Statistical mechanics of 2D sheets under uniaxial tension

Atomically thin sheets, such as graphene, are widely used in nanotechnology. Recently they have also been used in applications including kirigami and self-folding origami, where it becomes important to understand how they respond to external loads. Motivated by this, we investigate how isotropic sheets respond to uniaxial tension by employing the renormalization group. Previously, it was shown that for freely suspended sheets thermal fluctuations effectively renormalize elastic constants, which become scale-dependent beyond a characteristic thermal length scale (a few nanometers for graphene at room temperature), beyond which the bending rigidity increases, while the in-plane elastic constants reduce with universal power law exponents. For sheets under uniaxial tension, we find that beyond a stress-dependent length scale the Young’s modulus in the orthogonal direction scales with a different exponent. In addition, for moderate tensions we find a universal nonlinear force-displacement relation. For large tensions, in-plane fluctuations longitudinal with the axis of tension are suppressed and classical mechanics along this axis is recovered.