A length-dependent model for the thermomechanical response of ceramics

We present a length-dependent model for the thermomechanical response of ceramics through a concurrent multiscale scheme that accounts for: (i) the locally varying values of the sub-grain thermal conductivity tensor due to the interaction of phonons with microstructural features such as grain boundaries, and (ii) a continuum model of thermal stresses that explicitly resolves the polycrystalline structure of the material. At the sub-grain level, we compute the values of the thermal conductivity tensor using the Boltzmann transport equation under the relaxation time approximation. At the continuum level, the polycrystalline structure of the specimen is resolved explicitly by a finite element mesh and the texture of the polycrystal is assumed to be given. At this level, we adopt a Fourier model of heat conduction which utilizes values of thermal conductivity obtained at the lower scale. The mechanical response of the grains is modeled as elastic and anisotropic. The capabilities of the model are demonstrated through a series of examples, which highlight the potential of our approach for designing materials with improved thermomechanical response.