Step 1
As I've said we won't use the Mesh Tool at all, only the Blend Tool (W) from start to finish. Grab the Pencil Tool (N) or the Pen Tool (P) (which one you prefer) and draw a shape like below on the left side of the wood stack. Fill it with 7% black and reduce the Opacity to 0%. Draw a smaller shape in the center and select white as the fill color.
With both shapes selected, go to Object > Blend > Blend Options and choose 13 Specified Steps then go back to Object > Blend > Make (Alt-Control-B). Set the resulting blend-group to Blending Mode Overlay.