Computational homogenization for heat conduction in heterogeneous solids

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A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials (2017, methodology): “thermal [131,138], thermo-mechanical [132], electro–magneto-mechanical [139–143], diffusion [144], liquid-phase sintering [145], and problems involving chemical couplings [146].”
Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models (2016, background): “For example, in [91,92,107,118] the problem is addressed under the hypothesis of scales separation, requiring the use of a uniform temperature field in the micro-scale mechanical problem.”
Routes for Efficient Computational Homogenization of Nonlinear Materials Using the Proper Generalized Decompositions (2010, background): “So we can see that as in [36], the data of the macroscopic problem are composed with the macroscopic temperature and the gradient of temperature.”