Coupling extended multiscale finite element method for thermoelastic analysis of heterogeneous multiphase materials

• A multiscale method for the thermoelastic analysis of heterogeneous materials.
• The additional coupled terms are added to the numerical base functions.
• The downscale computation can be easily performed by the numerical base functions.
• The accuracy and validity of the method are demonstrated by numerical examples.

A coupling extended multiscale finite element method is developed for the thermoelastic analysis of heterogeneous multiphase materials. In the method, the weak coupling of thermal and structure is considered and two sets of numerical base functions are constructed for the temperature and displacement fields, respectively. To improve the accuracy of the base functions, the periodic boundary conditions and the oversampling technique are adopted. Numerical results of several representative examples indicate that the proposed method can not only capture the fine scale information in the macroscopic computation but also recover the fine scale solution conveniently.