A simple homogenized model for the non-Linear analysis of FRP strengthened masonry structures

A two-step model able to predict the non-linear response of FRP strengthened threedimensional 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 behaviour with limited tensile and compressive strength with softening. The homogenized stress-strain behaviour 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, with deterioration of the mechanical properties. FRP reinforcing strips are modelled through rigid triangles and non-linear interfaces between adjoining triangles. Delamination from the support is accounted for, by modelling FRP-masonry bond by means of non-linear softening triangular interfaces. Italian code CNR DT 200 0 formulas are used to evaluate peak interface tangential strength and post peak behaviour. A structural examples relying into a masonry deep beam is presented for validation purposes.