A numerical study on the physical couplings of a geometrically linear thermo-chemo-mechanical model

Physically coupled models are used in various research fields to solve problems concerning the interaction of solid materials with thermal, chemical or electrical boundary conditions. If beside the mechanical fields two or more additional fields (e.g. temperature and concentration) have to be taken into account, the determination of the impact on the mechanical fields (e.g. stress and yield strength) and the influence of the boundary conditions leads to an ambitious task. To deal with this issue, a thermo-chemo-mechanical model using a geometrically linear theory and a thermodynamically consistent derivation, is presented. The model is specified for linear elastic isotropic solid materials. A fully coupled set of partial differential equations is obtained. A Finite Element implementation using the User Element subroutine of ABAQUS is performed. A detailed description about the steps necessary to derive the corresponding element formulation is provided, thereby supporting the development of user-defined elements. The user-defined element is used for a series of simulations involving submodels with up to seven different combinations of active fields including thermo-chemical, thermo-mechanical and chemo-mechanical couplings. Three sets of boundary conditions are considered, leading to closed and open systems. This procedure, which is exemplified in one- and three-dimensional examples, enlightens strong and weak couplings and outlines the mechanical role on the interaction between the solid material and the chemical environment. Additionally, the implications of a geometrical linearization on the interpretation of the concentration is illustrated. • A UEL incorporating a geometrically linear thermo-chemo-mechanical model. • FE simulations with thermo-chemical, thermo-mechanical and chemo-mechanical submodels. • Elucidating the shortcoming of a geometrically linear theory. • Documentation of the UEL formulation including element residuals and tangents.