Nonlocal damage and interface modeling approach for the micro-scale analysis of FRCM
Introduction
Among the fibrous composites materials, increasing interest in the scientific community and in the civil structural field, was recently addressed by the Fiber Reinforced Cementitious Matrix (FRCM) composites. Indeed, this material type has shown promising results as strengthening of masonry or concrete structures, in particular as retrofitting of masonry structures of historical and monumental interest. The composite is made with a bidirectional open-mesh textile embedded in an inorganic cement-based or lime-based matrix. Many fibrous materials can be adopted such as carbon, AR-glass, basalt, polyparaphenylene benzo-bisoxazole (PBO) fibers. The main properties that characterize the FRCM composite are good fire resistance, permeability, applicability on wet surfaces, reversibility, easiness and reduced costs of installation. Many experimental and theoretical works have demonstrated the feasibility to use this kind of composite [1], [2], [3], [4], [5] and its effectiveness as flexural and shear strengthening material of masonry panels [6], [7], [8], [9], [10], [11] and concrete members [12], [13], [14], as well as confinement material for masonry or concrete columns subjected to axial loads [15], [16], [17].
Nowadays, the available design guidelines, the ACI 549.4R-13 [18] and the more recent Italian CNR-DT 215 [19] give some recommendations for the design and installation of FRCM composites applied to different masonry and concrete substrates. The characterization of the FRCM mechanical properties is obtained via direct tensile test performed on the composite [18] or on the fiber textile [19] and via direct-shear tests between the composite and the support. The testing results allow to apply the analytic formula suggested in the guidelines for the design of the strengthening interventions. Nevertheless, the study and the knowledge of the actual mechanical response of the FRCM material is a fundamental issue for reproducing the effective behavior of FRCM-strengthened members aiming to derive reliable analytic models and for optimizing the mechanical features of the composite. In this framework, the numerical study of the micro-mechanisms and the damage pattern that arise within the composite under tensile, shear or mixed load configurations could be an important research activity.
Some available numerical studies for reproducing the tensile response of FRCM material can be found in literature. In [20] the bond and failure mechanisms of FRCM composite at the micro-scale are investigated and the tensile FRCM stress–strain behavior is numerically simulated by means ofthe introduction of an ideal yarn used as a reference for bond mechanisms in the model. In [21] a reduced two-dimensional numerical model is suggested for reproducing the tensile response of the FRCM. In [22] commercial codes able to reproduce the FRCM behavior and to identify the mechanical behavior of the cementitious matrix are used. Leurini et al. [23] proposed a nonlinear numerical procedure based on the modeling of the FRCM as a membrane element distinguishing, after the crack phase, the different behavior of the cracked and uncracked part of the composite, taking into account the tension stiffening effects. In [24] a phase-field model, implemented in a finite element code to simulate the tensile behavior of FRCMs, accounting for brittle fracture of cementitious matrix and fabric reinforcement and possible slippage at the fabric-to-matrix interface is suggested. In [25] a 2D Augmented-Finite Element Method (A-FEM) approach is used, modeling the fabric as a continuum layer attached to the mortar with no-thickness cohesive elements and considering the position of the cracks preliminarily fixed on the FRCM specimen. In [26] a FE approach performed using the Abaqus code is described. The authors modeled the mortar body as solid elements and the textile as a shell element, introducing interface elements between the layers. The results showed that the use of a cohesive law for the interface elements leads to appropriate results. The nonlinear mechanisms arising within the FRCM material are taken into account via the introduction of interface elements in [27], [28], [29]. The suggested numerical approach, at the micro-scale, accounts for both the slippage of the fibers within the mortar and the cracking of the mortar. The model reproducing the FRCM response in tension is successfully validated with experimental results. In [30] a theoretical model carried out on the basis of equilibrium considerations taking into account the local behavior of the matrix, reinforcement and reinforcement/matrix interface is suggested. Summarizing, the adopted modeling approaches available in literature are mainly based on the introduction a priori of interfaces between the fibers and the mortar, not considering, in some cases, the effective damage of the mortar. This aspect can be overcome by adopting nonlocal damage models for the matrix that, in the best knowledge of the authors, have not been used yet for FRCM modeling. Nonlocal damage models have been successfully adopted to study the failure of fibre reinforced polymers (FRPs), as for instance in [31], [32], [33]. Indeed, FRCM and FRP behavior presents similarities and differences. Both the matrices, resin and mortar, show a brittle or quasi-brittle response, but polymeric matrix differently from the mortar can have a significant viscous or plastic behavior [34]. On the other hand, mortar exhibits finite strength in compression, much lower than resin. Even from geometrical point of view, differences between FRCM and FRP can be noted. Indeed, the FRPs are laminates characterized by stacked plies, each of them made with fibres laid in a single direction, while the FRCMs are made with two mortar outer layers and an inner layer made with mortar and fibers that laid into two orthogonal direction, as above described.
