In this communication we present a method exploiting displacement data measured at accessible parts of solid’s boundary, for the solution of boundary conditions and damage identification problems encountered in mechanics. Targeted applications are made of materials presenting a nonlinear mechanical behavior with damage-based approaches. A hybrid algorithm has been developed in order to identify the missing data by minimizing a gap-functional. It takes into account the incremental mechanical behavior of the material and the damage evolution inside the solid via the concept of piloting. An application on a solid made of mortar with synthetic measurements is presented to illustrate the efficiency and robustness of the algorithm.