, Volume 53, Issue 7, pp 1719–1736 | Cite as

Failure surface of quasi-periodic masonry by means of Statistically Equivalent Periodic Unit Cell approach

New Trends in Mechanics of Masonry


In this paper a homogenization procedure for the estimation of the failure surface of a quasi-periodic masonry, based on a mean stresses approach through the analysis of the Statistically Equivalent Periodic Unit Cell (SEPUC), is shown. The mean stresses approach consists in the identification of critical states for the homogenized continuum by means of an overall failure criterion, function of the mean stress state of each constituent. These macroscopic tensors are evaluated in the elastic field. The SEPUC definition refers to a statistical criterion applied to a population of Periodic Unit Cells generated taking into account the geometrical features of the quasi-periodic texture; moreover it is validated on the basis of the homogenized elastic properties in terms of components and Frobenius norm of the elastic matrix. By a multi-objective optimization approach, the obtained results highlight that the proposed SEPUC can be used to estimate the failure surface.


Homogenization Quasi-periodic masonry Statistically Equivalent Periodic Unit Cell Failure surface 



The Authors gratefully acknowledge support from the Italian Ministry of Education, University and Scientic Research, within the PRIN National Grant 2015 project “Advanced mechanical modeling of new materials and structures for the solution of 2020 Horizon challenges” (Prot. 2015JW9NJT).

Compliance with ethical standards

Conflict of interest

The Authors declare that they have no conflict of interest.


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of PerugiaPerugiaItaly

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