A damage model for the tensile behaviour of Masonry structures

The constitutive equation of masonry-like materials presented in [1] and [2], represents masonry as a non linear elastic material with small tensile st rength, a bounded compressive strength and the shear stress that is limited, on each plane, propor tionally to the acting normal stress. This constitutive law is fully specified, besides by the tensor of the elastic moduli, by the stress range, i.e. the set of all stress tensors that are compati ble with the characteristics of the material, that turns out to be a closed and convex subset of the space o f the symmetric tensors. The model has been implemented into the finite element code MADY, deve loped by the authors [2], and has been applied to the study of some monuments. It has been often used considering a null tensile strength as masonry tensile strength is generally low and it is not realistic to consider a ductility in tracti on, even in case if low value. In some applications, ho wever, it is desirable to take into account the material tensile strength that need to progressivel y reduced, together with the tensile stiffness. The main goal of the paper is, therefore, to genera lize the constitutive model. For this purpose, the material is considered to have different stiffness in traction and compression in the elastic range. A damage law is then formulated that, without alterin g the compressive stiffness, simultaneously reduces tensile stiffness and strength of the mater ial. The classical “no-tension” material is then a limit case that can be obtained as a result of a da mage process. Such enriched constitutive model is then applied to the static and dynamic analysis of some masonry buildings.