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We present in this investigation an advanced phenomenological approach combining the computational efficiency of classical phenomenological plasticity models and the accuracy and high resolution of multiscale crystal plasticity schemes. Within this advanced approach, a new phenomenological constitutive framework has been developed and implemented into ABAQUS/Standard finite element (FE) code. Compared to classical approaches, this framework allows accounting for initial and induced plastic anisotropy, isotropic nonlinear hardening and the full coupling with isotropic ductile damage. Material parameters corresponding to this phenomenological constitutive framework are identified based on multiscale polycrystalline simulations, where the self-consistent scheme is used to ensure the transition between the single crystal and polycrystal scales. The single crystal mechanical behavior is assumed to be elastoplastic (rate-independent), and microscopic material degradation is well-considered by introducing a scalar damage variable at each crystallographic slip system for each individual grain. The evolution of polycrystalline yield surfaces, induced by the evolution of crystallographic texture, is accurately reproduced by the new constitutive modeling, where the anisotropy parameters are assumed to evolve during plastic deformation. Their evolution laws are identified based on multiscale simulations. The different identification procedures are presented and extensively discussed. The robustness and reliability of this advanced model are analyzed through some relevant numerical predictions obtained by applying a combined tensile/shear test. French program Plan d'Investissement d'Avenir (PIA) Agence Nationale de la Recherche (ANR)

International audience; The present paper aims at providing a comprehensive investigation of the abilities and limitations of strain gradient crystal plasticity (SGCP) theories in capturing different kinds of localization modes in single crystals. To this end, the small deformation Gurtin-type SGCP model recently proposed by the authors, based on non-quadratic defect energy and the uncoupled dissipation assumption, is extended to finite deformation. The extended model is then applied to simulate several single crystal localization problems with different slip system configurations. These configurations are chosen in such a way as to obtain idealized slip and kink bands as well as general localization bands, i.e., with no particular orientation with respect to the initial crystallographic directions. The obtained results show the good abilities of the applied model in regularizing various kinds of localization bands, except for idealized slip bands. Finally, the model is applied to reproduce the complex localization behavior of single crystals undergoing single slip, where competition between kink and slip bands can take place. Both higher-order energetic and dissipative effects are considered in this investigation. For both effects, mesh-independent results are obtained, proving the good capabilities of SGCP theories in regularizing complex localization behaviors. The results associated with higher-order energetic effects are in close agreement with those obtained using a micromorphic crystal plasticity approach. Higher-order dissipative effects led to different results with dominant slip banding.

This work presents a numerical simulation of ballistic penetration and high velocity impact behavior of plain and reinforced concrete slabs. In this paper, we focus on the comparison of the performance of the plain and reinforced concrete slabs of unconfined compressive strength 41 MPa under ballistic impact. The concrete slab has dimensions of 675 mm × 675 mm × 200 mm, and is meshed with 8-node hexahedron solid elements in the impact and outer zones. The ogive-nosed projectile is considered as rigid element that has a mass of 0.386 kg and a length of 152 mm. The applied velocities vary between 540 and 731 m/s. 6 mm of steel reinforcement bars were used in the reinforced concrete slabs. The constitutive material modeling of the concrete and steel reinforcement bars was performed using the Johnson-Holmquist-2 damage and the Johnson-Cook plasticity material models, respectively. The analysis was conducted using the commercial finite element package Abaqus/Explicit. Damage diameters and residual velocities obtained by the numerical model were compared with the experimental results and effect of steel reinforcement and projectile diameter were studies. The validation showed good agreement between the numerical and experimental results. The added steel reinforcements to the concrete samples were found efficient in terms of ballistic resistance comparing to the plain concrete sample.

Fiber-reinforced polymers (FRP) have been introduced as alternative reinforcement for concrete members since decades. Nevertheless, current design codes prohibit the use of FRP bars as main reinforcement in compression members such as columns. Recently, several studies came into sight focusing on evaluating the compressive response of FRP-reinforced concrete (RC) columns. While many of these studies have praised the performance of FRP bars in RC columns, others conservatively neglected their contribution to the columns’ capacities. The objective of this study is to present a comprehensive literature review on FRP-reinforced columns in order to better understand their performance under various loading conditions. To do so, the authors collected and analyzed the results of more than 300 tests published in 43 different experimental and analytical studies in the scientific literature. The collected columns were classified according to their slenderness, loading regime, cross sections, concrete type, and reinforcement. The design equations proposed by several authors to predict the load-carrying capacities of the tested columns were collected and assessed. The work presents a critical review of the existing research on FRP-reinforced columns, identifies gaps in knowledge, and outlines directions for future research. The analysis of the collected data and the accuracy of several design approaches in predicting the behavior of FRP-reinforced columns suggests that it is time for code authorities to recognize the use of FRP in compression members.

A Master of Science thesis in Civil Engineering by Abdul Rahman M.Musif AlHafiz entitled, “Effect of Basalt Fibers on The Flexural Behavior of Beams Reinforced With BFRP Bars”, submitted in May 2018. Thesis advisor is Dr. Farid Abed. Soft and hard copy available.

One of the main disadvantages of steel bars is rebar corrosion, especially when they are exposed to aggressive environmental conditions such as marine environments. One of the suggested ways to solve this problem is to use composite bars. However, the use of these bars is ambiguous due to some weaknesses, such as low modulus of elasticity and linear behavior in the tensile tests. In this research, the effect of the hybridization process on mechanical behavior, including tensile strength, elastic modulus, and energy absorbed of composite bars, was evaluated. In addition, using basalt fibers because of their appropriate mechanical behavior, such as elastic modulus, tensile strength, durability, and high-temperature resistance, compared to glass fibers, as the main fibers in all types of composite hybrid bars, was investigated. A total of 12 hybrid composite bars were made in four different groups. Basalt and carbon T300 composite fibers, steel bars with a diameter of 6 mm, and steel wires with a diameter of 1.5 mm were used to fabricate hybrid composite bars, and vinyl ester 901 was used as the resin. The results show that, depending on composite fibers used for fabrication of hybrid composite bars, the modulus of elasticity and the tensile strength increased compared to glass-fiber-reinforced-polymer (GFRP) bars by 83% to 120% and 6% to 26%, respectively. Moreover, hybrid composite bars with basalt and steel wires witnessed higher absorbed energy compared to other types of hybrid composite bars.

