A discrete macro-model homogenized with a holonomic approach for the nonlinear static analysis of out-of-plane loaded masonry

A simple homogenized model based on a holonomic approach is presented, aiming at the study of the non-linear behaviour of masonrywalls subjected to two-way bending. Firstly, a representative volume element (RVE) of a running bond elementary cell is defined at a meso-scale. The RVE is subdivided into several layers along the thickness. For each layer a plane stress assumption is considered,whereas bricks are discretized as three node triangular elements and the joints reduced to interfaces. The non-linearity is present only at the interfaces, which exhibit a holonomic behaviour with softening. At structural scale, the obtained homogenized curves serve as input for the interfaces of a new discrete system implemented in a finite element commercial package, to perform non-linear static (pushover) analysis of masonry walls under two-way bending. The developed discrete macro-model is based on quadrilateral rigid element discretization, where flexural deformation is allowed only at the interfaces through a system of axial and torque trusses. The behaviour of the interfaces is obviously holonomic and orthotropic with softening, because they are derived from the aforementioned homogenization strategy. Several examples of technical relevance relying into windowed panels out-of-plane loaded up to failure are analysed in detail, finding a satisfactory match between present results and previously presented approaches available in the technical literature.