction" when used to determine strains for a strain based fatigue assessment.
A big however is that the methods presuppose that the elastic stresses include the effects of elastic stress concentration.

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[StressMan2506]

Thanks, mcclain. I am familiar with Neuber's method, presented in Roark 7 and I am aware that it is for cases where the beyond-elastic-limit stress arises from a stress concentration. I did not know of Glinka's method but you state that that too is valid for stress concentration cases. Unfortunately, my case arises from unrealistically high point moments in an FE analysis.