International audience; In this paper, hexagonal closed packed (HCP) sheet metal ductility for a viscoplastic material is analyzed by using a linear perturbation technique. It can be used for the analysis of local-ized necking. This technique is used to perturbate the material behavior in a rate dependent formulation by superimposing a perturbation to the basic flow which its stability or instability is characterized by the increasing or decreasing of the perturbation. Hardening and initial ani-sotropic parameters are fitted by experimental results from the literature. In this investigation, Cazacu yield function is used to predict the forming limit diagrams (FLDs) of HCP sheet metals. The coupling between analytic perturbation method and the behavior modelling is provided by an efficient implicit algorithm to solve the constitutive equations. After verifica-tions and validations of the numerical simulations from the literature, the ductility limit of a particular HCP magnesium alloy is numerically predicted. A parametric study is presented to analyze the effect of instability and mechanical parameters, viscosity and distortion on the FLDs. Moreover, a comparative study between Marciniak and Kuckzynski ductility approach and linear perturbation technique is done in this contribution.

Twelve concrete columns reinforced longitudinally with fiber-reinforced polymer (FRP) bars were tested under both concentric and eccentric loadings. The investigated parameters were the ty...

When it comes to sustainability, steel rebar corrosion has always been a big issue, especially when they are exposed to harsh environmental conditions, such as marine and coastal environments. Moreover, the steel industry is to blame for being one of the largest producers of carbon in the world. To supplant this material, utilizing fiber-reinforced polymer (FRP) and hybrid FRP bars as a reinforcement in concrete elements is proposed because of their appropriate mechanical behavior, such as their durability, high tensile strength, high-temperature resistance, and lightweight-to-strength ratio. This method not only improves the long performance of reinforced concrete (RC) elements but also plays an important role in achieving sustainability, thus reducing the maintenance costs of concrete structures. On the other hand, FRP bars do not show ductility under tensile force. This negative aspect of FRP bars causes a sudden failure in RC structures, acting as a stumbling block to the widespread use of these bars in RC elements. This research, at first, discusses the effects of different environmental solutions, such as alkaline, seawater, acid, salt, and tap water on the tensile and bonding behavior of different fiber-reinforced polymer (FRP) bars, ranging from glass fiber-reinforced polymer (GFRP) bars, and basalt fiber-reinforced polymer (BFRP) bars, to carbon fiber-reinforced polymer (CFRP) bars, and aramid fiber-reinforced polymer (AFRP) bars. Furthermore, the influence of the hybridization process on the ductility, tensile, and elastic modulus of FRP bars is explored. The study showed that the hybridization process improves the tensile strength of FRP bars by up to 224% and decreases their elastic modulus by up to 73%. Finally, future directions on FRP and hybrid FRP bars are recommended.

International audience; When manufacturing flexible devices, it is quite common that localized necking appears due to the low ductility of the metal sheets used. To delay the inception of such localized necking, several industrial companies have proposed a promising technical solution based on the bonding of elastomer substrates to the metal sheets used in the manufacturing processes. In this context, the comprehensive numerical understanding of the impact of such substrate coating on the improvement of the ductility of elastomer-supported metal layers still remains a challenging goal. To achieve this goal, the bifurcation approach as well as the Marciniak and Kuczynski model are used to predict the occurrence of localized necking. The mechanical behavior of the metal layer is modeled by a non-associated anisotropic plasticity model. The adoption of non-associated plastic flow rule allows separating the description of the plastic potential from that of the yield function, which is essential to accurately model strong plastic anisotropy characterizing cold-rolled sheets. As to the elastomer substrate, its mechanical behavior is described by a neo-Hookean law. The paper presents a variety of numerical results relating to the prediction of plastic strain localization in both freestanding and elastomercoated metal layers. The effects of the non-associativity of the plastic flow rule for the metal layer and the addition of an elastomer substrate on the predictions of localized necking are especially underlined. It is shown that the ductility limits predicted by the non-associated elasto-plastic model are lower than their counterparts determined by an associated plasticity model. It is also proven that adhering an elastomer layer to the metal layer can substantially delay the initiation of plastic strain localization.

Buckling and wrinkling of thin structures often lead to very complex response curves that are hard to follow by standard path-following techniques, especially for very thin membranes in a slack or nearly slack state. Many recent papers mention numerical difficulties encountered in the treatment of wrinkling problems, especially with path-following procedures and often these authors switch to pseudo-dynamic algorithms. Moreover, the numerical modeling of many wrinkles leads to very large size problems. In this paper, a new numerical procedure based on a double Taylor series is presented, that combines path-following techniques and discretization by a Trefftz method: Taylor series with respect to a load parameter (Asymptotic Numerical Method) and with respect to space variables (Taylor Meshless Method). The procedure is assessed on buckling benchmarks and on the difficult problem of a sheared rectangular membrane. National Research Agency ANR (Labex DAMAS, Grant No.ANR-11-LABX-0008-01). China Scholarship Council.

This paper aim to investigate the effect harsh conditions have on the flexural behavior of concrete beams reinforced longitudinally with Basalt Fiber Reinforced Polymer (BFRP) bars. Finite element (FE) software, ABAQUS, is used to develop a nonlinear model capable of simulating the behavior of exposed FRP reinforced beams in flexure. Data extracted from the numerical simulations were compared with experimental data to validate the FE model. Through a parametric study, this paper aims to study the effect of reducing the modulus of elasticity on BFRP reinforced beams. The values of modulus of elasticity are reduced from the by 10%, 20%, and 30% and the impact is observed. The paper also presents comparative analysis among different BFRP tensile strength values. The analysis of the effect of varying tensile strength values on the behavior of BFRP RC beams will be conducted on an under-reinforced beam. The BFRP tensile strength value is reduced by 10%, 20%, and 30% and the impact is observed. The results show that the reduction of the modulus of elasticity of the BFRP bar decreased the flexural capacity of the BFRP RC beam proportionally. The proportional decrease was not affected by the number of reinforcement bars used in the beams with similar axial stiffness. In addition, a reduction the tensile strength of the BFRP bars caused a disproportional decrease in the flexural capacity of the beams. Beams with lower tensile strength values failed at lower deflections.

Corrosion resistant alloy steel (MMFX) reinforcing bar is increasingly utilized in structural engineering applications due to their high yield strength and corrosion resistance. This paper ...

