Discrete approaches for the nonlinear analysis of in plane loaded masonry walls : Molecular dynamic and static algorithm solutions

The aim of the paper is to present and validate a non commercial discrete element model (DEM) code for the nonlinear analysis of in plane loaded masonry panels, with dry or mortar joints. Such model is based on the hypothesis of rigid blocks and joints modeled as interfaces, that turn out to be both suitable for representing the behavior of ancient masonry, characterized by joint size negligible with respect to block size and block stiffness larger than joint stiffness. Hence, the elastic and inelastic behavior of a masonry assemblage is concentrated at joints by defining their stiffness and adopting a Mohr-Coulomb law as a restraint for interfacial actions. The proposed strategy is based on two approaches: a static solution method and a molecular dynamics algorithm. The static solution method allows to determine the stiffness matrix of a masonry panel and to update such matrix accounting for actual joint stiffness and blocks arrangement. Such method turns out to be computationally faster and equally effective with respect to the molecular dynamics one for performing incremental analysis of in plane loaded masonry panels. On the other hand, the molecular dynamics method is computationally less onerous than the static solution method, since it does not require to define and update panel stiffness matrix and to invert it for determining displacements. Both approaches are used and critically compared for solving several case studies of masonry panels modeled by DEM. In addition, it must be pointed out that results in terms of ultimate loads and collapse mechanisms are in good agreement with existing experimental data and numerical solutions.