Liriope muscari, I would say.... I've got some here, a few different varieties, but I have to say they're not amongst my favourite plants...

Melissa.... you could have spicata there, I wouldn't know that one personally as I've not grown it, I believe it's considered invasive, but in your large garden that may not be a problem.... the muscari type is less vigorous and clump forming, which also means, as I have found, it's rather slow to establish.... I've grown it before at the base of a steep bank, and reasonably well too where they flowered, but in this garden here not so good, so it's probably my fault.... I grow 'Big Blue' and 'Ingwersens'... and 'Big Blue' is at least showing a bit more life, but both refuse to flower for me... I keep saying.. maybe next year...! I must have at least 20 plants along a border, as I made divisions last year....

...I think they're quite hardy, as I first became aware of them from a photo of a garden in New York City, some landscaping in a public park there or somesuch, and I thought how nice they looked...

...I'm glad you are happy with your plants, they are at least blooming...

I had some of my plant already in this bed where it has shown no sign of growing out of bounds, so I added some more a couple of days ago. The soil of the bed is amended, but it's surrounded by unimproved ground, where grass digs itself into the densest kind of slimy gray clay over rock, and that soil might serve as a barrier all by itself. My plants also enjoy the limiting effects of no summer water, which may discourage rampant growth.

Do liriopes like heat? Mine bloom for me regularly, and didn't appear in the least troubled by our latest summer, which I read was the hottest in 150 years. But you say liriope has flowered for you before.

I see interesting possibilities for liriope in my garden.

..maybe that's what they need Melissa, some decent heat...but yes they did bloom well enough in my last garden further south...about October time...

... I'll give mine another season and see what they do... they are recommended for shade here and tough places, and are supposed to be trouble free....and the arching leaves are quite elegant....

...roll on Spring...

You bet. But I want to see some winter first.

Liriope is very common here, and I do think of it as heat-loving, not just heat-tolerant. It is often unimaginatively used (and overused) hereabouts, and I grew up pretty much taking it for granted until I started looking at plants more carefully, and seeing it used well.

Here's a link to a photo I took a few years back of variegated liriope paired with Persian Shield at a local public park; I thought that was a very nice combo:

https://www.flickr.com/photos/96305364@N05/13658836103/in/datetaken/lightbox/

(That's an old Flickr account that I can't access anymore...)

Marlorena, it should be interesting to see if you get any growth/bloom with a future warm spell.

Virginia

Virginia, thanks. This would be a plant for the shade garden and woods, I believe. I'm caught between a desire to add variety to the woods, which can use it, and a wariness about adding an exotic and possibly invasive newcomer. The plant style would go well, but variegated liriope is calling to me, too, and that could be quite difficult to integrate into the woods as I imagine them. Possibly the shade garden or a transition area would be appropriate. Well, these are design considerations.

I have both pink and purple flowered liriope muscari to fill in hot, dry, shady areas under trees and they are excellent. Even after a spell of 40+ C, they never wilt or tip burn, or look chewed, although they receive little water other than rain. I find they are better than clivea, which can show some stress, or arthropodium cirratum, which is a snail magnet after rain, although the liriope and arthropodium do play nicely together. I am waiting for my DIL's clumps of variegated and white flowered liriopes to be big enough for me to nick a bit of each. I find also that they do not flower at the same time. The pink is blooming now, but the purple will not flower for another couple of months.