Tough plants for dappled shade?

Ok, thinking ahead a few years here but I'd like to plant this patch with tough, low-growing plants that are happy in dappled shade. In the tyre is my sambucus nigra 'black lace' that went in yesterday.

In the long run I want the area around it to be somewhere my dogs can lie in the shade and chill out if they want to (and they will!) but I don't want bare earth there and I definitely don't want grass!

This spot does get full sun most of the day so planting for now will be different (unless there is something suitable that's happy in either condition), but once the elder has grown a bit it'll be dappled shade. It's about a 6x3ish area to be planted, there will be another log-edged shasta daisy bed from the fence post on the right.

 

They would lie on them! All big dogs but mainly it'll be River, she likes lying in these sorts of places. She's small lab sized. So it's sort of a tough carpet effect I'm after.

It will of course be fenced off until everything is established - it already is to allow the elder to bed in without being broken.