FE, DE and FE/DE models to investigate the non-linear behaviour of masonry walls: a critical comparison

The study of the non-linear behaviour of masonry panels is of great interest; in literature several approaches may be found, based on the adoption of continuous or discrete models [1][2]. In this work, three different models for the investigation of the non-linear analysis of in-plane loaded masonry walls are presented: a Finite Element (FEM) model (i), a Discrete Element (DEM) model (ii) and a combined Finite-Discrete Element (FEM/DEM) model (iii). The FE model adopts a macro-modelling approach based on the smeared crack theory, where masonry, as a whole, is considered as a homogeneous material. Yield criterion is based on fracture energy taking into account the masonry softening response different for compression and tensile behaviour [3]. The DE and FE/DE models adopt a micro-modelling approach based on a discrete crack theory, where blocks are modelled as rigid bodies and mortar joints are modelled as zero thickness elasto-plastic Mohr-Coulomb interfaces. A comparison between DE and FE/DE approaches has been already proposed for the in plane non-linear analysis of masonry walls [4]. The FEM/DEM is here adopted with hypothesis of rigid infinitely resistant blocks and cracks may occur only in the mortar joints. However a triangular discretization of the domain with embedded crack elements, that activate whenever the peak strength is reached, is coupled with DEM. In the FEM/DEM the use of FE allows to reproduce elastic strain into continuum, while the use of DE is suitable to model the frictional cohesive behaviour exhibited by masonry structures. Moreover, crack may occur everywhere, also inside blocks. A comparison between the three different approaches is provided, in the aim to evaluate their applicability and reliability and the limit of application of each model. References [1] Addessi, D. and Sacco, E., “Nonlinear analysis of masonry panels using a kinematic enriched plane state formulation”, International Journal of Solids and Structures, 90, 194-214 (2016) [2] Lemos, J. V., Discrete element modeling of masonry structures. International Journal of Architectural Heritage, 1(2), 190-213, (2007). [3] Bello C.B.C., Cecchi A., Meroi E. and Oliveira D.V., Experimental and numerical investigations on the behaviour of masonry walls reinforced with an innovative sisal FRCM system, Submitted to Proceedings of MuRiCo5, Bologna, 28-30 June 2017, (under review). [4] Baraldi, D., Reccia, E. and Cecchi, A., “In plane loaded masonry walls: DEM & FEM/DEM models. A critical review”, Sumbitted to Meccanica, S.I. New Trends Mech. Mason. (under review)