A Direct Numerical Simulation (DNS) dataset of a turbulent premixed propagating flame with an Arrhenius one-step chemistry in an input–output configuration is examined. Combustion takes place in the ‘corrugated flamelets’ regime. Heat release causes the flow volumetric dilatation rate to be positive over most of the computational domain, with associated positive strain rates normal to iso-scalar surfaces and both positive or negative strain rates tangent to them. The normal propagation of convex and concave iso-surface infinitesimal area elements produces stretching and reduction, respectively, superposed to tangential flow strain rate effects. The normal propagation speed of iso-surfaces increases monotonically from ‘fresh gases’ to ‘hot products’, which draws two adjacent ones closer; this contribution, due to both chemistry and molecular diffusive transport, is much greater than that of the normal flow strain, and enhances mixing and chemical conversion. Many aspects of turbulent premixed flames traditionally explained in terms of tangential strain rates can likely be well understood using the normal ones.