PSI - Issue 37

Khalil Naciri et al. / Procedia Structural Integrity 37 (2022) 469–476 Khalil Naciri et al. / Structural Integrity Procedia 00 (2019) 000 – 000 3 The CDP yield envelop is a Drucker-Prager surface defined by the parameter introduced to allow for the difference between the compressive and the tensile yield strengths and by the ratio of the biaxial to the uniaxial compressive yield stresses ( 0 / 0 ). Additionally, the plastic deformation is computed by means of a non-associated rule in which the plastic potential is a Drucker-Prager function defined using dilation angle ( ). 2.2. Surface-based cohesive behavior Tensile cracking and shear sliding at the unit-mortar interface were simulated using the surface-based cohesive behavior model. Initially, interface has an elastic response governed by the tensile ( ) and shear ( ) stiffness coefficients until the damage initiation criterion, expressed in terms of tensile ( ) and shear ( ) strengths, is reached. Then, interface stiffness degradation begins following a linear evolution defined using tensile ( ) and shear ( ) fracture energies. Finally, the frictional contact at the debonded interfaces is described by the Coulomb's law, which is defined by the friction coefficient ( ). It is worth noting that the combination of these two models has already been used by the authors to simulate the in plane behavior of a masonry wall subjected to confined shear load (Naciri et al., 2021) and will be further validated in this paper against an experimental bending test of a masonry arch under multiple in-plane forces. 3. Benchmark Example In this section, the benchmark example used to assess the effectiveness of the DMM and MSM techniques to reproduce masonry arch behavior is presented. The experimental test, conducted by (Vermeltfoort, 2001), is a parabolic arch subjected to four in-plane vertical loads applied to the external surface at the four positions indicated in Fig. 2. The arch was first subjected to three loading-unloading cycles under equal loads of 5 kN. In the second step, all loads were maintained at 5 kN. Then, only the load at position 2 was increased until the specimen failure. The maximum value of the load at position 2 was 40.7 kN. Due to the arch deformations, loads 1, 3 and 4 increased as well, see Fig. 2c. 471

Fig. 2. Description of the experimental test conducted by (Vermeltfoort, 2001): (a) Step 1 : loading-unloading cycles; (b) Step 2 : loading under 4 × 5 kN forces; (c) Step 3 : increasing the F2 load until failure.