  We here focus on only one graphene ring and examine to which stress tensor
components the E2g and the A1g vibration mode of graphene correspond. These
modes are typically related with the G-peak and the D-peak, respectively, and
are strongly related to the stress distribution along the specimen. We adopt
the theoretical framework of Admal and Tadmor ([1]) for the macroscopic
definition of the Cauchy stress tensor and we introduce into this framework the
E2g and the A1g as appropriate perturbations. We use these perturbations to the
stress tensor expression and evaluate which stress tensor components are
related to each vibrational mode. This approach, though qualitative in nature,
incorporates all the main physics and reveals that E2g and A1g vibration modes
should be related to shear as well as axial stress components when graphene is
at rest (i.e. no external applied loading). To bring our framework closer to
more concrete results, we evaluate the instantaneous Hardy stress tensor for a
pair potential which correspond to the E2g and A1g modes at rest. Our analysis
expands to take into account an applied external tensile field. Taking the
armchair direction to be along the x-axis, when tension applies along the
armchair direction, it is the axial $\sigma$11 stress component which dominates
over $\sigma$12, $\sigma$22, which are of smaller order. When tension is along
the zig-zag direction, it is the axial $\sigma$22 stress component that
dominates over $\sigma$12, $\sigma$11. When tension is at an arbitrary
direction between the armchair and the zig-zag direction, all stress components
are of the same order and should all be taken into account even at small
strains.
