Coupled thermoelastic theory and associated variational principles based on decomposition of internal energy

A new framework of coupled thermoelasticity is constructed in this paper based on a decomposition of internal energy into free internal energy and dissipative energy. Fundamental equations (i.e. divergence and gradient equations, constitutive equations including evolving laws) along with proper boundary conditions are all included in this framework, from which two novel dual-complementary variational principles with explicit functionals are proposed. Unlike the conventional thermoelastic theory, the proposed variational principles for thermoelasticity are established without the approximate assumption of small temperature changes. To verify the usefulness of the proposed variational principles in simulating coupled thermoelastic problems, a coupled thermoelastic example is numerically implemented.