Metal plate beneath Linothorakes or Spolades

[PMBardunias]

Some vases show them standing freely, so I would assume they were fairly ridged, or at least enough so that they could support themselves.

In playing around with tube shaped things like a rolled doormat or single layer of rug, you'll see that it does not have to be all that rigid to stand up on end like some of the T-Y depictions. This same tube will flatten if you lay it on its side in manner just like that vase image. Of course the added scales and plates makes the need for support greater, but the general principle of standing on end yet collapsing on its side still holds true.