the neck appears numerically when the slope of the behavior law is lower of the stress value. With explicit code the wave propagation will help by localising the neck area by creating the instability, for implicit code the localization comes from other instabilities mesh, accuracy, type of elements ... 

That's right. The neck formation is not based on any theoretical equation, In fact it is quite interesting question, especially for implicit (or more precisely, static) solver. Theoretically, for perfect mesh and perfect accuracy of computation, the stress will be never localised and necking will never occur. So, if you will make too good model, you will never get correct result (necking)!!!

This phenomenon is similar to the nonlinear simulation of buckling. A perfect model will never buckle, many people introduce initial geometrical imperfections to achieve buckling behaviour. In fact, for more complicated models, buckling is possible without imperfection because of numerical and mesh instabilities mentioned by Franck.

Thank you Dr. Frank and Dr. Iluk,

from my own experiences, the numerical prediction of the necking are very dependent to the values of the last three stress points in the tabular stress-strain curve implemented to the solution.

I also knew that the ABAQUS is trying to keep the stability conditions in the explicit solvers using the wave propagation theories where decreasing the area of the specimen locally is the result o this manipulations which is quiet accurate. 

i just wondered how ABAQUS is doing these manipulation and I thank Dr. Frank for his answer which clarifies it simply.

"when the numerically calculated stress value by constitutive model  is under the extrapolated stress value in the solution, ABAQUS tries to compensate this difference in the next increment where  ABAQUS decreases the area intentionally for the next increment to achieve the given stress values in some points.  stress wave propagation is used to locate the element where this localization necking should start. where if the solution is quasi static, the necking takes place in the middle element of the UTT test for example."

Am I right buddies?

Shahram,

"if the solution is quasi static, the necking takes place in the middle element of the UTT test for example"

How ABAQUS can know, where is the middle element of the UTT specimen? In quasi static simulation there is no stress wave propagation.

Artur

from the ABAQUS documentation, Explicit solvers use the stress wave propagation technique as far as I know, and it is not related to the quasi static or dynamic solution type. for UTT test, the middle element which i mean, is the element which is located geometrically in the middle of the gauge length (50 mm based on ASTM E517).

Soheil

thank you for your answer but there is not any discussion about the theoretical background of the necking itself. the problem is that what is the background of the necking in the ABAQUS explicit solvers and how ABAQUS indicates the location of the necking.

I and you know exactly where is the middle element, but that I've asked for is how the ABAQUS can know it?

And again - how the stress wave can propagate is quasi static solution, then there is no time? That is the speed of this wave in quasi static condition?

i think The location indication is related directly to the stability condition of the explicit solutions which is dependent to the element size and type, material type and deformation speed. these parameters directly affect the stress wave amplitude and frequency based on the formulations for the stability time determination for ABAQUS Explicit solutions in the Theory manual. But, how the wave propagates and how the damping phenomenon in the boundary conditions affect the wave are what i don't really know. i could not find any explanation about the way stress waves propagate in the material during the forming in the ABAQUS documentation but i have seen some articles also which have given a statement about the necking prediction by by ABAQUS using stress wave propagation.

Dear Friends

I wonder why unexpected necking occurs in a cyclic loading of a specimen in Abaqus!

I have not defined the necking, however I can see it during the loading. And interesting, this occurs only in cyclic loading not in tension loading!!!

can anyone help?