## 1 Introduction  
Reinforced concrete beams are subject to deterioration or damage due to environmental, seismic, or other hazards and need to be strengthened and repaired [1]. The FRP grid-PCM reinforcement method lays FRP grids on the concrete surface and utilizes PCM as the bonding material and protection so that the three become a single unit that is subjected to joint stresses, thus improving the structural capacity, stiffness, and durability of the structure [2]. In this method of reinforcement, layer thickness is small, has low environmental dependence, and construction is simple, with high construction efficiency [3]. It overcomes the shortcomings of FRP reinforcement, such as easy aging of epoxy resin, poor resistance to high temperature and fire, and poor adhesion to concrete in humid environments [4]. Few scholars have systematically studied the flexural performance of reinforced concrete beams strengthened with FRP grid-PCM composite. [PERSON] et al. [5] studied the flexural performance of reinforced concrete beams reinforced with different inorganic mortars composited with FRP grids; it was found that the polymer cement mortar has a relatively dense microstructure, which can form an integral whole with the FRP grids well. [PERSON] et al. [6] found that the externally applied FRP grid-PCM composite layer could effectively inhibit the formation and development of concrete cracks, and the FRP grids could effectively improve the flexural stiffness and ultimate load capacity of the test beams. [PERSON] et al. [7] studied the influence of mesh geometry on the anti-bending effect. It was found that doubling the spacing of meridional carbon fiber grids reduces the contribution of CFRP grids to the overall flexural bearing capacity of RC beams, while the zonal grid spacing has no substantial negative effect on the flexural strength of reinforced concrete beams. [PERSON] et al. [8] found that the stiffness and flexural capacity of the reinforced beams were greater when a greater unit reinforcement amount of CFRP grids was used; at the same time, the failure mode of the reinforced beams was changed to the debonding failure of the reinforcement layer. [PERSON] et al. [9] carried out bending tests on RC beams strengthened with CFRP grids. The prefabrication and cast-in-place installation of the reinforced layer are considered in the study. When bonding CFRP grids with ECC or epoxy mortar, reliable end anchoring is required to prevent peeling failure. The higher the stiffness of CFRP, the more prone to debonding failure. [PERSON] et al. [10] confirmed that the damage of FRP grid-PCM-reinforced beams is often due to the debonding of the composite layer from the substrate. Therefore, it is necessary to quantify and predict the effectiveness of the FRP grid-PCM composite layer. [PERSON] et al. [11] found that the relationship between bending moment and curvature of the CFRP grid-PCM-strengthened beam members were in good agreement with the theoretical values, so it can be assumed that the CFRP grid-strengthened beam members still satisfy the flat cross-section assumption, and the formula for calculating the flexural capacity of the strengthened beams can be deduced accordingly. [PERSON] [12] analyzed the mechanical properties of FRP grid-PCM-strengthened RC beams undergoing concrete crushing and FRP grid rupture and proposed the formulae for predicting the flexural capacity in these two states, but the prediction of specimens in which the composite layer was debonded from the concrete substrate was poor. Currently, the research on FRP grid-PCM-composite-strengthened RC beams is mostly based on experimental studies, but the actual experimental process is cumbersome, and the experimental conditions are easily restricted, while finite element simulation can overcome such difficulties. [PERSON] et al. [13] verified the reliability of a concrete damage plasticity model in the nonlinear analysis of concrete structures. [PERSON] et al.