We consider the construction of a probabilistic model which allows realizations of random elasticity tensors to be simulated, under the constraint that the mean distance, defined with respect to the Riemannian metric, to a given class of material symmetry is specified. Following the eigensystem characterization of the material symmetries, the proposed approach relies on the probabilistic model derivedfrom the nonparametric probabilistic approach, allowing the variance of selected eigenvalues of the elasticity tensor to be partially prescribed. A new methodology and parameterization of the model are then defined. The proposed approach is exemplified considering a constraint defined with respect to the mean distance to transverse isotropy, corresponding to the modeling of unidirectional reinforced composites for instance.
