A plastic-damage orthotropic 3D model for nonlinear analysis of masonry structures under earthquake loading

The response of masonry structures under seismic loading is very complex, as it is governed by the anisotropic and quasi-brittle nature of masonry. In recent past, this has driven the development of mechanical descriptions at different scales of representation, including micro-, meso- and macro-scale models and multi-scale approaches. In general micro- and meso-scale descriptions enable an accurate prediction of crack patterns and damage-induced anisotropy, as they explicitly allow for masonry bond and the interaction between units and mortar joints. Nevertheless, at present their use is restricted to the simulation of the nonlinear response up to collapse of masonry components like walls and arches, but not entire building structures because of the excessive computational cost required. Thus, in the analysis of realistic masonry structures, macro-models representing masonry as a continuum material are usually employed as they are much more computationally efficient. However, accurate response predictions entails complex material formulations calibrated on the physical response at structural component level or on more expensive micro or mesoscale models. In most previous macroscale models, masonry is modelled by using 2D representations, focusing on the monotonic response up to collapse. Moreover, very few masonry macroscale models allow for strength and stiffness degradations under cyclic loading, which strongly affect the behaviour when masonry structures are subjected to earthquakes. Isotropic descriptions are often utilised in practice, as they are generally simpler and computationally robust. However, they may not be representative of masonry characterised by regular bond patterns. In this paper, a novel 3D material model for the nonlinear analysis of masonry structures under seismic loading is described. The model is based on uncoupled damage and plasticity, which guarantees computational efficiency and robustness at the local level. The elastic behaviour and yield surface account for the orthotropic behaviour linked to the specific regular bond pattern, where stiffness and strength degradation and opening-closure of cracks are accurately represented. The potential of the proposed macroscale modelling strategy is shown in several numerical examples on masonry walls and building structures under earthquake loading.