# Stress-Strain Graph Under Uniaxial and Biaxial Strain

I was going through a recently published journal paper by ACS (Applied Nano Materials) about gas separation using nanoporous Graphene.
DOI No. - https://dx.doi.org/10.1021/acsanm.0c02340
Supporting Information - https://pubs.acs.org/doi/suppl/10.1021/acsanm.0c02340/suppl_file/an0c02340_si_001.pdf

I'm quoting the exact part where I'm facing some problems-

Figure 2 shows the stress-calculated strain curves of graphene under uniaxial and biaxial strains. Herein, nominal strain and stress are used, which are defined as the length change divided by the original length and the tensile force divided by the original area of cross-section, respectively (nominal thickness of 3.4 Å is adopted).

Figure 2a shows that the mechanical responses of nanoporous graphene stretched along the armchair direction become distinct from that along the zigzag direction with the increasing strain, resulting from the strain-induced symmetry breaking. The strain to failure of this nanoporous graphene loaded along with the armchair and zigzag directions are 11 and 17%, respectively, which defines the maximum strains that can be applied to the structure. In addition to uniaxial strain, we also investigate the elastic responses of biaxial strain and the strain to failure can also exceed 10% (Figure 2b). Considering the structural stability based on these investigations, we explore the gas separation performance of nanoporous graphene under uniaxial and biaxial strains below 10%.

However, I understand that this is a Stress vs Strain graph. But I have some doubts regarding this -

1. What they mean by uniaxial and diaxial strain
2. What exactly they mean by armchair direction and zigzag direction
3. Lastly, it'll be very helpful for me if one can explain the graph clearly (I'm getting a vague understanding about that)
• AC and ZZ: commons.wikimedia.org/wiki/File:Graphene_edge_names.svg To find the zig-zag direction find a direction where you can move in almost a straight line, with only a small alternating left-right-left-right zigzag motion. Perpendicular to that is the armchair direction where you have two atoms in a straight line, then a larger jump left-right, then two atoms in a straight line... It looks like hexagonal armchairs where people are seated looking alternately to the left and to the right of the direction of motion.
– uhoh
Dec 12 '20 at 1:52
• I've always assumed that in the honeycomb net context "uniaxial strain" is strain in either AC or ZZ direction onlybut not both, and that biaxial strain in this context means strain in both AC and ZZ directions but not necessarily the same amount. If it's the same in both I believe it's called "uniform strain" or "equi-biaxial strain" but I don't know for sure. ncbi.nlm.nih.gov/pmc/articles/PMC4678326/figure/f1 In that image $Exx$ is in the AC direction and $Eyy$ is in the ZZ direction.
– uhoh
Dec 12 '20 at 2:00
• Thanks, @uhoh...you helped me a lot...Those answers cleared all my doubts...😊😊😊 Dec 12 '20 at 2:35
• That's great! But let's wait for some confirmation from others. I'm no expert in this, it's just my current understanding.
– uhoh
Dec 12 '20 at 3:44
• Sure!!!...but I think your understanding is right as it successfully explains the graph as well as the results...😊😊😊 Dec 12 '20 at 7:32