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

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to evaluate its stability against actions caused by the environmental actions, thermal shock cycles, differential settlement of the foundation soil, and seismic disasters. The complexity of analyzing masonry as a composite material, and, in particular, curved structures, has motivated the growth of a wide variety of investigation methods. One of the first approaches was developed by (Heyman, 1969) through the application of the Limit Analysis theory. Today, with the development of powerful computers and modern software, finite element method (FEM) and discrete element method have provided a more sophisticated analysis of the vaulted structures response and failure modes (Lengyel, 2017; Lengyel and Bagi, 2015; Theodossopoulos et al., 2003, 2002). A detailed review on classical and modern theories can be found in (Roca et al., 2010). When dealing with the FEM, three techniques are commonly adopted to model masonry (Lourenço, 1996). In the case of small-scale studies, discrete modeling of bricks, mortar, and interfaces between them lead to the overall behavior of masonry (Fig. 1a). This approach, called detailed micro-modeling (DMM), is characterized by a high level of precision. However, it has serious limitations in real structural applications due to its extensive computing requirements. A less expensive computational alternative is the simplified micro-modeling (SMM), which proposes to model masonry units as extended bricks by adding the half mortar thickness at each face. Extended bricks are then separated by interface elements (Fig. 1b). Finally, it is more practical for large-scale investigations to assume masonry as one homogeneous material (Fig. 1c). The macroscopic mechanical characteristics of the composite can be derived from those of brick and mortar through a homogenization procedure. This technique, known as multi-scale modeling (MSM) is a transitional solution from DMM to macro-modeling (MM). Instead of investigating the whole structure, homogenization makes use of the regular periodic pattern of masonry to bring the study down to the level of a so called representative volume element (RVE). It is the minimum volume of masonry containing all the geometrical and constitutive information necessary to reproduce the entire structure by periodic translations. Several valuable homogenization techniques have been proposed in the literature. However, most of them are based on complex mathematical models and require a wide theoretical background (Kawa et al., 2008; Milani et al., 2013; Milani and Tralli, 2012; Quinteros et al., 2012; Stefanou et al., 2015). They are more intended for experts rather than engineers. In this work a simple procedure is proposed to derive the homogenized characteristics of a masonry arch based on simple numerical tests conducted on the RVE. Simulation of the experimental in-plane bending test conducted by (Vermeltfoort, 2001) was performed using both DMM and MSM. Results and computational costs of the two approaches were compared and discussed.

Fig. 1. Masonry modeling techniques: (a) detailed micro-modeling; (b) simplified micro-modeling; (c) macro-modeling. (Lourenço, 1996).

2. Constitutive models The constitutive models applied to simulate the masonry response are briefly introduced in this section. The mathematical description of these models and their parameters significance, hereafter introduced, can be found in (ABAQUS, 2010). 2.1. Concrete damaged plasticity Concrete damaged plasticity model (CDP) is a plasticity-damage based model developed by (Lubliner et al., 1989) to simulate the quasi-brittle materials response. The two principal failure modes of this model are cracking in tension and crushing in compression. Therefore, it was used in this work to describe the nonlinear behavior of bricks, mortar, and homogenized masonry.