, Volume 53, Issue 7, pp 1819–1855 | Cite as

Homogenization towards a mechanistic Rigid Body and Spring Model (HRBSM) for the non-linear dynamic analysis of 3D masonry structures

New Trends in Mechanics of Masonry


A mechanistic model with rigid elements and interfaces suitable for the non-linear dynamic analysis of full scale 3D masonry buildings is presented. The model relies into two steps: in the first step, a simplified homogenization is performed at the meso-scale to deduce the mechanical properties of a macroscopic material, to be used in structural applications; the second step relies into the implementation of a Rigid Body and Spring Model (RBSM) constituted by rigid elements linked with homogenized interfaces. In the homogenization step, a running bond elementary cell is discretized with 24 three-node plane-stress elastic triangular elements and non-linear interfaces representing mortar joints. It is shown how the mechanical problem in the unit cell is characterized by few displacement variables and how homogenized stress–strain curves can be evaluated by means of a semi-analytical approach. The second step relies on the implementation of the homogenized curves into a RBSM, where an entire masonry structure can be analyzed in the non-linear dynamic range through a discretization with rigid elements and inelastic interfaces. Non-linear structural analyses are conducted on a church façade interconnected with a portion of the perpendicular walls and on a small masonry building, for which experimental and numerical data are available in the literature, in order to show how quite reliable results may be obtained with a limited computational effort.


Masonry Full 3D structures Semi-analytical homogenization approach Rigid Body and Spring Model Non-linear dynamic analyses 


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 Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Architecture, Built Environment and Construction Engineering ABCPolitecnico di MilanoMilanItaly

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