Simple homogenized model for the nonlinear analysis of FRP-strengthened masonry structures. I: Theory

A suitable and simple two-step model able to predict the non-linear response of FRP strengthened three-dimensional masonry structures is presented. In the first step, non-strengthened masonry is substituted by a macroscopically equivalent homogeneous material through a kinematic model based on finite elements and working on a heterogeneous assemblage of blocks. Non-linearity is concentrated exclusively on joints reduced to interfaces, exhibiting a frictional behavior with limited tensile and compressive strength with softening. The homogenized stress-strain behavior evaluated at the meso-scale is then implemented at a structural level in a finite element non-linear code, relying on an assemblage of rigid infinitely resistant six-noded wedge elements and non-linear interfaces, exhibiting deterioration of the mechanical properties. FRP reinforcing strips are modeled through rigid triangles and non-linear interfaces between adjoining triangles. Delamination from the support is accounted for, by modeling FRP-masonry bond by means of non-linear softening triangular interfaces. Italian code formulas are used to evaluate peak interface tangential strength and post peak behavior. In this first part, the theoretical base of the model and the non-linear stress strain behavior at a cell level are discussed. Structural examples will be analyzed in the accompanying paper devoted to the structural scale.