The behavior of fiber-reinforced polymer (FRP) bars under compression is not fully understood yet due to the limited research in this area. However, the long-term durability, weathering resistance, and exceptional mechanical properties of FRP bars justify the need for their use in compression members. The main objectives of this study are to evaluate the mechanical properties of glass FRP (GFRP) and basalt FRP (BFRP) bars under compression and examine their performances as main longitudinal reinforcements in reinforced concrete (RC) columns. In the first part of this research, a series of static compression tests were conducted on GFRP and BFRP bars of different diameters. The second part of this research numerically investigated the behavior of FRP-RC columns under concentric and eccentric loading using the mechanical properties of the FRP bars obtained experimentally. Nonlinear finite element models were developed to simulate the compressive behavior of the concrete columns reinforced with GFRP and BFRP bars. The FE models were verified with the experimental results conducted previously. The verified FE models are then utilized to conduct a parametric analysis considering two different column geometries and cross-sections, five reinforcement ratios, two concrete compressive strengths, three types of ties materials, and several loading eccentricities to develop a set of interaction diagrams that may provide valuable data for design purposes. The results indicated that the FRP bars could have a significant contribution to the overall capacity of FRP-RC columns by up to 35% of the total force at failure, depending on the reinforcement ratio. The performance of both the GFRP- and BFRP-RC columns was almost similar in terms of capacity, deflection, and bar strength contribution.

International audience; Elasto-plastic multiscale approaches are known to be suitable to model the mechanical behavior of metallic materials during forming processes. These approaches are classically adopted to explicitly link relevant microstructural effects to the macroscopic behavior. This paper presents a finite strain elastoplastic self-consistent model for damaged polycrystalline aggregates and its implementation into ABAQUS/Standard finite element (FE) code. Material degradation is modeled by the introduction of a scalar damage variable at each crystallographic slip system for each individual grain. The single crystal plastic flow is described by both the classical and a regularized version of the Schmid criterion. To integrate the single crystal constitutive equations, two new numerical algorithms are developed (one for each plastic flow rule). Then, the proposed single crystal modeling is embedded into the self-consistent scheme to predict the mechanical behavior of elasto-plastic polycrystalline aggregates in the finite strain range. This strategy is implemented into ABAQUS/Standard FE code through a user-defined material (UMAT) subroutine. Special attention is paid to the satisfaction of the incremental objectivity and the efficiency of the convergence of the global resolution scheme, related to the computation of the consistent tangent modulus. The capability of the new constitutive modeling to capture the interaction between the damage evolution and the microstructural properties is highlighted through several simulations at both single crystal and polycrystalline scales. It appears from the numerical tests that the use of the classical Schmid criterion leads to a poor numerical convergence of the self-consistent scheme (due to the abrupt changes in the activity of the slip systems), which sometimes causes the computations to be prematurely stopped. By contrast, the use of the regularized version of the Schmid law allows a better convergence of the self-consistent approach, but induces an important increase in the computation time devoted to the integration of the single crystal constitutive equations (because of the high value of the power-law exponent used to regularize the Schmid yield function). To avoid these difficulties, a numerical strategy is built to combine the benefits of the two approaches: the classical Schmid criterion is used to integrate the single crystal constitutive equations, while its regularized version is used to compute the microscopic tangent modulus required for solving the self-consistent equations. The robustness and the accuracy of this novel numerical strategy are particularly analyzed through several numerical simulations (prediction of the mechanical behavior of polycrystalline aggregates and simulation of a circular cup-drawing forming process).

This paper aims to investigate the flexural behavior of concrete filled tubes (CFSTs) made of seamless steel which can handle more pressure than welded steel. Experimental, Theoretical and Finite Element Analyses are utilized for this purpose. The experimental program consists of four-point bending tests of six CFSTs and three hollow steel tubes (STs) for three different Diameter-to-thickness (D/t) ratios of 7.82, 13.5 and 17.5. The test results included are the moment versus displacement and strains, failure modes and ultimate capacities. The contribution of the concrete infill to the flexural capacity was more significant in specimens with higher D/t ratios. All CFST beams exhibited ductile mode of failure with no local buckling. The experimental moments are compared to theoretical nominal moments calculated by well-known international design codes such as the Architectural Institute of Japan (AIJ), the British Standard (BS), the AISC-LRFD, and the Euro code4. Only the AIJ equations predicted non-conservative capacities particularly at the highest D/t ratio. The other codes and standards were more conservative since they did not consider the effect of concrete confinement in their design equations. Finite Element (FE) simulation of the flexural response of CFST is also conducted by developing a nonlinear 3D model considering both material and geometric nonlinearities. The FE model is verified using the present experimental results and a good agreement was achieved in terms of the moment capacity, the failure mode and the moment-mid span deflection curves. In addition, the verified finite element model was used to carry out a parametric study considering wider ranges of D/t ratios and yield strengths.

International audience; In the present paper, an efficient numerical tool is developed to investigate the ductility limit of polycrystalline aggregates under in-plane biaxial loading. These aggregates are assumed to be representative of very thin sheet metals (with typically few grains through the thickness). Therefore, the plane-stress assumption is naturally adopted to numerically predict the occurrence of strain localization. Furthermore, the initial crystallographic texture is assumed to be planar. Considering the latter assumptions, a two-dimensional single crystal model is advantageously chosen to describe the mechanical behavior at the microscopic scale. The mechanical behavior of the planar polycrystalline aggregate is derived from that of single crystals by using the full-constraint Taylor scale-transition scheme. To predict the occurrence of localized necking, the developed multiscale model is coupled with the bifurcation theory. As will be demonstrated through various numerical results, in the case of biaxial loading under plane-stress conditions, the planar single crystal model provides the same predictions as those given by the more commonly used three-dimensional single crystal model. Moreover, the use of the two-dimensional model instead of the three-dimensional one allows dividing the number of active slip systems by two and, hence, significantly reducing the CPU time required for the integration of the constitutive equations at the single crystal scale. Furthermore, the planar polycrystal model seems to be more suitable to study the ductility of very thin sheet metals, as its use allows us to rigorously ensure the plane-stress state, which is not always the case when the fully three-dimensional polycrystalline model is employed. Consequently, the adoption of this planar formulation, instead of the three-dimensional one, allows us to simplify the computational aspects and, accordingly, to considerably reduce the CPU time required for the numerical predictions.

International audience; In several modern technological applications, the formability of functional metal components is often limited by the occurrence of localized necking. To retard the onset of such undesirable plastic instabilities and, hence, to improve formability, elastomer substrates are sometimes adhered to these metal components. The current paper aims to numerically investigate the impact of such elastomer substrates on the formability enhancement of the resulting bilayer. To this end, both the bifurcation theory and the initial imperfection approach are used to predict the inception of localized necking in substrate-supported metal layers. The fullconstraint Taylor scale-transition scheme is used to derive the mechanical behavior of a representative volume element of the metal layer from the behavior of its microscopic constituents (the single crystals). The mechanical behavior of the elastomer substrate follows the neo-Hookean hyperelastic model. The adherence between the two layers is assumed to be perfect. Through numerical simulations, it is shown that bonding an elastomer layer to a metal layer allows significant enhancement in formability, especially in the negative range of strain paths. These results highlight the benefits of adding elastomer substrates to thin metal components in several technological applications. Also, it is shown that the limit strains predicted by the initial imperfection approach tend towards the bifurcation predictions as the size of the geometric imperfection in the metal layer reduces.

