Ask Mr. Smarty Plants

Allelopathy (negative effects on growth of other plant species from chemicals produced by another) is listed as strong to moderate for the roots of  Acer saccharum (Sugar maple) in an article, Potential Allelopath in Different Tree Species, by Kim Coder from the Warnell School of Forest Resources.  Pinus strobus (Eastern white pine) is on the same list with a slight allelopathic effect from its roots.  This may be one of the reasons you aren't able to grow grass under your sugar maples.  However, the fact that it is dry and very shady underneath the tree is probably the more serious barrier to growing many plants.

We can do a search in our Native Plant Database for plants that will tolerate dry soils and shade (less than 2 hours of sun per day) by doing a COMBINATION SEARCH and choosing Tennessee from the Select State or Province list, then 'Shade - less than 2 hours of sun per day' from Light requirement and 'Dry - soil does not exhibit visible signs of moisture' from Soil moisture.

Here are some possibilities for plants from that list that should work for you.  I wasn't able to find information, however, about native plants that withstand possible allelopathic effects of sugar maple roots so I can't be absolutely positive that this won't be a problem.  Also, you need to realize that you will have to provide some water at first to get these plants established.

Many sedges such as Carex blanda (Eastern woodland sedge) and Carex pensylvanica (Pennsylvania sedge), that are very grass-like, will do well in dry shade.

One grass that grows very well in the shade and is very attractive is Chasmanthium latifolium (Inland sea oats).  It does like a moderate amount of moisture, however, but perhaps your area would have enough.

Here are some other low-growing plants from the list that do well in dry shade.

Aquilegia canadensis (Eastern red columbine)

 Gaultheria procumbens (Checkerberry)

Hypericum prolificum (Shrubby St. Johnswort)

Pteridium aquilinum (Western bracken fern)

Salvia urticifolia (Nettleleaf sage)

Here are photos from our Image Gallery: 

Carex blanda

Carex pensylvanica

Chasmanthium latifolium

Aquilegia canadensis

Gaultheria procumbens

Hypericum prolificum

Pteridium aquilinum

Salvia urticifolia