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

## 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.

## Keywords

Continuum damage mechanics Crack-tracking Cyclic shear loading Intersecting cracks Masonry walls## Notes

### Acknowledgements

This research has received the financial support from the MINECO (Ministerio de Economia y Competitividad of the Spanish Government) and the ERDF (European Regional Development Fund) through the MULTIMAS project (Multiscale techniques for the experimental and numerical analysis of the reliability of masonry structures, ref. num. BIA2015-63882-P).

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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