Challenges, tools and applications of tracking algorithms in the numerical modelling of cracks in concrete and masonry structures

The importance of crack propagation in the structural behaviour of concrete and masonry structures has led to the development of a wide range of finite element methods for crack simulation. A common standpoint in many of them is the use of tracking algorithms, which identify and designate the location of cracks within the analysed structure. In this way, the crack modelling techniques, smeared or discrete, are applied only to a restricted part of the discretized domain. This paper presents a review of finite element approaches to cracking focusing on the development and use of tracking algorithms. These are presented in four categories according to the information necessary for the definition and storage of the crack-path. In addition to that, the most utilised criteria for the selection of the crack propagation direction are summarized. The various algorithmic issues involved in the development of a tracking algorithm are discussed through the presentation of a local tracking algorithm based on the smeared crack approach. Challenges such as the modelling of arbitrary and multiple cracks propagating towards more than one direction, as well as multi-directional and intersecting cracking, are detailed. The presented numerical model is applied to the analysis of small- and large-scale masonry and concrete structures under monotonic and cyclic loading

Tracking multi-directional intersecting cracks in numerical modelling of masonry shear walls under cyclic loading

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

An enhanced finite element macro-model for the realistic simulation of localized cracks in masonry structures: A large-scale application

Finite element macro-modeling approaches are widely used for the analysis of large-scale masonry structures. Despite their efficiency, they still face two important challenges: the realistic representation of damage and a reasonable independency of the numerical results to the used discretization. In this work, the classical smeared crack approach is enhanced with a crack-tracking algorithm, originating from the analysis of localized cracking in quasi-brittle materials. The proposed algorithm is for the first time applied to a large-scale wall exhibiting multiple shear and flexural cracking. Discussion covers structural aspects, as the response of the structure under different assumptions regarding the floor rigidity, but also numerical issues, commonly overlooked in the simulation of large structures, such the mesh-dependency of the numerical results

Finite element modelling of internal and multiple localized cracks

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

Out-of-plane seismic response and failure mechanism of masonry structures using finite elements with enhanced strain accuracy

The out-of-plane response is a complex and at the same time key aspect of the seismic vulnerability of masonry structures. It depends on several factors, some of which are the material properties, the quality of the walls, the geometry of the structure, the connections between structural elements and the stiffness of the diaphragms. During the last years, a wide variety of numerical methods has been employed to assess the out-ofplane behaviour of unreinforced masonry structures. Finite element macro-modelling approaches are among the most famous as they allow modelling large structures at a reasonable computational cost. However, macro-modelling approaches may result in a non-realistic representation of localized cracks and a dependency of the numerical solution on the finite element mesh. Mixed strain/displacement finite elements have been recently proposed as a remedy to the above numerical pathologies. Due to the independent interpolation of strains and displacements these finite element formulations are characterized by an enhanced accuracy in strain localization and crack propagation problems, being at the same time practically mesh independent. For these reasons, mixed finite elements are employed in this work for the out-of-plane assessment of unreinforced masonry structures, being at the same time their first real-scale application. A full-scale experimental campaign of two masonry structures, a stone and a brick one, subjected to shaking-table tests is chosen as reference benchmark. Their structural response under seismic actions is numerically assessed through nonlinear static analysis. The proposed approach is validated through the comparison of the numerical results with the experimental ones, as well as with the results obtained using standard irreducible finite elements