Let's review a bit. The aspis was a dome shaped shield. Domes are supremely suited to transferring force applied to their face around to their base. On a micro-scale this explains why pieces of armor like the Napoleonic cuirasse at right are curved. Because some portion of force applied to a curved face is transferred to the area around it, a curved plate makes stronger armor than a flat plate. 
A blow to a curved plate will compress the metal around the site of the impact as in figure A. An impact on a flat or bowl shaped plate, as in B, will stretch the adjoining metal rather than compressing it. Thus only the tensile strength of the metal resists the impact. Compressive strength is always higher in metals than tensile strength.
So on a small scale we can see that curvature helps resist impact. This is probably not a driving force behind the evolution of the aspis because the front of the dome, precisely where we would want this property maximized is flattened.
Once again we must seek a reason for the flattened dome shape.
