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We here focus on only one graphene ring and examine to which stress tensorcomponents the E2g and the A1g vibration mode of graphene correspond. Thesemodes are typically related with the G-peak and the D-peak, respectively, andare strongly related to the stress distribution along the specimen. We adoptthe theoretical framework of Admal and Tadmor ([1]) for the macroscopicdefinition of the Cauchy stress tensor and we introduce into this framework theE2g and the A1g as appropriate perturbations. We use these perturbations to thestress tensor expression and evaluate which stress tensor components arerelated to each vibrational mode. This approach, though qualitative in nature,incorporates all the main physics and reveals that E2g and A1g vibration modesshould be related to shear as well as axial stress components when graphene isat rest (i.e. no external applied loading). To bring our framework closer tomore concrete results, we evaluate the instantaneous Hardy stress tensor for apair potential which correspond to the E2g and A1g modes at rest. Our analysisexpands to take into account an applied external tensile field. Taking thearmchair direction to be along the x-axis, when tension applies along thearmchair direction, it is the axial $\sigma$11 stress component which dominatesover $\sigma$12, $\sigma$22, which are of smaller order. When tension is alongthe zig-zag direction, it is the axial $\sigma$22 stress component thatdominates over $\sigma$12, $\sigma$11. When tension is at an arbitrarydirection between the armchair and the zig-zag direction, all stress componentsare of the same order and should all be taken into account even at smallstrains.

Stress intrepretation of graphene E-2g and A-1g vibrational modes: theoretical analysis