Ceramic matrix composite materials are used for their high mechanical resistance to temperature (1000°C and more). Whatever the CMC family (oxide/oxide, carbon reinforcement, SiC reinforcement), these materials function through damage that occurs from the first stresses. For a large number of them, the elastic domain is almost non-existent. It is therefore necessary to propose a constitutive law model accounting for this damage and its effect on the mechanical behavior. We propose within the framework of this thesis to develop formalisms allowing to take into account phenomena hitherto treated in a phenomenological way:

- The friction caused during the closing of the cracks, responsible for the hysteresis observed during the load/unload cycles and also responsible for the restoration of the elastic moduli in compression;

- The tensorial character of the damage in certain families of CMC, which is currently modeled by a so-called pseudo-tensorial model without the exact tensorial formalism having been sufficiently developed.

The objective of the thesis is to develop solid physical formalisms that can lead to behavior laws that can be used in finite element codes while being compatible with current computing resources. In the case of complex problems, they may be used to validate and improve existing approaches.

These developments will be illustrated by the application to C/SiC materials (continuous fiber carbon reinforcement). The experimental data at ambient temperature and at temperature will be partly obtained within the laboratory, in particular by in situ tests under X-ray tomography, but also through a collaboration already initiated with a university laboratory (Mines d'Albi).

Finally, these developments of constitutive law models will be done in collaboration with ONERA within which several weeks of work are planned.