Keywords: masonry, non-linear analysis, micro-modelling, homogenization, engineering applications.

Masonry is a building material that has been used for more than ten thousand years. In many countries, masonry structures still account for 30 to 50% of the new housing developments. Also, most structures built before the nineteenth century and still surviving are built with masonry. Research in the field is essential to understand masonry behaviour to develop new products, to define reliable approaches to assess the safety level and to design potential retrofitting measures. To achieve these purposes, researchers have been trying to convert the highly indeterminate and non-linear behaviour of masonry buildings into something that can be understood with an acceptable degree of mathematical certainty. The fulfilment of this objective is complex and burdensome, demanding a considerable effort centred on integrated research programs, able to combine experimental research with the development of consistent constitutive models.

The relevance of the internal structure of masonry in the structural response is known. The first part of this lecture focuses on two possibilities to incorporate the internal structure of masonry in the constitutive model, be it by explicitly considering it or by the mathematical process of homogenization. On the one hand, different approaches are possible to represent heterogeneous media, namely, the discrete element method, the discontinuous finite element method and limit analysis. These approaches are reviewed briefly and a powerful interface model for cyclic loading of masonry is discussed. On the other hand, homogenisation techniques represent a popular and active field in masonry research. A brief review is presented and a polynomial expansion of the stress field coupled with limit finite elements analysis is discussed. Recent advances with respect to blast analysis and quasi-periodic masonry are introduced.

Constraints to be considered in the use of advanced modelling for engineering applications are the cost, the need of an experienced user or engineer, the level of accuracy required, the availability of input data, the need for validation and the use of the results. Cost and the need of an experienced user seem straightforward arguments. As a rule, advanced modelling is a necessary means for understanding the behaviour and damage of (complex) historical construction. An emblematic monument is used to demonstrate the relevance and applicability of advanced computations for engineering applications.

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