Non-linear 1D 16-DOF finite element for Fiber Reinforced Cementitious Matrix (FRCM) strengthening systems

The paper presents a novel non-linear one-dimensional finite element with 16 degrees of freedom aimed at modelling Fiber Reinforced Cementitious Matrix strengthening systems. Such composite is typically constituted by three superimposed layers -namely an outer matrix, a central fiber textile and an inner matrix- subjected to a prevailing longitudinal monoaxial stress state. They interact by means of interfaces exchanging both tangential and -when the reinforcing system is applied to curved substrates- traction/compression stresses. Matrix is made by mortar -possibly reinforced- exhibiting medium to high strength, whereas the fiber net can be aramid, carbon, glass, steel, basalt, etc. The reinforcing system is then connected to a substrate by means of a further interface. The finite element is a two-noded assemblage of three trusses representing matrix and fiber layers. Shear and normal springs are lumped at the nodes, mutually connecting contiguous trusses and the inner matrix to the substrate. They represent the interfaces and exchange normal and shear actions between contiguous layers or transfer them from the reinforcing system to the substrate. The degrees of freedom, 8 per node, are the longitudinal and transversal displacements of the three layers and of the substrate, evaluated at the nodes. Material non-linearity can be considered both for trusses and springs, giving the possibility to account for all the experimentally documented damaging cases that can be encountered in practice. Both softening and inelastic behavior are numerically tackled with a fully explicit algorithm where the elastic modulus of the layers and the stiffness of the interfaces are reduced at the new iteration if in the previous one the elastic limit is exceeded. The stiffness matrix is provided straightforwardly also in the inelastic case, showing the promising simplicity of the element when coupled with the non-linear solver. The performance of the novel finite element is validated against a comprehensive experimental dataset referring to curved masonry pillars reinforced with Fiber Reinforced Cementitious Matrix and tested in single lap shear.