Some years ago I cut out circles of felt and sewed them onto two boys sweatshirts for my two boys Christmas gifts. I embroidered animal shapes on each one, probably with three strands of embroidery floss and whipstitched around the circle's edges. I remember washing them in the washing machine many times and they held up very well. I don't know what kind of felt it was, but it must have been polyester, the way that it held up. I did not do anything special as far as backing on the felt.