On the basis of these considerations, aim of the present work is to propose a micro-scale modeling approach based on an efficient nonlocal damage and plasticity model for reproducing the mechanical behavior of FRCM. In order to capture the possible slippage of the fiber within the mortar matrix, interfaces subjected to damage and friction are introduced only between the fibers and the mortar in the inner layer. The herein adopted models are described in details and the associated computational aspects are discussed. A repetitive Unit Cell (UC) is identified due to the material periodicity. The damage pattern at the micro-scale of the mortar and of the interfaces between the fiber and the mortar is illustrated and a parameter sensitivity analysis is performed.
Among the possible retrofitting techniques, the application of the FRCM material on structural elements subjected to shear load, e.g. masonry walls subjected to in-plane loads, is one of the most used. In order to numerically study the behavior of such strengthened members, an accurate numerical modeling should also take into account the constitutive shear behavior of the composite. To the best of authors’ knowledge, although many experimental results refer to tensile tests on FRCM coupons, there are no experimental works that investigate this feature. Thus, the shear response of the FRCM material is numerically analyzed and the results, in terms of overall response and damage pattern, are commented and discussed. Finally, the stress–strain law of the composite subjected to compressive and shear load is assessed.
Section snippets
Problem statement
The influence of the micromechanical nonlinear phenomena on the overall response of cementitious-based materials is well-known. As a matter of fact, the cracking nucleation and the damage propagation in the mortar is evident at the micro-scale for the FRCM materials [27], [28], [35]. Indeed, for this type of composites the mortar damaging and the slippage of the fibers within the mortar strongly affect the overall tensile behavior of the composite, as demonstrated by the experimental evidence
Computational aspects
A step-by-step time-integration algorithm is developed to solve the evolutive equations above described. In particular, the analysis process is subdivided into a finite number of steps. The time integration is performed adopting a backward-Euler implicit integration procedure. The solution at the actual time is evaluated, once the solution at time is determined. For sake of clarity, in the following, the quantities relative to the previous time step are denoted with the
Numerical applications
The nonlocal damage model, the interface elements and the numerical procedures presented in the previous sections are implemented in the finite element code FEAP [49] to study the response of the FRCM material and to assess the damage of the composite at the micro-scale. In particular, the FRCM cell, as described in Section 2, is considered. In order to assess the capability of the proposed model in providing a reliable prediction of the response of FRCM materials, a case study [50] available
Conclusions
The paper presented a technique for deriving the mechanical response of FRCM material. The proposed technique is based on the homogenization method for periodic composite material. In fact, the FRCM is regarded as a composite with constituents characterized by nonlinear response. The mortar has been modeled considering two damage variables, one in tension and the other in compression, and a plastic strain in compression. Interfaces has been introduced to simulate the possible slippage of the
Appendix
In uniaxial compression let’s suppose that and . Thus, the yield function in eq. (12) becomes:The consistency equation is:Moreover, from eq. (13), the incremental plastic strain can be written as:Then, substituting eq. (A3) in eq. (A2), it results:Thus:In [43] the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This study was funded by ReLUIS (Italian Department of Civil Protection) e by the Excellent Center “Distretto tecnologico per le nuove tecnologie applicate ai beni e alle attività culturali”.
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2022, Composite StructuresCitation Excerpt :In detail, the most frequent failure mode between FRCM and masonry occurs within the composite material, due to the slippage of the yarn within the mortar or to the fiber tensile failure [3]. Therefore, the tensile response of the FRCM material strongly affects the adhesion of the retrofit material to the substrate and it depends on the specimen geometry and on the mechanical features of the constituents [18–21]. For this reason, Ascione et al. (2015) [8] proposed a procedure that combines the FRCM tensile law with the shear bond law between FRCM and masonry supports, experimentally obtained, in order to evaluate the conventional stress and strain to be used for the design of the externally bonded reinforced members.
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