Citation: Oddo, M.C.; Minafó, G.; Di Leto, M.; La Mendola, L. Numerical Modelling of the Constitutive Behaviour of FRCM Composites through the Use of Truss Elements. Materials 2023, 16, 1011. https:// doi.org/10.3390/ma16031011 Academic Editor: Enzo Martinelli Received: 31 December 2022 Revised: 17 January 2023 Accepted: 19 January 2023 Published: 22 January 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). materials Article Numerical Modelling of the Constitutive Behaviour of FRCM Composites through the Use of Truss Elements Maria Concetta Oddo † , Giovanni Minafó * ,† , Marielisa Di Leto † and Lidia La Mendola † Department of Engineering, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy * Correspondence: giovanni.minafo@unipa.it; Tel.: +39-091-23896749 † These authors contributed equally to this work. Abstract: The modeling of the mechanical behavior of Fabric Reinforced Cementitious Matrix (FRCM) composites is a difficult task due to the complex mechanisms established at the fibre-matrix and composite-support interface level. Recently, several modeling approaches have been proposed to simulate the mechanical response of FRCM strengthening systems, however a simple and reliable procedure is still missing. In this paper, two simplified numerical models are proposed to simulate the tensile and shear bond behavior of FRCM composites. Both models take advantage of truss and non-linear spring elements to simulate the material components and the interface. The proposed approach enables us to deduce the global mechanical response in terms of stress-strain or stress-slip relations. The accuracy of the proposed models is validated against the experimental benchmarks available in the literature. Keywords: FRCM; masonry; modeling; tensile behavior; shear bond behavior 1. Introduction The use of Fabric Reinforced Cementitious Matrix (FRCM) materials is today a very common practice in the field of structural retrofitting of existing buildings. The FRCM composites consist of fiber grids of various nature (e.g., basalt, glass, carbon, polypara- phenylene benzobisoxazole, aramid) embedded between two layers of mortar and are based on lime or cement binders. Their popularity is mainly due to the use of the inorganic matrix that provides an improved compatibility with the stone and masonry support [1,2] compared to the well-known Fiber Reinforced Polymers (FRPs). It should be noted that Naser et al. [3] stressed that in the presence of different kinds of loads, it is of fundamental importance to model the constitutive bond behavior of the matrix-to-support interface and to address its dependence on the materials that it comes into contact with. Recently, the technical community has increased its interest towards this new emerging class of composite materials as demonstrated by the rapid development of recent Interna- tional Standards, which aim to define the experimental procedures and reliable methods for assessing the constitutive behavior of FRCM materials. The provisions reported in these standards are the summary of a large amount of experimental work developed in recent years, which aimed to investigate the role of all the test variables on the mechanical behavior of FRCM composites. The focus of the research on these materials, and generally on Fiber Reinforced Concrete (FRC) materials, is on the influence of the fiber’s characteristic properties. In Shi et al. [4], it is shown how the fibers clearly affect the matrix post-cracking behavior. While Bai et al. [5] analytically studied how the tensile behavior changes as the fiber content changes, as well as the effects of this parameter on the initiation and expansion of microcracks. Studies have also been conducted on the response of FRCM material in presence of different environ- mental conditions [6], effects of rising damp and salt crystallization cycles [7] and with the effect of the wet-dry cycle [8]. These also show how the external conditions influence the Materials 2023, 16, 1011. https://doi.org/10.3390/ma16031011 https://www.mdpi.com/journal/materials