Thermomechanically coupled theory in the context of the multiphase-field method

The modeling and simulation of microstructure evolution is usually subject to the multiphase-field method. In this context, thermomechanical coupling is often neglected, even when non-isothermal phase transformations are considered. Using a simplified example, the present work shows that this assumption is not justified for small strains and small strain rates with respect to a non-vanishing coefficient of thermal expansion. To this end, both a thermomechanically coupled and a thermomechanically weakly coupled theory are briefly revisited. The difference between the coupled and the weakly coupled theory regarding the growth of an inclusion is discussed. The considered elastoplastic inclusion, subjected to eigenstrains, is embedded in an elastoplastic matrix under load. It is shown, that the weakly coupled theory overestimates the growth of the inclusion, and, thus, the volume concentration, compared to the coupled theory. Moreover, only the application of the coupled theory reflects a load-induced anisotropic growth of the inclusion, which exhibits an isotropic material behavior, due to non-vanishing uniaxial Neumann boundary conditions. In addition, it is shown that the smaller the heat conduction coefficient, the more pronounced the anisotropic growth of the inclusion.