A 2D Nonlinear Finite Element Model for Curved Masonry Pillars Reinforced with FRCM and Tested under Direct Shear Conditions

This paper presents a finite element code for the nonlinear analysis of curved masonry pillars reinforced with FRCM and subjected to direct shear (FEMANOLA v4.0). The FRCM reinforcement is modeled using a one-dimensional nonlinear finite element with 16 Degrees of Freedom (16-DOF), while unreinforced masonry is represented by a heterogeneous approach. In this method, bricks are discretized with four-noded elastic elements, whereas mortar joints are treated as interfaces with a nonlinear cohesive-frictional behavior, including softening, capable of simulating mixed Mode I and II failures. The 16-DOF element consists of three layers—an outer matrix, a central fiber textile, and an inner matrix—subjected to longitudinal uniaxial stress. These layers interact through interfaces that transfer tangential stresses and, in the case of curved surfaces, also radial tensile/compressive ones. The finite element is a two-noded truss, in turn, composed of three in parallel trusses representing the fiber and matrix layers. Such layers are interconnected by normal and tangential springs. Each node features 8 degrees of freedom, accounting for the longitudinal and transverse displacements of the reinforcement layers and the substrate. The nonlinear interfaces representing mortar joints are modeled using isogeometric four-noded elements, where normal stress along the interface direction is assumed to be negligible. The accuracy of the proposed model is validated by comparing numerical results with experimental data and previously developed computational models for curved masonry pillars reinforced with FRCM and tested under direct shear.