Gradient-elasticity and more generally gradient-enhanced continuum models have been extensively developed since the beginning of the twentieth century. These models have shown the ability to account for the effect of the underlying material heterogeneity at the macroscopic scale of the continuum. Despite of a great theoretical interest, gradient-enhanced models are usually difficult to interpret physically and even more to identify experimentally. This paper proposes an attempt to validate and identify from experimental data, a gradient-elasticity model for a material with a periodic microstructure. A set of dedicated experimental and numerical tools are developed for this purpose: first, the design of an experiment, then two-scale displacement field measurements by digital image correlation with dedicated post-processing techniques and finally a model updating technique. This paper ends up with the full set of first and second-order elastic constants of a gradient-elastic model which macroscopic kinematic has been validated by investigating the deformation of the unit cells at the microscopic scale.