Each arapaima scale is a laminate. The outer layer is heavily mineralised and hard; beneath it lie sheets of collagen fibrils arranged in a rotating, plywood-like stack known as a Bouligand structure. Hardness stops the tooth entering; the ductile inner layers spread and absorb the load, so cracks are deflected between plies rather than running straight through.
Engineers at the University of California tested this directly, pressing piranha teeth into arapaima scales. The tooth failed before the scale was penetrated. The scales are also imbricated, overlapping so that flexing the body does not open a gap in the armour, which is why the design attracts interest from people building flexible protective materials.
Less certain is how much of the arapaima's real-world protection comes from the scales themselves and how much from sheer size, since a fish of two metres is beyond the reach of most predators regardless of its skin.