External application of FRCM (Fabric Reinforced Cementitious Matrix) composites to building surfaces is increasingly adopted in building reinforcement, especially for masonry structures due to a better compatibility and reversibility of the materials. The bond between FRCM and masonry often determines the effectiveness of the strengthening, which is usually investigated by shear tests, and is also studied by many existing analytical and numerical models. Among them, analytical models with assumptions of CML (Cohesive Material Law) are favored by many researchers due to their computational stability and rapidity, however, these models usually consider only the fiber-matrix interface failure, as it is the most common failure mode appearing in the shear tests. In this paper, a mathematical model that can consider both fiber-matrix and matrix-masonry interface failures, as well as mortar matrix damage is proposed. The two interface CMLs are characterized by stepped relationships, to reproduce the degradation of the interfacial bond capacity during loading. Also, the constitutive law of mortar is characterized by the stepped shape to consider the decrease of tensile strength with cracking of the mortar matrix. With the above relationships and equilibrium conditions, the debonding problem can be described by an ODE system that can be solved by boundary conditions. In this paper, the BVP (Boundary Value Problem) is converted into an IVP (Initial Value Problem) by shooting methods, and the solution of the above ODE system can be obtained quickly by a bisection procedure. The proposed approach is very attractive for complex nonlinear models as proposed here, furthermore the obtained results are compared with the experimental data and exhibit a good predictive performance.
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