# Stress concentrations in elongated sample in tension (p p p)

Hi,

I am running some simple tensile tests on an elongated (200x10x5) specimen with fix deform in the x. I was testing to see if there were any stress concentrations at the root or tip of the elongated sample. Given that the boundary conditions are periodic I would not expect concentrations. To check for concentrations I create three regions (root, middle, tip) and get the px term in each region, divided by the volume, to get the stress in that region. I think get the slope of stress, strain to get a modulus in each region:

stress root: 167
stress middle: 137
stress tip: 149

This averages to a modulus of 141 (based on the end regions being 10% of the volume each), which is close to the total modulus using pxx. But why am I see concentrations at the root and tip? Is this boundary effects? I think not as it is periodic, but still confused.

Thanks

Liam

saintvenant.txt (4.28 KB)

Hi Liam, I’m not familiar with the EAM pair style’s implementation. But my guess is that because EAM is a many-body potential, the virial is computed not from the individual forces, but using the total force on each atom, \vec{F} \otimes \vec{r}. This would end up favoring the contribution of the atoms near the boundaries of the unit cell, where |\vec{r}| is largest. The total virial stress of the system would be correct, but this is one of the cases where computing a local virial contribution from a region may not be so useful.

Let me know if it makes sense to you.

Giacomo

The PBC or absolute atom positions should not have any effect on per-atom stress. The reason is that EAM potential is a function only of relative positions. We explain this further in the associated paper (see compute stress/atom doc page).

The small effect you are seeing may be statistical fluctuations or it may be an artifact of how you are driving the system.

I suggest doing a test of a fully equilibrated case, no fix deform, remove all unnecessary stuff. Use ave/chunk to generate 1D stress profiles.

Thanks to all of you for the advice.

This makes sense Dr. Thompson. I did a test without the deform and fixed my region command and it cleared up the findings. The results are now as expected.

Much appreciated,

Liam