Résumé
Analogies between thermal diffusion and optical propagation in metal optics [1] allowedto generalize transformation optics [2,3] to the field of thermal [4-7], hence expandingcloaking and mimicking principles to thermodynamics. As a result, thermal metamaterialssupported on homogenization techniques have been emphasized for the managementof heat flow.In this talk we first present our recent work on thermal metamaterials, including theoretical,numerical and technological aspects. Realistic applications are discussed withinthe framework of given objects to cloak or mimic. Heat conduction and thermal radiationare considered.The second part of the talk concerns the design of metamaterials. Homogenization andsingular perturbations problems in stratified media have been studied in [8,9]. These resultsare revisited and extended in the setting of both the heat equation and the equationsof linear elasticity.