We study homogenization of G-equation with a
ow straining term (or the strain G-equation) in two dimensional periodic cellular
ow. The strain G-equation is a highly non-coercive and non-convex level set Hamilton-Jacobi equation. The main objective is to investigate how the
ow induced straining (the nonconvex term) in
uences front propagation as the
ow intensity A increases. Three distinct regimes are identified. When A is below the critical level, homogenization holds and the turbulent
ame speed sT (effective Hamiltonian) is well-defined for any periodic
ow with small divergence and is enhanced by the cellular
ow as $s_T \ge O(A/logA)$. In the second regime where A is slightly above the critical value, homogenization breaks down, and $s_T$ is not well defined along any direction. Solutions become a mixture of
fast moving part and a stagnant part. When $A$ is sufficiently large, the whole
ame front ceases to propagate forward due to the
flow induced straining. In particular, along directions $p = (1; 0)$ and $(0;1)$, $s_T$ is well-defined again with a value of zero (trapping). A partial homogenization result is also proved. If we consider a similar but relatively simpler Hamiltonian, the trapping occurs along all directions. The analysis is based on the two-player di erential game representation of solutions, selection of game strategies and trapping regions, and construction of connecting trajectories.