The use of FRCM composites to reinforce building surfaces, particularly masonry structures, is becoming increasingly popular due to the compatibility and reversibility of the materials. The effectiveness of FRCM reinforcement is largely dependent on the bond between FRCM and masonry, which has been commonly investigated by shear tests, and various analytical and numerical models have been developed to reproduce the bond behavior during the tests. However, the existing simplified models often only consider the failure of either the fiber-mortar interface or the mortar-substrate interface, and often ignore the cracking of the mortar. This paper proposes a mathematical model that takes into account both fiber-matrix and matrix-masonry interface failures and mortar matrix damage. The interfacial bond laws are characterized by jagged relationships to reproduce the degradation of the interfacial bond capacity during loading. The constitutive law of mortar is also characterized by the jagged shape to represent the decrease of tensile strength with cracking of the mortar matrix. The debonding problem can be described by an ODE system that can be solved by converting the BVP into an IVP by shooting method, and the solutions can be obtained quickly by a 2D-bisection procedure. The results obtained by the current model are compared with existing experimental data and models, exhibiting a good performance in predicting the global stress-slip curves.
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