In a tension test, the area under the true stress - true strain curve is the work done per unit volume (the specific work). We also know that the area under the load-elongation curve represents the work done on the specimen. If you divide this latter work by the volume of the specimen between the gage marks, you will determine the work done per unit volume (assuming that all deformation is confined between the gage marks). Will this specific work be the same as the area under the true stress - true strain curve