Pergamon Int. J. Solids Structures Vo!. 34, No. 24, pp. 3191-3208, 1997 © 1997 EIsevier Science Ltd All rights reserved. Printed in Great Britain PII:S0020-7683(96)00167-9 0020-7683/97 $17.00 + .00 HOMOGENIZATION TECHNIQUE AND DAMAGE MODEL FOR OLD MASONRY MATERIAL RAIMONDO LUCIANO and ELIO SACCO Department of Industrial Engineering, University of Cassino, Via Zamosch 43-03043 Cassino, Italy (Received 23 June 1995; in revised/orm 27 July 1996) Abstract-Masonry is a composite material realized by the inclusion of bricks into the matrix of mortar. In the present paper, a micromechanical approach for defining the properties of a periodic masonry material is proposed. A damage model for old masonries is presented. In fact, it is assumed that the damage is due to the coalescence and growth ofthe fractures only in the mortar. A repetitive unit cell is chosen and eight possible undamaged and damaged states for the masonry are identified. The homogenization theory for material with periodic microstructure is used to define the overall moduli of the uncracked and cracked masonry. Variational formulations of the periodic problem are given. A numerical procedure for the computation of the elastic properties of the undamaged and damaged masonry material is developed. Then, the damage evolution of the masonry, which accounts for the exact geometry and for the mechanical properties of the constituents of the composite, is obtained. Energy and local strength criteria for the mortar are proposed. The behavior of a typical masonry material is studied and the results are put in comparison with the ones available in the literature. Finally, a simple structural application is developed. © 1997 Elsevier Science Ltd. I. INTRODUCTION Many historical buildings and monumental structures are made of masonry material. Hence the analysis of the behavior of masonry structures has always received a great interest from the scientific community. Two different models, i.e., the continuous model and the discrete block model, have been developed to capture the linear and nonlinear response of the masonry material. One of the most used continuous model is the so-called no-tension material. According to this model the masonry is indefinitely elastic in compression and cannot support tensile stresses. The no-tension material has been proposed by Heyman (1966), who formulated a theory for the limit analysis of masonry structures. The principal hypothesis is that the tensile strength of the masonry is negligible with respect to the compression strength, and therefore the collapse is generally achieved because of the fractures opening in traction. In the last two decades the no-tension material has been the object of many researches especially in Italy (Como and Grimaldi, 1985; Giaquinta and Giusti, 1985; Romano and Sacco, 1987). Monumental structures are mostly realized by superimposed blocks. The analysis of these structures is carried out by schematizing the blocks as linear elastic, and the interfaces governed by unilateral with Coulomb friction law. The study of the block structures have been developed by adopting simplified analytical approaches, as for instance in Yim et al. (1990), or in conjunction with the finite element method, e.g., Chiostrini and Vignoli (1989), Grimaldi et al. (1992) and Lofti and Benson Shing (1994). A full finite element analysis of a masonry wall which considers the actual micro- structure of the material would lead to a very expansive computational problem. In fact, to discretize the mortar joints, a very fine mesh would be considered. The masonry is a heterogeneous material composed by bricks and mortar disposed in a regular or completely random arrangement. For the most important masonry con- structions the adopted material presents a very regular geometry at the micro scale level. In fact, the bricks are joined by horizontal and vertical beds of mortar, and generate a periodic microstructure. Hence, the regular masonry material is a periodic composite material. For this reason, some micromechanical methods have been used in order to evaluate the 3191