Modeling and numerical analysis of masonry structures

We model masonry structures as elastodynamic systems assembled from a large number of elastic bodies (bricks or stone‐blocks) in unilateral, frictional contact. The problem is formulated as a quasi‐variational inequality and discretised using piecewise polynomial finite elements in conjunction with an energy consistent time integration scheme. At each time‐step, the quasi‐variational inequality is reformulated as a nonlinear complementarity problem. An iterative splitting of the contact problem into normal contact and frictional contact, together with a primal‐dual active‐set method is employed to calculate deformations and openings in the model structures. Numerical results are presented to illustrate the efficiency of the resulting approach in predicting the mechanical behaviour of a bidimensional arch‐ring made of bricks, deformed due to body forces and surface tractions.