  We propose a predictive model of the turbulent burning velocity $S_T$ in
homogeneous isotropic turbulence (HIT) based on Lagrangian statistics of
propagating surfaces. The propagating surfaces with a constant displacement
speed are initially arranged on a plane, and they evolve in non-reacting HIT,
behaving like the propagation of a planar premixed flame front. The universal
constants in the model of $S_T$ characterize the enhancement of area growth of
premixed flames by turbulence, and they are determined by Lagrangian statistics
of propagating surfaces. The flame area is then modelled by the area of
propagating surfaces at a truncation time. This truncation time signals the
statistical stationary state of the evolutionary geometry of propagating
surfaces, and it is modelled by an explicit expression using limiting
conditions of very weak and strong turbulence. Another parameter in the model
of $S_T$ characterizes the effect of fuel chemistry on $S_T$, and it is
pre-determined by very few available data points of $S_T$ from experiments or
direct numerical simulation (DNS) in weak turbulence. The proposed model is
validated using three DNS series of turbulent premixed flames with various
fuels. The model prediction of $S_T$ generally agrees well with DNS in a wide
range of premixed combustion regimes, and it captures the basic trends of $S_T$
in terms of the turbulence intensity, including the linear growth in weak
turbulence and the `bending effect' in strong turbulence.
