An Energetic Analysis of Apparent Hardening and Ductility in FRP Plate Debonding

We investigate the progressive debonding of FRP reinforcements using an analytical framework based on fracture mechanics and a bilinear softening cohesive law. This study focuses on the energetic analysis of the “apparent hardening” phase observed in the force–slip (F−Δ) curve. It is shown that this non-linear response is a structural phenomenon caused by stress redistribution as the softening zone develops. Full analytical expressions for all energy components (stored and dissipated) are derived, and the energy balance is established. The analysis links the amount of elastic energy stored during the hardening phase to the definitions of toughness (area under the curve) and ductility (post-peak behavior), explaining the transition from ductile to brittle failure.