, Volume 53, Issue 7, pp 1699–1717 | Cite as

Homogenization of heterogeneous masonry beams

  • Daniela AddessiEmail author
  • Elio Sacco
New Trends in Mechanics of Masonry


This study presents a two-scale model to describe the out-of-plane masonry response. One-dimensional (1D) structural elements, like masonry columns or strips of long wall characterized by the periodic repetition of bricks and mortar arranged in stack bond, are considered. A damage-friction plasticity law is adopted to model the mortar joint constitutive response, while the bricks are assumed as linear elastic. A 1D beam formulation is introduced at both the structural and micromechanical scale, linking the two levels by means of a kinematic map. This expresses the microscopic beam strains in the masonry unit cell (UC) as function of the macroscopic generalized strains. The kinematic field in the UC is completed by adding an unknown periodic fluctuation term. A nonlinear homogenization procedure is developed, proposing a semi-analytical solution for the micromechanical problem, based on the fiber discretization of the mortar joints. A force-based beam-column finite element procedure is adopted at the structural scale and the solution algorithm for the element state determination is illustrated in details. Some numerical applications, showing the UC constitutive response and the behavior of masonry structural elements, are finally presented.


Masonry Multiscale model Damage Plasticity Beam force-based finite elements 



This study was funded by ReLUIS (Italian Department of Civil Protection), MIUR-PRIN, University of Cassino and Southern Lazio and University of Rome Sapienza.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Strutturale e GeotecnicaUniversità di Roma SapienzaRomeItaly
  2. 2.Dipartimento di Ingegneria Civile e MeccanicaUniversità di Cassino e del Lazio MeridionaleCassinoItaly

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