Adhesively bonded strengthening systems using self-prestressing iron-based shape memory alloys (Fe-SMA) have demonstrated significant potential. However, the premature nonlinear behavior of Fe-SMA during debonding failure presents challenges in ensuring the integrity of the adhesive joint. A recent study indicated that this behavior may lead to premature joint failure, and a similar conclusion can be drawn concerning plasticity in thin adherends. To characterize the failure process of Fe-SMA bonded joints, a method capable of measuring traction–separation relationships of thin adherends bonded with tough adhesives is essential. An algorithmic method, supported by an analytical nonlinear beam-on-foundation model and a minimization scheme, is shown to offer a solution. To benchmark the method against the J-integral approach, experiments are conducted using two types of adherends: thick steel with thickness-limiting plasticity and Fe-SMA with material behavior that inevitably leads to nonlinear deformation. Comparison of methods shows both measurement method are valid and allow for proper predictive modeling using the finite element method. The proposed method can be readily employed to characterize various thin adherends with elasto-plastic material behavior.