Identification of a prior probabilistic mesoscale model with experimental multiscale observations of one specimen under external loads

We consider a microstructure of a material for which, at mesoscale, the apparent elasticy tensor field is modeled by a random tensor field and, at macroscale, the effective elasticity tensor is modeled by a random tensor constructed by using any available homogenization method. The objective of this work is to identify the parameters of a prior probabilistic model of the random apparent elasticity tensor field at mesoscale using simultaneously macroscale and mesoscale field measurements carried out on one specimen.