Simple holonomic homogenization model for the non-linear static analysis of in-plane loaded masonry walls strengthened with FRCM composites

A two-step homogenization procedure for fast non-linear static analyses of FRCM (Fabric Reinforced Cementitious Matrix) composites reinforced masonry walls in-plane loaded is presented and benchmarked on a series of FRCM strengthened tuff panels experimentally tested under diagonal compression at the University of Naples, Italy. The numerical model relies into a first homogenization step where the unreinforced masonry is substituted with an equivalent homogenized non-linear orthotropic material exhibiting softening. The elementary cell is discretized by means of few triangular elastic elements (bricks) and holonomic interfaces (joints) where all the non-linearity is lumped. The standard homogenization model so obtained is characterized by either two or three unknowns under biaxial and shear stress states, respectively. The homogenized behavior of the elementary cell is thus deduced solving small scale non-linear equations systems. The second step relies into the strengthening application to the already homogenized material at a structural level. In such phase, masonry is modeled with rigid quadrilateral elements and homogenized holonomic interfaces, whereas FRCM by means of equivalent trusses with limited tensile strength and fragile behavior, connecting adjoining rigid elements. Equivalent mechanical properties of the trusses can be eventually tuned accounting for FRCM debonding or rupture of the fibers. In order to further assess the results obtained using homogenization, a 3D large scale heterogeneous micro-modeling strategy is used to reproduce experimental results. Pros and cons of the two approaches are discussed with respect to their reliability in fitting experimental force-displacement curves and crack patterns, as well as to the rather different computational effort required by the two strategies.