Modeling masonry with limit analysis finite elements: review, applications and new directions

The mechanics of masonry structures have been for long underdeveloped in comparison with other fields of knowledge. Presently, non-linear analysis is a popular field in masonry research and homogenization techniques play a major role, despite the mathematical and conceptual difficulties inherent to the approach. Here, a simple micro-mechanical model for the homogenized limit analysis of masonry is reviewed. Assuming brickwork under plane stress condition and adopting a polynomial expansion for the stress field, a linear optimization problem is derived on the elementary cell in order to recover the homogenized failure surface of the brickwork. The implementation of the homogenized failure surfaces for in-plane and out-of-plane behaviour in a finite element limit analysis code is addressed. Relevant structural examples are treated with particular emphasis on the upper bound method, and are compared with competing approaches. Finally, the aspects of reliability and safety of masonry structures are discussed using the proposed modelling strategy.