This Letter introduces an ab initio study of the full activation-volume tensor of crystalline defects as a means to make contact with mechanical response experiments. We present a theoretical framework for the prediction of the internal friction associated with divacancy defects and give the first ab initio value for this quantity in silicon. Finally, making a connection with defect alignment studies, we give the first unambiguous resolution of the debate surrounding ab initio verification of the ground-state structure of the defect.