The fracture mechanism of amorphous materials, which are of crucial importance in various fields of engineering, remains a long-standing fundamental problem of science despite intensive efforts over the years. On the basis of a novel rheological model of fracture, we demonstrate that nonlinear behaviour associated with fracture is a consequence of the coupling between density fluctuations and deformation fields: shear-induced enhancement of density fluctuations is self-amplified by the resulting enhancement of dynamic and elastic asymmetry between denser and less-dense regions. This positive feedback may be the origin of fracture. We propose novel criteria for the onset of mechanical instability, extending from ductile to brittle fracture. Their validity is checked by comparing them with numerical solutions of our model and existing experimental results of metallic and polymeric glass formers. The criteria enable us to predict and design fracture behaviour of materials from the pressure dependence of their viscoelastic properties.