Reactive powder concrete (RPC) is an ultra-high performance concrete (UHPC) with an enhanced microstructure. Over the past few years, the demand for RPC has increased due to its superior properties. However, RPC is characterized by its low water-to-binder ratio, high cement and silica fume (SF) content, and absence of coarse aggregates which not only harm sustainable development, but also increase the production costs of RPC and generate shrinkage problems. Within this framework, many studies attempted to use different materials to address these problems and produce eco-friendly RPC with similar performance to that of the traditional RPC. The primary objective of this paper is to present an updated review of the literature on the list of materials used for RPC production and assess their viability as partial and full replacement of cement, SF, and quartz sand/powder to produce ultra-high strength RPC. The effects of employing different curing regimes and mixing procedures on the compressive strength of RPC will also be reviewed. The results highlight that 1) the use of alternative mineral admixtures (glass powder, limestone & phosphorous slag) can successfully replace cement by up to 50%; 2) replacing SF with mineral admixtures such as slag and fly ash is possible and can yield comparable results by monitoring the molar Ca/Si ratio of the mixes; 3) Quartz sand/powder can successfully be replaced with other types of aggregates/fillers (titanium slag, glass sand, glass powder, rice husk ash , etc); 4) Waste steel fibers can yield comparable strength results to that of steel fibers and the hybridization of glass-steel and polypropylene-steel improves the strength compared to steel or other types alone; and 5) Four-stage mixing yields better strength properties (up to 22% enhancement) compared to three-stage mixing, but further research is required to confirm this finding and establish standard guidelines for the mixing of RPC.

The main goal of this research is to experimentally investigate the flexural response of concrete filled steel tubes (CFSTs) considering different cross-sections and concrete types. For this purpose, a total of 12 circular and 8 rectangular CFST beams with different Diameter (depth)-to-thickness ratios were cast using normal and recycled aggregate concrete mixes and were tested under four-point bending. Concrete compressive strengths of 30 and 50 MPa and recycled aggregate (RA) replacement percentages of 50 and 100% were used in the experimental investigation. The test results revealed promising outcomes on the feasibility of using RA in CFST systems under flexure . The flexural behavior of RACFSTs was found to be very similar to NACFSTs, and the change in the concrete compressive strength and RA percentages slightly affected the flexural behavior of RACFSTs. In addition, the experimental flexural capacity of RACFST beams were compared to the theoretical nominal moments predicted by well-known design codes and methods. The Architectural Institute of Japan design code was the most accurate to predict the flexural capacity of RACFSTs with an average of 5% difference only, while the British Standard significantly underestimated the flexural capacity of the tested RACFST beams by an average of 34%.

Fiber reinforced cementitious matrix (FRCM), a noncorrosive two-dimensional high strength fiber reinforced polymer (FRP) mesh saturated with inorganic cementitious mortar is evolving as a viable option for retrofitting damaged RC structures . While numerous studies investigated the potential of FRCM strengthening in shear and flexural applications, limited studies explored the confinement of short and slender columns, particularly using finite element (FE) analysis. In this study, a three-dimensional (3D) nonlinear finite element (FE) model is developed using ABAQUS to study the behavior of corrosion damaged RC columns retrofitted with poly-paraphenylene-ben-zobisoxazole (PBO) FRCM systems. Geometric and material nonlinearities in concrete, cement mortar and composite are incorporated in the FE model that is validated through axial capacity and failure mode comparisons against published literature. A comprehensive parametric study involving 180 models is conducted considering the effects of five parameters: (a) cross section type (square vs circular), (b) FRCM wraps (1, 2, 3 and 4 layers), (c) pre-damage level (mild, moderate and severe), (d) eccentricity ratio (0.0, 0.3, 0.5, 0.75, 1.0, 1.25 and 1.5) and (e) column length (short and slender). Concrete compressive strength of 30 MPa and a longitudinal reinforcement ratio of 2% are adapted in all models. Results indicated that retrofitting corrosion damaged RC columns with PBO-FRCM effectively resorted and enhanced the original axial capacity and ductility of all column specimens and at all damage levels. A positive correlation between number of FRCM layers and axial capacity and ductility enhancement was observed and was more pronounced in circular columns. Increasing the number of FRCM layers also increased the axial capacity of eccentrically loaded columns irrespective of damage level and eccentricity ratio. Finally, comparison of axial capacity using ACI 549.4R-13 provisions against FE results disclosed that the code provisions underestimated the axial capacity of short RC columns retrofitted with PBO-FRCM by about 20%.

Over the last decade, the utilization of fiber-reinforced polymers (FRP) has been increased due to their versatile properties in concrete columns as a replacement of steel bars and their contribution to the axial load-carrying capacity of short concrete columns (SCC). Different researchers proposed equations to understand the load-carrying capacity of FRP rebars in SCC at the ultimate limit state (ULS). However, the current design practices have their reservation on the use (or taking the contribution) of FRP bars as the main vertical reinforcement in SCC. The present study aims to provide reliability analysis of all well-known physical models (for predicting the effect of FRP in SCC under concentric loading at ULS) through Artificial Neural Network (ANN) models (which do not base on mechanics) and new proposed equation (having a constant parameter to incorporate the lateral confinement effect). For this purpose, a database of 108 samples of SCC with FRP bars under concentric loading only, with detailed information (i.e., cross-section Ag, length of column L , Elastic Modulus of FRP Ef , compressive strength of concrete fc (MPa), longitudinal reinforcement ratio ρl (%), transverse reinforcement ratio ρt (%), and the ultimate axial load Pexp (kN), is collected from previous studies. The predicted axial load values (Ppred) from the ANN model (R = 0.94 and RMSE = 0.32) and proposed equation (R = 0.94 and RMSE = 0.32) exhibited closer results to the experimental values ( Pexp)as compared to counterpart physical models. Comparative studies of ratio Pexp/Ppred against the critical parameters exhibited better accuracy of the ANN model and proposed equation as compared to counterpart physical models.

