Macroscopic strength domains of transversally loaded masonry walls defined by a Method of cells-type approach

The paper generalizes an upper-bound limit analysis approach, recently presented by the authors to estimate the in-plane homogenized failure surfaces of masonry walls with joints of finite thickness, to walls subjected to lateral loads. Following an approach similar to the Method of Cells for fiber-reinforced composites, a typical representative volume is subdivided into a few sub-cells, and a piecewise differentiable velocity field perpendicular to the element mid-plane, depending on a limited number of degrees of freedom and fulfilling suitable periodicity conditions, is proposed. Approximated macroscopic failure surfaces in the space of the macroscopic bending and twisting moments are obtained in the framework of the kinematic theorem of limit analysis. By means of standard linear programming, different points of the approximated failure surface are determined, each one representing an upper bound to the ultimate load bearing capacity of the wall under given moment combinations. The upper bounds to the macroscopic failure surfaces are found to match well, at a reduced computational cost, those obtained with previously presented alternative numerical approaches.