Corded pettis were a sort of pre-hoop skirt support. 1840-50s mostly. (even so, I do wear mine for 1860s events) I wear one or two plain, full gathered petticoats over the corded. It gives quite a nice bell shape to skirts. Much less bothersome than my cage hoop!
For the material, I use white cotton muslin. Cording is Sugar 'n' Cream cotton cording. The cords are sewn into tiny channels between the fabric and the facing with a zipper foot. Quite tiresome and time consuming, but the results are worth it!