Amyloid fibrils are ubiquitous proteinaceous aggregates occurring in vivo and in vitro, with an invariant structural fingerprint at the molecular length scale. However, interpretation of their mesoscopic architectures is complicated by diverse observable polymorphic states. We here present a constitutive model for amyloid fibrils based on the minimization of the total energy per fibril. The model is benchmarked on real amyloid fibrils studied by atomic force microscopy. We use multistranded ss-lactoglobulin amyloid fibrils as a model system exhibiting a rich polymorphism. The constitutive model quantitatively recapitulates the main mesoscopic topological features of amyloid fibrils, that is, the evolution of fibril periodicity as a function of the ionic strength of the solution and of the fibril width. A universal mesoscopic structural signature of the fibrils emerges from this picture, predicting a general, parameter-free law for the periodicity of the fibrils, that depends solely on the number of protofilaments per fibril. These predictions are validated experimentally and conclusively highlight the role of competing electrostatic and elastic contributions as the main players in the establishment of amyloid fibrils structure.