Homogenization models for nonlinear and limit analysis of FRP-strengthened masonry

This chapter discusses two advanced numerical approaches for the analysis of fiber reinforced polymer (FRP)-reinforced masonries, namely a novel adaptive upper bound limit analysis (UBLA) and a nonlinear procedure with rigid elements based on sequential quadratic programming. Both are tools for an effective structural analysis of FRP-reinfoced masonry, requiring a preliminary homogenization of the masonry material at the mesoscale. When dealing with the UB limit analysis approach, a genetic algorithm (GA)-nonuniform rational b-spline (NURBS)-based general framework suitable for a mesh adaptation-applied to curved masonry structures is discussed. A given FRP-reinforced masonry vault can be geometrically represented by a NURBS parametric surface, and a NURBS mesh of the given surface can be generated. Each element of the mesh is a NURBS surface itself and can be idealized as a rigid body. An UBLA formulation, which takes into account the main characteristics of masonry material and FRP reinforcement, is deduced, with internal dissipation allowed exclusively along element interfaces. GA helps in progressively adjusting the shape of the NURBS elements to closely approximate the real failure mechanism activating. When dealing with the nonlinear approach, finite element discretization without mesh adaptation constituted by both rigid wedge elements (masonry) and rigid triangular elements (FRP) interconnected by nonlinear homogenized interfaces is discussed. The step-by-step nonlinear problem is solved as constrained minimization of the quadratic energy function. Both approaches are capable of well predicting the load-bearing capacity of any kind of FRP-reinforced masonry structure (in particular, vaults of arbitrary shape, which are the most complex), with the nonlinear model having the additional features of accurately predicting initial stiffness, postpeak behavior, and displacements at failure. Both approaches are benchmarked through a number of numerical simulations applied to FRP-reinforced masonry structures tested in experiments taken from the literature.