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 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. Under uniaxial tension, we find that the bending rigidity along the axis of tension diverges with a different power law exponent beyond a stress-dependent length scale whereas the Young’s modulus in the orthogonal direction renormalizes to zero. As a consequence, for moderate tensions we find a universal nonlinear force-displacement relation and the universal Poisson’s ratio. For large tensions, in-plane fluctuations longitudinal with the axis of tension are suppressed and classical mechanics along this axis is recovered.