Spontaneous Tilt of Thermalized Elastic Sheets

Through molecular dynamic simulations and theoretical analysis, we show that a thermalized elastic sheet clamped on one edge spontaneously tilts out of the plane of clamping, hence breaking the inversion symmetry of the system. For a given temperature, a rectangular sheet only tilts if its aspect ratio is sufficiently large. Using the thermalized membrane as a reference state, we show that tilt is a type of buckling instability. We derive the critical aspect ratio for tilt as a function of temperature by analyzing the in-plane stress and strain of the elastic sheet due to clamping.