Within the framework of linear elasticity theory and fracture mechanics, this work deals with the statistical identification of a phase field model [1] for brittle fracture in random heterogeneous elastic media. Such a phase field model is typically parameterized by the critical energy release rate (or fracture toughness) and the regularization length (describing the actual width of the smeared crack representation) which are considered as deterministic and homogeneous parameters to be identified. We consider a random heterogeneous material for which the apparent elasticity properties at a given mesoscale are modeled as a non-Gaussian tensor-valued random field [2]. The identification of the fracture properties of a cracking heterogeneous elastic material requires solving a challenging statistical inverse problem. An identification method with an ad hoc cost function is specifically developed for solving this statistical inverse problem. The performances of the proposed identification method are illustrated on a classical benchmark problem for brittle fracture. REFERENCES [1] J.-Y. Wu, V.P. Nguyen, C.T. Nguyen, D. Sutula, S. Sinaie, and S.P.A. Bordas. Chapter One - Phase-field modeling of fracture. volume 53 of Advances in Applied Mechanics, pages 1–183. Elsevier, 2020. [2] C. Soize. Uncertainty Quantification: An Accelerated Course with Advanced Applications in Computational Engineering, volume 47 of Interdisciplinary Applied Mathematics. Springer International Publishing, 1st edition, 2017.