We get this question regularly. There is no groundcover, including grass, that withstands heavy paw traffic in shade. Most grasses do not like shade and those that tolerate it do not do so for heavy traffic. But there are many groundcovers that like shade. Experiment with these, but do not be tempted to plant non-native invasive species, such as English ivy. Some nurseries still stock invasive plants, so check which plants to avoid on the Home and Garden Information Center website. The best you may be able to do is to direct your dog to certain areas or paths by fencing or raised planting beds; rotate the areas if possible. Spread wood chips on the most heavily trafficked areas, or possibly stepping stones, bricks, etc.