Topological constraint model for the elasticity of glass-forming systems

The elastic response of glass is one of its most important properties for a wide range of applications in architecture, transportation, information display, and healthcare. Unfortunately, there is currently no model to predict quantitatively accurate values of elastic moduli from the underlying network topology of the glass. Here we introduce a topological model to calculate the Young's modulus of glass in terms of the free energy density of rigid constraints in the network. The model shows quantitatively accurate agreement with glasses across a variety of compositional families. More remarkably, the variation of modulus with temperature can also be predicted by accounting for the temperature dependence of the constraints, including the approach to the viscoelastic region near the glass transition.