Indeed; quite generally, it is possible to theoretically relate the Cauchy stress tensor with a 'chemical potential tensor', as can be see from (e.g.): M.A. Grinfel'd, "Stability of heterogeneous equilibrium in systems containing solid elastic phases", Doklady Earth Sci. Sect., 1984, 21-24, Engl. transl. from: Doklady Akademii Nauk (Proc. Russian Acad. Sci.), 265(4), 1982, 836-840.