A Constitutive Model for Rubble Masonry Allowing for Spread Micro-Cracks and Localized Macro-Cracks

Abstract

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 micro- cracks, 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 macro- cracks, 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

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