An orthotropic variant of the equilibrium gap method applied to the analysis of a biaxial test on a composite material

In this paper, it is proposed to apply the equilibrium gap method to orthotropic composite materials to retrieve damage laws from measured displacement fields. A finite difference implementation method is first proposed. A linear system is formed, for which the unknowns are piecewise constant orthotropic rigidities, while the measured displacements are input (known) data. In this example, a cruciform specimen is considered for biaxial test. It is shown that, by referring to FE computed displacement fields a prescribed contrast map can be identified. Corrupted artificial displacement fields obtained through non-linear simulations are also used. When considering shear damage, a procedure using estimated contrast maps to identify a damage law is validated. An experimental biaxial test on a 2.5 C/C composite is finally analysed following the proposed approach. For each unloading step, a contrast map for all moduli is obtained from full-field measurements. By assuming that the shear moduli contrasts result from a damage mechanism, one subsequently obtains damage maps, and therefore, a growth law. The results are first validated by comparing measured and FE reconstructed displacement fields, and by comparing the identified damage fields with post-processed ones.