Localisation analysis in masonry using transformation field analysis

Transformation field analysis is used for the multi-scale analysis of cracking localisation in masonry. The evaluation of the corresponding consistent homogenised tangent stiffness required in acoustic tensor-based localisation analysis is derived. The average representative volume element mechanical response is studied for two sets of micro-mechanical material laws for mortar joints, based on damage and damage coupled with plasticity. Localisation analyses for stress proportional loading show that meaningful average localisation orientations are properly detected by the acoustic tensor-based loss of ellipticity criterion. The ability of the procedure to reproduce the failure envelope of running bond masonry subjected to uniform biaxial loads is demonstrated. The energetic aspects for the selection of localised solutions are discussed. It is shown that transformation field analysis yields meaningful homogenised localisation results, thereby allowing envisioning its use in nested multi-scale computations.