Simple homogenized model for the non-linear analysis of FRP strengthened masonry structures. Part I : theory

Abstract

A suitable and simple two-step model able to predict the non-linear response of FRP strengthened 13 three-dimensional masonry structures is presented. In the first step, non-strengthened masonry is 14 substituted by a macroscopically equivalent homogeneous material through a kinematic model 15 based on finite elements and working on a heterogeneous assemblage of blocks. Non-linearity is 16 concentrated exclusively on joints reduced to interfaces, exhibiting a frictional behavior with 17 limited tensile and compressive strength with softening. The homogenized stress-strain behavior 18 evaluated at the meso-scale is then implemented at a structural level in a finite element non-linear 19 code, relying on an assemblage of rigid infinitely resistant six-noded wedge elements and non-linear 20 interfaces, exhibiting deterioration of the mechanical properties. FRP reinforcing strips are modeled 21 through rigid triangles and non-linear interfaces between adjoining triangles. Delamination from the 22 support is accounted for, by modeling FRP-masonry bond by means of non-linear softening 23 triangular interfaces. Italian code CNR DT 200 (2004) formulas are used to evaluate peak interface 24 tangential strength and post peak behavior. In this first part, the theoretical base of the model and 25 the non-linear stress strain behavior at a cell level are discussed. Structural examples will be 26 analyzed in the accompanying paper devoted to the structural scale.