Nowadays, there is a significant demand on developing and expanding the existing infrastructure which necessitates the implementation of fast and cost effective construction methods such as the secant pile walls. The secant pile walls constructed in a circular plan layout to form a vertical shaft provide unique advantages such as compression ring behaviour. Compression rings act as a single-unit system in resisting lateral earth pressure and converting loads from all directions to compressive forces which can be resisted only by low concrete strength. Secant pile walls require stringent drilling tolerances to be achieved in order to behave as a compression ring and to perform as an effective groundwater cut-off wall. This paper presents a parametric study that investigates various aspects of the behaviour of circular shafts constructed using secant pile walls. The aspects that are studied include the identification of the magnitude and distribution of earth pressures exerted on circular shafts by ...

Constitutive equations, as extremely useful computational/numerical tools in describing metals’ thermomechanical behavior, strongly depend on crystal structure, chemical composition and the range of applied strain, strain rate and temperature. Therefore, utilizing one constitutive equation for a wide range of field variables (strain, temperature, and strain rate) is less likely to accurately capture the behavior observed in experiments. It is particularly challenging to derive an inclusive constitutive model for a multiphase alloy such as Ti-6Al-4V , considering its phase transformation (HCP-BCC crystal structure change), variation in reported chemical compositions and a spectrum of different microstructural morphologies. In this work, a microstructures-based constitutive relation based on the Voyiadjis-Abed (VA) model is presented to describe the thermoviscoplastic behavior of Ti64 Alloy by additively decomposing the coupling effect of temperatures and strain rates on yielding and strain hardening. The present modeling is compared with the empirical relation of Johnson-Cook (JC) at a wide range of temperatures (up to 1000 K) and strain rates (up to 6000 s −1 ). The isothermal and adiabatic deformation behavior of the alloy are predicted and compared using three different sets of experimental results. The findings of this work suggest that the VA model is more capable in predicting the thermomechanical behavior of the alloy, with at most a 5% deviation compared to experimental results.

This paper's main objective is to study the flexural behavior of concrete beams reinforced with basalt fiber-reinforced polymer (BFRP) bars that were exposed to harsh environmental conditions before casting. The bars were placed in a tank outdoors for a year where they were exposed to direct heat from the sun, humidity and occasional rain. A four-point test was conducted on four concrete beams reinforced longitudinally with unexposed and exposed BFRP bars, respectively. A 30 MPa concrete compressive strength was used to cast all beams, which were designed to be over-reinforced, and thus were expected to fail by concrete crushing. The effects of exposure and reinforcement ratio were studied by investigating the cracking moments, load-deflection curves and failure modes. Results indicated that exposure had no significant effect on ductility and did not affect the failure mode. Also, increasing the reinforcement ratio increased the capacity of the beams as per the theoretical prediction by the ACI440-1R.15.

This paper aim to investigate the flexural behavior of concrete beams reinforced longitudinally with Basalt Fiber Reinforced Polymer (BFRP) bars. Finite element (FE) modeling software, ABAQUS, is used to develop a nonlinear model capable of simulating the behavior of FRP reinforced beams in flexure. To validate the FE model, data extracted from ABAQUS were verified through a comparison with published experimental data. Through a parametric study, this paper aims to study the effect of varying the reinforcement ratio on the flexural behavior of BFRP reinforced beams. The reinforcement ratios studied are 0.003, 0.0047, 0.0068, and 0.0123. The paper also present comparative analysis among various FRP reinforcement bars. BFRP reinforced beam is compared with Glass Fiber Reinforced Polymer (GFRP) and Carbon Fiber Reinforced Polymer (CFRP) reinforced beams with similar reinforcement ratio. A third parametric study was conducted to evaluate the effect of varying the number of reinforcement bars while keeping the axial stiffness constant. The results showed an increasing trend of flexural capacity with the increase in reinforcement ratio. The results also indicated the much larger deflection resistance of the CFRP reinforced beams as compared to BFRP and GFRP beams. Lastly, varying the number of reinforcement bars had no effect on the strength of the beam but rather on the stiffness.

This paper presents a numerical study of axial behavior of circular concrete columns reinforced with Glass Fiber Reinforced Polymer (GFRP) bars and spirals. A nonlinear finite element (FE) model was developed using ABAQUS to predict the compressive behavior of the concentrically loaded columns. Initially, the FE model was verified using an existing experimental paper which investigate the axial capacity of circular concrete columns reinforced with GFRP bars and spirals. The concrete used in the experiment had a compressive strength of 41.9 MPa. Parametric study aiming at evaluating the effect of varying the longitudinal and transverse GFRP reinforcement ratios in the columns was carried out. The results indicated that both the ductility and peak load increase when the reinforcement ratio increases. For spirals, when the diameter increases or the pith decreases, the ductility and capacity increase but with keeping a pitch that allows confinement in the case of changing the spiral diameter.

International audience; In numerical strategies developed for determining the efective macroscopic properties of heterogeneous media, the efcient and robust computation of macroscopic tangent moduli represents an essential step to achieve. Indeed, these tangent moduli are usually required in several numerical applications, such as the FE2 method and the prediction of the onset of material and structural instabilities in heterogeneous media by loss of ellipticity approaches. This paper presents a comparative study of three numerical techniques for the computation of such tangent moduli in the context of periodic homogenization: the perturbation technique, the condensation technique and the fuctuation technique. The practical implementations of these techniques within ABAQUS/Standard fnite element (FE) code are especially underlined. These implementations are based on the development of a set of Python scripts, which are connected to the fnite element computations to handle the computation of the tangent moduli. The extension of these techniques to mechanical problems exhibiting symmetry properties is also detailed in this contribution. The reliability, accuracy and ease of implementation of these techniques are evaluated through some typical numerical examples. It is shown from this numerical and technical study that the condensation method reveals to be the most reliable and efcient. Also, this paper provides valuable reference guidelines to ABAQUS/Standard users for the determination of the homogenized tangent moduli of linear or nonlinear heterogeneous materials, such as composites, polycrystalline aggregates and porous solids.

