Abstract

From the theoretical point of view, systems composed by masonry arches or vaults would require, during construction, the simultaneous activation of all structural elements in order to reach the optimum balance of thrusts. This is not obviously the case of complex ancient masonry constructions, whose long and gradual building process may have contributed to their deformed condition and even to damage.In this paper, the possible influence of the construction process as well as that of later long-term deformation on the final condition of the building is investigated in the case of a complex and large historical structure, namely Mallorca Cathedral. A FE code has been specifically developed for the present study. The code is able to account for construction processes through sequential-evolutionary analyses, with the description of masonry mechanical damage and long-term deformation. The representative bay of the cathedral is analyzed taking into account different construction phases, as emerged from historical research. The response of such substructure to transverse earthquake equivalent forces is then investigated. In this case, the damage model is improved with a local crack-tracking algorithm. This numerical strategy models the tensile damage as distinct cracks, leading to a better prediction of realistic collapsing mechanisms.

Abstract

This paper presents an implicit orthotropic model based on the Continuum Damage Mechanics isotropic models. A mapping relationship is established between the behaviour of the anisotropic material and that of an isotropic one. The proposed model is used to simulate the failure loci of common orthotropic materials, such as masonry, fibre-reinforced composites and wood. The damage model is combined with a crack-tracking technique to reproduce the propagation of localized cracks in the discrete FE problem. The proposed numerical model is used to simulate the mixed mode fracture in masonry members with different orientations of the brick layers.

Abstract

Tracking algorithms constitute an efficient numerical technique for modelling fracture in quasi-brittle materials. They succeed in representing localized cracks in the numerical model without mesh-induced directional bias. Currently available tracking algorithms have an important limitation: cracking originates either from the boundary of the discretized domain or from predefined “crack-root” elements and then propagates along one orientation. This paper aims to circumvent this drawback by proposing a novel tracking algorithm that can simulate cracking starting at any point of the mesh and propagating along one or two orientations. This enhancement allows the simulation of structural case-studies experiencing multiple cracking. The proposed approach is validated through the simulation of a benchmark example and an experimentally tested structural frame under in-plane loading. Mesh-bias independency of the numerical solution, computational cost and predicted collapse mechanisms with and without the tracking algorithm are discussed.

Abstract

In-plane cyclic loading of masonry walls induces a complex failure pattern composed of multiple diagonal shear cracks, as well as flexural cracks. The realistic modelling of such induced localized cracking necessitates the use of costly direct numerical simulations with detailed information on both the properties and geometry of masonry components. On the contrary, computationally efficient macro-models using standard smeared-crack approaches often result in a poor representation of fracture in the simulated material, not properly localized and biased by the finite element mesh orientation. This work proposes a possible remedy to these drawbacks of macro-models through the use of a crack-tracking algorithm. The macro-modelling approach results in an affordable computational cost, while the tracking algorithm aids the mesh-bias independent and localized representation of cracking. A novel methodology is presented that allows the simulation of intersecting and multi-directional cracks using tracking algorithms. This development extends the use of localized crack approaches using tracking algorithms to a wider field of applications exhibiting multiple, arbitrary and interacting cracking. The paper presents also a novel formulation including into an orthotropic damage model the description of irreversible deformations under shear loading. The proposed approach is calibrated through the comparison with an experimental test on a masonry shear wall against in-plane cyclic loading.