A mixed elastic-rigid model for masonry structures

Abstract

Masonry is one of the oldest construction materials used by man and still widespread worldwide. Historic buildings with a masonry structure are generally admirable engineering works with paramount socio-economic value and profile of cultural heritage. Despite their high durability when compared to other types of structures (e.g., concrete or steel structures) the masonry structures are especially vulnerable to settlements so that an accurate predictions of their capacity against settlements is of some importance. In the last decades, intensive research has been carried out to develop numerical models with different degrees of complexity able to describe the non-simple behavior of masonry structures under external loads and settlements, but the theme is still open and there is not yet a universally recognized analysis method applicable to any kind of problem. This dissertation focuses on fracture mechanisms in unilateral masonry-like structures on spreading abutments. Structures composed of unilateral masonry like material are, usually, modelled as a multibody composed of both rigid or elastic blocks, with unilateral no-friction contact condition. However, in this dissertation I present a new approach in which the multibody is composed of a mixed elastic-rigid (i.e., pseudo-rigid) material with unilateral friction contacts subjected to a Principle of Maximum Dissipation. The key contributions of this dissertation consist, on one hand, in introducing a vanishing “fictitious” elasticity useful to give mathematical convergence of the problem and, on the other hand, in taking into account frictional sliding of the blocks with an associative flow rule (i.e., Tresca law). This last assumption implies a normal dilatancy (in real cases essentially due to the roughness of the contact), which gives a useful interpretation of real frictional joints, and produces a frictional contact problem which is expressed through an elliptic variational inequality formulation and can be treated as a standard Convex Optimization Problem. In this setting, two approaches are implemented: a Piecewise Elastic-Rigid Displacement approach and a Continuous Elastic-Rigid displacement approach. The first approach reduces the Convex Optimization Problem to a Linear Programming Problem, via a block-based approximation, the second one reduces the Convex to a Second-Order Cone Optimization Problem via a FEM-like approximation. Three applications to real structural engineering problems are presented in order to highlight the features, the reliability and the innovation of the proposed method from both a methodological and a practical viewpoint emphasizing the contribution to the issue. [edited by Author]