A mathematical model and obtain the constitutive equations for the carbon embrittlement of high-temperature superconductor YBCO, taking into account the combined effects of these physical processes: (a) the diffusion of carbon, (b) the deposition of carbonate, (c) the flow of non-mechanical energy, and (d) the deformation of the composite “cuprate / carbonate” . The destruction of the material is modeled using decohesion model that takes into account the time variation of energy decohesion due to time-dependent process of carbonate precipitation.