International audience; During the last decades, a family of assumed-strain solid-shell finite elements has been developed with enriched benefits of solid and shell finite elements together with special treatments to avoid locking phenomena. These elements have been shown to be efficient in numerical simulation of thin 3D structures with various constitutive models. The current contribution consists in the combination of the developed linear and quadratic solid-shell elements with complex anisotropic plasticity models for aluminum alloys. Conventional quadratic anisotropic yield functions are associated with less accuracy in the simulation of forming processes with metallic materials involving strong anisotropy. For these materials, the plastic anisotropy can be modeled more accurately using advanced non-quadratic yield functions, such as the anisotropic yield criteria proposed by Barlat for aluminum alloys. In this work, various quadratic and non-quadratic anisotropic yield functions are combined with a linear eight-node hexahedral solid-shell element and a linear six-node prismatic solid-shell element, and their quadratic counterparts. The resulting solid-shell elements are implemented into the ABAQUS software for the simulation of benchmark deep drawing process of a cylindrical cup. The predicted results are assessed and compared to experimental ones taken from the literature. Compared to the use of conventional quadratic anisotropic yield functions, the results given by the combination of the developed solid-shell elements with non-quadratic anisotropic yield functions show good agreement with experiments.

International audience; In the present contribution, a two-surface plasticity model is coupled with several diffuse and localized necking criteria to predict the ductility limits of hexagonal closed packed sheet metals. The plastic strain is considered, in this two-surface constitutive framework, as the result of both slip and twinning deformation modes. This leads to a description of the plastic anisotropy by two separate yield functions: the Barlat yield function to model plastic anisotropy due to slip deformation modes, and the Cazacu yield function to model plastic anisotropy due to twinning deformation modes. Actually, the proposed two-surface model offers an accurate prediction of the plastic anisotropy as well as the tension–compression yield asymmetry for the material response. Furthermore, the current model allows incorporating the effect of distortional hardening resulting from the evolution of plastic anisotropy and tension–compression yield asymmetry. Diffuse necking is predicted by the general bifurcation criterion. As to localized necking, it is determined by the Rice bifurcation criterion as well as by the Marciniak & Kuczynski imperfection approach. To apply both bifurcation criteria, the expression of the continuum tangent modulus associated with this constitutive framework is analytically derived. The set of equations resulting from the coupling between the Marciniak & Kuczynski approach and the constitutive relations is solved by developing an efficient implicit algorithm. The numerical implementation of the two-surface model is assessed and validated through a comparative study between our numerical predictions and several experimental results from the literature. A sensitivity study is presented to analyze the effect of some mechanical parameters on the prediction of diffuse and localized necking in thin sheet metals made of HCP materials. The effect of distortional hardening on the onset of plastic instability is also investigated.

International audience; The scientific literature has shown the strong effect of void size on material response. Several yield functions have been developed to incorporate the void size effects in ductile porous materials. Based on the interface stresses of the membrane around a spherical void, a Gurson-type yield function, which includes void size effects, is coupled with the bifurcation theory for the prediction of plastic strain localization. The constitutive equations as well as the bifurcation-based localization criterion are implemented into the finite element code ABAQUS/Standard within the framework of large plastic deformations. The resulting numerical tool is applied to the prediction of forming limit diagrams (FLDs) for an aluminum material. The effect of void size on the prediction of FLDs is investigated. It is shown that smaller void sizes lead to an increase in the ductility limits of the material. This effect on the FLDs becomes more significant for high initial porosity, due to the increase of void-matrix interface strength within the material.

International audience; Due to their attractive properties, perforated sheets are increasingly used in a number of industrial applications, such as automotive, architecture, pollution control, etc. Consequently, the accurate modeling of the mechanical behavior of this kind of sheets still remains a valuable goal to reach. This paper aims to contribute to this effort by developing reliable numerical tools capable of predicting the occurrence of necking in perforated sheets. These tools are based on the coupling between the periodic homogenization technique and three plastic instability criteria. The periodic homogenization technique is used to derive equivalent macroscopic mechanical behavior for a representative volume element of these sheets. On the other hand, the prediction of plastic instability is based on three necking criteria: the maximum force criterion (diffuse necking), the general bifurcation criterion (diffuse necking), and the loss of ellipticity criterion (localized necking). The predictions obtained by applying the three instability criteria are thoroughly analyzed and compared. A sensitivity study is also conducted to numerically investigate the influence on the prediction of necking of the design parameters (dimension, aspect-ratio, orientation, and shape of the holes), the macroscopic boundary conditions and the metal matrix material parameters (plastic anisotropy, hardening).

International audience; In this work, nonlinear dynamic analysis of thin structures is investigated using quadratic solid-shell (SHB-EXP) elements. The proposed SHB-EXP elements are based on a fully three-dimensional formulation using an in-plane reduced-integration scheme along with the assumed-strain method in order to alleviate most locking phenomena. These developments consist of a twenty-node hexahedral element, denoted SHB20-EXP, and its fifteen-node prismatic counterpart, denoted SHB15-EXP. The formulation of these elements is combined with fully three-dimensional behavior models, including elastic behavior as well as anisotropic plastic behavior for metallic materials. The resulting formulations are implemented into ABAQUS explicit/dynamic software package in the framework of large displacements and rotations. First, to assess the performance of the SHB-EXP elements, four representative nonlinear dynamic benchmark tests have been conducted. Then, impact / crash problem and deep drawing of cylindrical cup have been performed to demonstrate the capabilities of the SHB-EXP elements in handling various types of nonlinearities (large strains, anisotropic plasticity, and double-sided contact). Comparisons with results obtained by ABAQUS elements as well as with reference solutions taken from the literature show the good capabilities of the developed quadratic SHB-EXP elements for the explicit dynamic simulation of thin structures.

International audience; For biaxial stretching strain paths, which are typically encountered in sheet metal forming, the stress triaxiality ranges from 0.33 to 0.67. At this low level of triaxiality, voids change their shape from spherical to general spheroidal shape. In the literature, unit cell studies show the dependency of void shape on the lode parameter, especially at low stress triaxiality. Several authors also pointed out the influence of lode parameter on ductile failure. In the current study, lode parameter dependent Gurson-based models are combined with bifurcation analysis for the prediction of formability limits of TRIP780 steel sheet. Moreover, Thomason’s coalescence criterion is considered for the prediction of critical porosity. For the anisotropic plastic behavior of the dense material, the quadratic Hill’48 yield surface is considered. Contribution to porosity evolution due to shear mechanism is also analyzed. In addition, the effect of lode parameter on the prediction of forming limit diagram (FLD) is investigated. It is observed that the accelerated evolution of porosity, due to the consideration of lode parameter, induces lower ductility limits for the modified Gurson-based model, as compared to the original Gurson model. The results also demonstrate that the use of the Thomason coalescence criterion for the determination of critical porosity plays an important role in the prediction of FLDs, as compared to fixed critical porosity used in the Gurson-Tvergaard-Needleman model.

