  In order to design tougher materials, it is crucial to understand the
relationship between their composition and their resistance to fracture. To
this end, we investigate the fracture toughness of usual sodium silicate
glasses (NS) and complex calcium--silicate--hydrates (CSH), the binding phase
of cement. Their atomistic structure is described in the framework of the
topological constraints theory, or rigidity theory. We report an analogous
rigidity transition, driven by pressure in NS and by composition in CSH.
Relying both on simulated and available experimental results, we show that
optimally constrained isostatic systems show improved fracture toughness. The
flexible to stressed--rigid transition is shown to be correlated to a
ductile-to-brittle transition, with a local minimum of the brittleness for
isostatic system. This fracture toughening arises from a reversible molecular
network, allowing optimal stress relaxation and crack blunting behaviors. This
opens the way to the discovery of high-performance materials, designed at the
molecular scale.
