The present thesis aimed at investigating the relationships which exist between the microstructure of refractories and their thermomechanical properties, and especially, better understanding the microstructure key-points allowing to develop a non-linear mechanical behaviour. From the grain size distribution of industrial magnesia-spinel materials, used in cement rotary kilns for their thermal shock resistance, simpler two-phase materials, composed of a magnesia "matrix" and spinel inclusions, were elaborated with different spinel contents. The thermal expansion mismatch between spinel and magnesia induces, during cooling, matrix microcracking around the spinel inclusions. The experimental part allowed to clarify, and quantify, the thermal damage occurrence during the cooling stage within these magnesia-spinel composites, in relation with their spinel inclusions content. Then, the influence of this thermal damage on the non-linearity of the mechanical behaviour of these composites was studied. The main objective of the numerical part was to build a consistent 3D FEM model able to well depict the microcracks occurence within these magnesia-spinel materials during a uniform temperature decrease beginning at high temperature (stress-free state) and able to provide, after this cooling step, a macroscopic non-linear mechanical behaviour. The design of simple, but quasi-isotropic, Representative Volume Elements (R.V.E) by periodic homogenisation, and the use of an anisotropic damage model, with a regularisation method, have allowed to simulate, locally, the matrix microcracking around the inclusions during cooling, and the damage growth in the volume during a subsequent tensile test. Moreover, the global evolutions of homogenised simulated parameters, during both the cooling stage and the tensile test, were in good agreement with previous macro-scaled experiments results.