This work deals with complex materials to be modeled with respect to their complexity level at the micro-scale. Despite that at macro-scale, these materials are often modeled as homogeneous elastic media for which the effective mechanical properties can be identified using experimental tests, they are not only heterogenous and random at micro-scale but they often also cannot be properly described in terms of mechanical constituents. This is the reason why a meso-scale is considered and for which the elastic medium is modeled with apparent properties represented by a non-Gaussian tensor-valued random field. A general methodology using displacement field measurements at both macro-and meso-scales has been proposed in [2] for the identification of an ad hoc probabilistic model of the tensor-valued random field [1] modeling the apparent elastic properties at meso-scale. Such a multiscale identification was carried out by setting a statistical inverse problem, requiring an optimization problem to be solved and introducing three indicators for quantifying distances between the experimental measurements and a probabilistic computational model for simulating the experimental measurements. In this work, we present an improvement of this methodology by introducing an additional meso-scale indicator that allows for replacing the global optimization (genetic) algorithm used in [2] by a fixed-point iterative algorithm that drastically reduces the computational cost incurred by the identification procedure. [1] C. Soize, Non-gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators.