Failure Criterion for Brick Masonry: A Micro-Mechanics Approach

The paper deals with the formulation of failure criterion for an in-plane loaded masonry. Using micro-mechanics approach the strength estimation for masonry microstructure with constituents obeying the Drucker-Prager criterion is determined numerically. The procedure invokes lower bound analysis: for assumed stress fields constructed within masonry periodic cell critical load is obtained as a solution of constrained optimization problem. The analysis is carried out for many different loading conditions at different orientations of bed joints. The performance of the approach is verified against solutions obtained for corresponding layered and block microstructures, which provides the upper and lower strength bounds for masonry microstructure, respectively. Subsequently, a phenomenological anisotropic strength criterion for masonry microstructure is proposed. The criterion has a form of conjunction of Jaeger critical plane condition and Tsai-Wu criterion. The model proposed is identified based on the fitting of numerical results obtained from the microstructural analysis. Identified criterion is then verified against results obtained for different loading orientations. It appears that strength of masonry microstructure can be satisfactorily described by the criterion proposed.