Two different mechanical tests are performed on a laminated composite coupon to induce an anisotropic damage affecting essentially shear modulus softening. The first test is a uniaxial tension loading on a straight coupon, which is used to evaluate the damage law using a conventional approach, while the second contains a notch that enhances dramatically the strain (and hence damage) heterogeneity. A global digital image correlation approach is used to quantify the kinematic fields all along the loading path of the second experiment. Displacement fields are hence evaluated based on a finite element type discretization. A further exploitation based on the reconditioned equilibrium gap method (and without any further information) gives access to a quantitative measurement of the damage law. The latter approach makes use of a finite element model based on the very same mesh and element shape function. This full-field-based identification method compares very well with traditional techniques, up to the stage where macroscopic localization prevents their subsequent exploitations. Moreover, it is shown that neither the type of mechanical test, nor the discretization of the displacement field, affects the identification of the damage law.