In the present paper a theory describing effects of strong flame stretch on turbulent flame propagation [L. P. H. de Goey and J. H. M. ten Thije Boonkkamp, "A flamelet description of premixed laminar flames and the relation with flame stretch," Combust. Flame 119, 253 (1999)] is extended to volume averaged quantities and validated with direct numerical simulation (DNS). The extended theory describes the fuel consumption rate in terms of subgrid scale contributions connected to propagation effects including strong flame stretch. In case there is no preferential diffusion present, it is predicted that the total consumption rate is not affected by local stretch at all. Then the total consumption is described by the unstretched mass burning rate multiplied with the flame surface density. DNSs of turbulent flame kernels have been carried out in order to support the results from the theory. The chemistry is described by application of the flamelet generated manifold technique. The strong stretch theory is shown to be valid up to realizations in the thin reaction zone regime by three independent methods. The local effects of stretch are described, evaluated, and interpreted. Locally the mass burning rate changes by fuel leakage tangential to the flame, but this has no integral effect. The method can be used for subgrid scale modeling of turbulent flame propagation.