The main aim of this paper is to investigate the behavior of short concrete column reinforced longitudinally with Basalt Fiber-Reinforced Polymers (BFRP) rebar. A nonlinear 3D finite element (FE) model is developed using the commercial software ABAQUS to conduct the analysis. Geometric and material nonlinearities were utilized to simulate the inelastic large deformation of concrete material. The FE model was first validated by comparing its capability to predict the compressive strength with the analytical solution for concrete short columns reinforced with conventional steel bars. Concentric and eccentric loading cases were considered for this verification analysis. The validated FE model was then used to develop an interaction diagram for BFRP-RC short columns. Values of axial capacities and moments at different points were used to plot interaction diagrams.

The aim of this paper is to develop a 3D non-linear finite element model to simulate the behavior of Concrete-Filled Steel Tubes (CFSTs) under compressive loading. The FE model was developed in the commercial software ABAQUS. The proposed FE model was validated by comparing numerical results to their experimental counterparts obtained from previous study. The model was then utilized to perform a parametric study that examines the effect of geometric and material properties on the compressive behavior of CFSTs. Compression tests of CFST samples with different (D/t) ratios were simulated in the proposed model. It was found that both axial load capacity and stiffness of CFST decrease with increasing (D/t) ratios. The effect of steel yield strength on the behavior of CFST samples was also investigated using the FE model. The numerical simulation showed that axial load capacity increases as steel yield strength increases.

This paper presents a three-dimensional nonlinear Finite Element (FE) model of an Ultra-High Performance Concrete (UHPC) beam reinforced with High-Strength Steel (HSS) bars. The UHPC and HSS mechanical parameters were acquired from experimental tests of two distinct studies. As a result, these parameters were employed in an FE software package, Abaqus, and were able to simulate the nonlinear behavior of UHPC and HSS bars implemented in beams. A mesh sensitivity analysis was performed to obtain a sufficient mesh size that allowed the analysis to converge while avoiding any computation complexities. Afterwards, a parametric study was conducted by employing a Python-written macro that commanded the CAE environment to vary the beam's depth and steel ratio. This allowed the authors to investigate the impacts of varying the beam's depth and steel ratio on its moment-deflection response. It was concluded that the main parameter contributing to the accuracy of the FE model was the depth of the UHPC beam.

This paper experientially investigates the effect of adding basalt microfibers to the concrete mix on the shear response of short beams reinforced longitudinally with Basalt Fiber Reinforced Polymer (BFRP) bars. The main objective is to study the feasibility of enhancing the shear capacity and cracking response of BFRP-RC deep beams due to the presence of microfibers. A total of eight beams with a length of 2000 mm and a cross-section of 150 mm × 260 mm each were cast for this purpose. Six beams were cast using basalt microfibers, one beam was cast using synthetic fibers and one was cast using plain concrete. The test parameters included shear span-to-depth ratio, longitudinal reinforcement ratio, concrete compressive strength , and the type of microfibers used in the concrete mix. Experimental results showed that the presence of basalt microfibers and synthetic fibers have a significant influence in enhancing the overall stiffness, toughness, and ultimate shear strength of the tested beams. The presence of basalt microfibers resulted in an increase in the maximum load carrying capacity by 42%. The experimental results are then compared with the strut-and-tie model (STM) predictions according to ACI-318-14. The constructed STM model resulted in a conservative prediction of the ultimate shear strength of tested beams.

The Hopkinson Split Pressure Bar system allows to carry out compression tests at high impact velocities corresponding to high strain rates up to 5000 s −1 . For composite materials, however, negative phenomena related to wave propagation and specimen geometry may disturb experimental analysis and, therefore, should be taken into account. Potential errors are mainly due to friction, inertia and wave dispersion. In order to provide a complete analysis of experimental results for composite materials under dynamic compression, a procedure was developed to estimate friction and dispersion effects at the specimen-bar contact zone. For this purpose, dynamic tests were carried out on woven glass-fiber-reinforced Polyamide (PA6) composites using Hopkinson׳s bar and pin-on-disk tribometer tests techniques. Results showed that the state of friction characterizing the PA6/glass material differs as per the orientation of fibers. The frictional regime is relatively more severe in case where the fibers are normal to the direction of friction.

The objective of this research is to generate design maps to identify functionally graded microstructures with enhanced fracture toughness. Several Functionally Graded Materials (FGMs) with an edge crack and membrane loading are considered and the resulting J-integral values are computed numerically using Finite Element Analysis. In order to capture the resulting stress fields accurately, Barsoum elements are used in the vicinity of the crack tip and the simulations are carried out for several crack lengths (a) and material contrasts (κ). The averages of the J-integral values are used to determine the normalized Stress Intensity Factors which are then benchmarked with existing analytical solutions in special cases. Furthermore, in order to facilitate an objective comparison between FGMs and homogeneous materials, a constraint is imposed on each of the microstructure so that the volume averaged modulus remains the same although the spatial variation is very different. Subsequently, we demonstrate that a FGM could perform either better or worse than the reference homogeneous material depending upon the crack length, the type of functional gradation and the material contrast (thereby the local gradient of the modulus at the crack tip). Finally, the notion of ‘Fracture Index’ is introduced using which ‘design maps’ are created in the (a−κ) space that reveal microstructures with enhanced fracture resistance. These maps are universal since any Functionally Graded Material can be mapped as a point on this space.

The buckling of slender columns with functionally graded microstructures is studied. In such columns, the flexural modulus is varied in a controlled manner along the column length. The objective is to identify microstructures that maximize (and minimize) the critical buckling load when compared to a reference homogeneous column. Several microstructures are examined and a constraint is imposed so that the volume averaged flexural modulus remains the same in all columns. The buckling load is determined using both the linear perturbation analysis as well as the Rayleigh–Ritz method. A relationship between the material distribution and the corresponding mode shape is established.

International audience; In this paper, four plastic instability criteria, which are based on the bifurcation theory, are coupled with the GTN damage model for the prediction of diffuse and localized necking. General bifurcation (GB) criterion and limit-point bifurcation (LPB) criterion are used to predict diffuse necking, while loss of ellipticity (LOE) criterion and loss of strong ellipticity (LOSE) criterion are used to predict localized necking. The resulting constitutive equations and instability criteria are implemented into the finite element code ABAQUS/Standard. The constitutive equations are formulated within the framework of large deformations and fully three-dimensional approach. Since the developed numerical tools have intended applications mainly for thin sheet metals; therefore, the plane-stress conditions are considered within the instability criteria. The present contribution focuses on the effect of destabilizing mechanisms, due to non-associative plasticity and non-normal plastic flow rule, on the prediction of forming limit diagrams (FLDs). Theoretical classification of the bifurcation criteria, in terms of their order of prediction of critical necking strains, is first presented. Then, several variants of the GTN model are combined with the bifurcation criteria for the prediction of FLDs for fictitious materials. It is shown that the hierarchical prediction order of the different instability criteria is consistent with the theoretical classification, for all the considered variants of the GTN model. More specifically, it is shown that the GB criterion provides a lower bound to all bifurcation criteria, in terms of necking prediction, while the LOE criterion represents an upper bound.

