In the Mid-South region, turfgrasses Zoysia and Bermuda are better suited for our climate and require more than 6 hours of direct sunlight to prosper. On the other hand, Fescue will grow well in the shade of your trees and can eliminate those "undesirable bare ground areas" under the trees.
The Fescue family of grasses is the only grass that can be sustained year-round in heavily shaded areas. Fescue, regardless of variety, will thin out over time. That is why it is necessary to overseed periodically to increase turf density. The average period between seedings is 1 to 3 years, depending upon various factors such as sunlight, irrigation, and fertilization.