A robust and efficient damage material model for nonlinear analysis of masonry structures

Finite element analysis of masonry structures is often challenging because of their marked nonlinear behaviour, whose numerical representation may lead to significant computational issues. In practice, this often leads to lengthy trial-and-error analysis settings, long computing times and possible lack of convergence, and justifies the use of other more approximate methodologies, e.g., limit analysis, when the ultimate conditions are investigated. For many problems, however, the complete evolution of the structural response over time is needed and finite element analysis remains the preferred approach. Hence, the development of numerical models representing a controlled compromise between accuracy, robustness and efficiency is a research topic of relevant practical interest. In this paper, a novel computational strategy for masonry structures, entailing a strain-driven damage model equipped with implicit-explicit solution method is proposed. The model is conceived to be robust at local level (no iterations are needed to find stresses and update internal variables from given strains) and at global level, where the material tangent stiffness matrix is ensured to be constant in the time increment. This leads to a finite element analysis where no or very few iterations are needed at each step. The accuracy and the computability of the approach are shown through several examples, from the integration point level to walls subjected to in-plane and out-of-plane loads. In-depth investigation on various aspects of the numerical approach is carried out, showing the potential of the methodology for analysis of masonry structures in various numerically challenging conditions.