Homogenized model for herringbone bond masonry: Linear elastic and limit analysis

A kinematic procedure to obtain in-plane elastic moduli and macroscopic masonry strength domains in the case of herringbone masonry is presented. The model is constituted by two central bricks interacting with their neighbors by means of either elastic or rigid plastic interfaces with friction, representing mortar joints. A sub-class of possible elementary deformations is a-priori chosen to describe joints cracking under in- plane loads. Suitable internal macroscopic actions are applied on the Representative Element of Volume REV and the power expended within the 3D bricks assemblage is equated to that expended in the macroscopic 2D Cauchy continuum. The elastic and limit analysis problem at a cell level are solved by means of a quadratic and linear programming approach, respectively. When dealing with the limit analysis approach, several computations are performed investigating the role played by (1) the direction of the load with respect to herringbone bond pattern inclination and (2) masonry texture.