A constitutive model for rubble masonry allowing for spread micro-cracks and localized macro-cracks

Starting from a discussion on the experimental results obtained from diagonal compression tests executed on in-situ masonry panels, the paper presents a constitutive model, together with a numerical formulation, to describe the cracking phenomena in rubble masonry structures. A classical finite element discretization is assumed with the hypothesis of a homogenous continuum material. The adopted constitutive model identifies three different phases: (i) the elastic phase; (ii) the micro-cracking phase, in which the formation of microcracks, spread in the structural members, is accounted assuming a plastic material with a strain hardening stable behavior; (iii) the macro-cracks phase, in which the formation of macrocracks, developing along the edges of finite elements, are simulated by means of localized softening plastic deformation. While the numerical description of spread plasticity in the finite element framework is a topic that has been widely addressed in the past, the representation of localized plastic deformation and its implementation in a finite element code is an original contribution of the authors. From a computational point of view, the value of plastic deformations (i.e. crack openings) is found by solving a parametric linear complementarity problem (LCP) using mathematical programming algorithms. The main advantage of using an LCP method is its ability to deal also with configurations in which instability and a multiplicity of solutions are possible (e.g. softening behavior). The numerical simulation of a diagonal compression test and the comparison of the results with the experimental evidence are presented to validate the model.