Reliable shade plants are hostas, ferns, astible. Check your local nursery to see how they fit in your climate zone. If you want some height to soften your concrete foundation, if applicable, you will need to widen the area.

The Liriopes or Ophiopogons would do great for you. Dwarf Mondograss (Ophiopogon japonicus 'Nana') spreads out, looking like a gorgeous turfgrass. Only it grows under the heavy shade of trees where no grass will grow!

I'm talking about the DWARF cultivar, not the species. 'Nana' will never grow any taller than 3 or 4 inches, tops. Mow it once a year to get rid of the winter burn. ;-)

I would post your question on the Texas Gardening Forum. I've tried both hostas and astilbe in DFW and have not been thrilled. Slugs devour hostas, and I think astilbes don't like our heat. Dwarf to medium size nandina would work as they grow more upright rather than out and up. Aucuba might work - they can get large but grow very slowly and can be pruned occassionally. Add in for interest perennials like holly fern, autumn fern, Texas Gold Columbine, Helebores, dwarf hydrangea, purple oxalis, veriegated flax flower, pigeonberry, bletilla, the list is endless. But, for low maintenance, I would try to stick with Texas natives and well adapted plants. Google "Texas Smartscape" for some more very good Texas plants. Best of luck.
Debi