Generalized variational principles for thermo-chemo-mechanical coupling systems based on decomposition of internal energy

A novel theoretical framework of thermo-chemo-mechanical coupling problems is proposed in this paper based on a decomposition of the internal energy into the free internal energy and the dissipation energy. Fundamental equations (i.e., constitutive equations, divergence and gradient equations) along with corresponding boundary conditions are all included in this framework, on which a pair of dual-complementary Hu–Washizu type generalized variational principles (GVPs) with explicit functionals is established. Therein, two energy functionals complementing to each other are introduced for the first time. The newly developed GVPs treat all variables as independent ones, and some well-known variational principles in the literature can be reduced from them by setting some preconditions, which indicates that these variational principles share the same theoretical basis and shows the universality and adaptability of the present theory.