PSI - Issue 44

Ingrid Boem et al. / Procedia Structural Integrity 44 (2023) 2238–2245 I. Boem, B. Patzák, A. Kohoutková / Structural Integrity Procedia 00 (2022) 000–000

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2. The numerical model The models were developed by using the free, open-source finite element code OOFEM (Patzák, 2002; Patzák, 2012). The multi-layer modelling approach was based on 20-nodes brick elements with dimensions 167x167x t mm 3 , being t the overall wall thickness. A stacking sequence of different plies oriented along the sample thickness was defined, representing the masonry, the mortar coating and the fiber-based reinforcement (Fig. 1b). The layers were assumed as perfectly bonded; the Gauss integration rule was used for setting up integration points through the thickness of a layer, which number was specified independently for each and, in particular, equal to 12 for masonry layer, 6 for the mortar coating and 1 for the fiber-based reinforcement. Nonlinear-static analyses at displacement control were performed (Newton-Rapshon solver) considering the nonlinearities of the materials, all assumed homogeneous and isotropic (Table 1). A unitary thickness was assigned to the GFRP reinforcement layer, with an elastic-brittle tensile behavior: the material parameters were evaluated on the basis of the experimental values obtained from tensile test carried out on single yarns; but the actual properties necessitated to be scaled to the unitary thickness of the uniform layer (Table 2). The compressive contribution of the grid was neglected.

Table 1.The OOFEM parameters set for the different material layers. ID OOFEM parameters GFRP

Idm1 (n°) d 0 E 3811.52 n 0.01 tAlpha 0 equivstraintype 3 damlaw 1 e0 0.02 ef 0.035 k 0.00075

Mortar con2dpm (n°) d 0.00002 E 14430 n 0.25 talpha 0. ft 0.85 fc 6.29 wf 0.035 bhard 0.002 asoft 4. helem 1. hp 0. stype 1 ft1 0.45 wf1 0.0045 Masonry con2dpm (n°) d 0.000021 E 4000 n 0.45 talpha 0. ft 0.104 fc 2.48 wf 0.004 bhard 0.022 asoft 5 helem 1. hp 0. stype 0 kinit 0.165 Note: ID parameters according to the OOFEM material manual (Patzák, 2002).

Table 2. GFRP layer properties. GFRP property

ID T W

Value 5.1 kN 252 kN 66 mm

Average tensile strength of a single yarn Average axial stiffness of a single wire

EA W

Grid pitch

p

Equivalent tensile strength of the GFRP layer 77.3 MPa Equivalent Young modulus of the GFRP layer E W,eq = EA W / (p·1mm) 3818.2 MPa f t,W = T W / (p·1mm)

For the mortar coating layer, the Concrete-Damage Plasticity material model “Cdpm2” (Grassl et al., 2013) was considered. The Young modulus and the compressive strength were those already calibrated for the previous detailed level models, assessed by characterization tests (E = 14.4 GPa; f c = 6.3 MPa). The behavior in tension was calibrated so to reproduce approximately the equivalent, experimental behavior of CRM coupons subjected to direct tensile characterization tests (Gattesco and Boem, 2017a). The CRM coupon model, composed of double-layer brick elements (mortar + GRFP reinforcement) was modelled and subjected to tension; the comparison between experimental and numerical results is reported in Fig. 2a, also with indication of the equivalent tensile behavior set up for the mortar.

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Fig. 2. Calibration of material properties: (a) direct tensile tests on CRM coupons and (b) compression tests on plain masonry elements.