PSI - Issue 44

Sara S. Lucchini et al. / Procedia Structural Integrity 44 (2023) 2206–2213 Lucchini et al. / Structural Integrity Procedia 00 (2022) 000–000

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2. Numerical study and comparison with experimental results The present section reports and discusses the results of the Non-Linear Finite Element Analyses (NLFEA) carried out to simulate the behavior of the test walls. The Finite Element (FE) program Diana 10.5 was used to perform the simulations. 2.1. Constitutive models The behavior of masonry and SFRM was simulated by a rotating smeared-crack model based on principal stress strain constitutive formulations. The main mechanical properties of materials adopted in the simulations are summarized in Table 1. About masonry, the compressive behavior was represented by the parabolic law proposed by Feenstra that depends on the elastic modulus (E), the compressive strength (f c ) and the compressive fracture energy (G c ). The Hordijk’s law, based on the tensile strength (f t ) and the mode-I tensile fracture energy (G I f ), represented the behavior in tension of the material. To make the energy dissipated during failure independent from the numerical discretization, a proper characteristic length was incorporated in the continuum equations. The mesh objectivity was restored by using a characteristic length equal to the square root of the single element area. The compressive behavior of the SFRM was represented by the Thorenfeldt’s model, whose formulation depends only on the compressive strength (f c ). A linear elastic law with constant elastic modulus (E) governed the tensile behavior up to the achievement of the tensile strength (f t ). After cracking, the tensile behavior was represented by a multilinear stress-crack width relationship that was calibrated by the FE back analysis of the three-Point Bending Tests (3PBTs) reported in Lucchini et al. (2021). The uniaxial tensile stress (f)-crack width (w) law obtained from the calibration process was defined by the four points (f i ,w i with i=1,…,4) listed in Table 1. An elastic-perfect plastic law was used to model the behavior of both the steel screws connecting the wall to the SFRM coating and the reinforcing bars placed within the coating. The elastic modulus of steel was assumed equal to 210 GPa whereas the yield strength implemented in the Von Mises criterion was equal to 500 MPa. 2.2. Model description Fig. 4a depicts the mesh adopted to simulate the test walls. Eight-node quadrilateral isoparametric plane stress elements (CQ16M) with a 2x2 Gaussian integration scheme and a size of about 10x20 mm were used to model the specimens. A double fixed-end boundary condition was chosen to represent the actual restraints acting at the supported ends of the panels. The rigid restraints adopted in the model are shown in the schematic of Fig. 4a. The SFRM coating layer was modelled with plane stress elements rigidly connected (i.e., perfect bond condition) to masonry. The 6 mm diameter steel screws connecting the masonry wall to the SFRM layer and the 8 mm diameter steel rebars embedded in the SFRM coating were modelled by three-node 2D class-III beam elements (CL9BE in Diana code) with a regular 2-points Gaussian integration scheme. Particular attention was devoted to properly represent the boundary conditions of SFRM coating. The upper edge of the SFRM layer was fully restrained to simulate the continuity of coating applied on the building façade. On the contrary, the bottom side of the SFRM layer was not restrained to represent the discontinuity between the coating and the foundation of the building. However, as the foundation was connected to the coating by a steel rebar, the end of the beam element representing the rebar was vertically restrained to simulate the continuity with the foundation. Before applying the two lateral loads, which consisted of line loads uniformly distributed over the 140 mm wide loading steel plates, an initial vertical (axial) load of 20.8 kN was applied to the masonry wall to consider the gravity loads acting at the top of the wall. The numerical analyses were performed by monotonically increasing the lateral load and by controlling the post-peak response with the arc-length technique. A Table 1. Material parameters of the FE model. Material E (MPa) ν (-) f c (MPa) f t (MPa) G c (N/mm) G I f (N/mm) f 1 ;w 1 (MPa;mm) f 2 ;w 2 (MPa;mm) f 3 ;w 3 (MPa;mm) f 4 ;w 4 (MPa;mm) Masonry 2100 0.25 2.3 0.12 3 0.02 - - - - SFRM 21000 0.2 36 2.0 - - 2.0;0.0 3.0;0.8 1.5;3.5 0.0;6.0