Un semplice modello micromeccanico per la derivazione delle equazioni costitutive di pareti in muratura (A simple micro-mechanical model for the derivation of masonry constitutive equations)

Two main approaches have been developed for the constitutive description of masonry work, known in the technical literature as micro modelling and macro modelling. According to the first approach, mortar joints and bricks are represented separately, whereas the second one does not make any distinction between them, averaging the effect of joints through the formulation of a fictitious homogeneous material. Only a few papers take advantage of the homogenisation techniques, which have been extensively developed for periodic media. In this paper, a very simple model is developed for the solution of the field problem in the unit cell. It consists in assuming fully equilibrated stress fields in the representative volume element; assigning suitable displacement fields on the cell boundary, the non-linear behaviour of the homogenised material can be obtained assuming generic stress-strain relationships for the constituent materials. In the elastic case, very accurate homogenised moduli are achieved for any rate of the Young moduli of bricks and mortar. Assuming an elasto-plastic behaviour, the available experimental results of Page are satisfactory reproduced.