This study investigates the behaviour of concrete columns reinforced with longitudinal and transverse basalt fiber-reinforced polymer (BFRP) bars, the most recent of FRP composites. Twelve full-scale concrete columns reinforced with longitudinal BFRP bars and either steel or BFRP ties were tested under both concentric and eccentric loadings. The investigated parameters included the type and spacing of the transverse reinforcement (BFRP and steel ties) and the load eccentricity-to-width ratio (e/h = 0, 22.2%, 44.4%). The test results showed that reducing the spacing of the BFRP ties improved the ductility and confinement efficiency of the BFRP-reinforced concrete (BFRP-RC) columns. However, reducing the ties’ spacing had an insignificant effect on both the load-carrying capacities of the columns and the contribution of the longitudinal bars to their ultimate capacities. Moreover, BFRP-RC columns confined with BFRP ties exhibited ultimate capacities, bar strength contribution, and confinement efficiency comparable with their counterpart columns confined with steel ties at the same spacing. This study displayed that the current code provisions of CSA-S806-R17 and ACI440.1R-15 for FRP transverse reinforcement can ensure adequate confinement of the concrete core for BFRP-RC columns.

Fiber-reinforced cementitious matrix (FRCM) systems have recently emerged as an innovative technique to strengthen and retrofit reinforced concrete structures. These non-corrosive systems involve the use of high strength reinforcing textiles sandwiched between layers of cementitious mortars. This paper aims to study the effect of retrofitting newly constructed short columns with FRCM using PBO type of textiles. The experimental program consisted of testing 4 rectangular columns and 4 circular columns under concentric loading. All columns had a reinforcement ratio of 0.02 and were cast with concrete of 30 MPa compressive strength. For each type of cross-section, columns were wrapped with 1, 2 or 4 layers of PBO FRCM. Overall, the strengthened columns exhibited higher load carrying capacity than their control unwrapped counterpart with an increase ranged between 5.1% and 36%. The confining effect of FRCM layers was more pronounced in the circular columns than in the square ones. It was also noticed that all columns exhibited similar responses in terms of load -strain relationship irrespective of the column shape and the number of FRCM layers used. Furthermore, the displacement levels increased as the number of layers increased which indicated an increase in ductility of columns wrapped with FRCM.

Beams are structural components that are mainly utilized to resist flexure. However, beam sections are also commonly used to resist axial tension and compression in certain situations such as when they are used as truss members or braces. Pretwisting compression members strengthens their weak flexural plane and weakens their strong flexural plane, leading to an overall improvement in the buckling capacity. In this paper, pretwisting is applied to structural steel UB100 × 50 × 9.3 beam sections, both experimentally and numerically using finite element (FE) analysis, in an attempt to improve their critical buckling capacity. The experimental study consists of fourteen specimens of three different lengths and a variety of pretwist angles, while the linear-perturbation FE analysis considers ninety-one specimens of eight length groups and a pretwist angle range between 0° and 180°. In both studies, it was found that pretwisting improves the critical buckling capacity of UB100 × 50 × 9.3 beams. The linear-perturbation analysis also showed that the length of the members has no effect on the buckling capacity improvement, and that this improvement is highly significant under fixed-fixed end conditions but not under pinned-pinned conditions.

This paper presents finite element (FE) analysis of the structural behavior of a concrete sandwich panel that is 210 mm thick. The analyzed section is composed of two concrete layers that are 70 mm thick, and a thermal polystyrene insulation layer that is 70 mm thick placed in between. This wall section is commonly used as a precast non-bearing external wall. However, the intent of this study is to investigate the structural performance of such a sandwich panel as a load-bearing element under eccentric axial loading. A nonlinear FE model for a concrete sandwich panel was developed for this purpose using ABAQUS commercial software, implementing a displacement-controlled analysis to trigger failure of the wall element. The composite action of the sandwich panel resulted in a ductile failure mode instead of sudden crushing, and its ultimate capacity exceeded the design load expected for a typical G+2 residential building. The load vs axial displacement response of the panel exhibited a linear behavior up to 70% of the ultimate capacity in which the two concrete layers displayed equal lateral displacements. However, different lateral displacements were encountered along the height of the two concrete layers during the nonlinear stage, starting from the top and continuing to grow down to separate the two layers. First and second modes of buckling were observed at the linear and nonlinear stages, respectively.

International audience; In most voided metallic materials, the failure process is often driven by the competition between the phenomena of void coalescence and plastic strain localization. This paper proposes a new numerical approach that allows an accurate description of such a competition. Within this strategy, the ductile solid is assumed to be made of an arrangement of periodic voided unit cells. Each unit cell, assumed to be representative of the voided material, may be regarded as a heterogeneous medium composed of two main phases: a central primary void surrounded by a metal matrix, which can itself be assumed to be voided. The mechanical behavior of the unit cell is then modeled by the periodic homogenization multiscale scheme. To predict the occurrence of void coalescence and macroscopic strain localization, the above multiscale scheme is coupled with several relevant criteria and indicators (among which the bifurcation approach and an energy-based coalescence criterion). The proposed approach is used for examining the occurrence of failure under two loading configurations: loadings under proportional stressing (classically used in unit cell computations to study the effect of stress state on void growth and coalescence), and loadings under proportional in-plane strain paths (traditionally used for predicting forming limit diagrams). It turns out from these numerical investigations that macroscopic strain localization acts as precursor to void coalescence when the unit cell is proportionally stressed. However, for loadings under proportional in-plane strain paths, only macroscopic strain localization may occur, while void coalescence is not possible. Meanwhile, the relations between the two configurations of loading are carefully explained within these two failure mechanisms. An interesting feature of the proposed numerical strategy is that it is flexible enough to be applied for a wide range of void shapes, void distributions, and matrix mechanical behavior. To illustrate the broad applicability potential of the approach, the effect of secondary voids on the occurrence of macroscopic strain localization is investigated. The results of this analysis reveal that the presence of secondary voids promotes the occurrence of macroscopic strain localization, especially for positive strain-path ratios.

The main objective of this study was to investigate experimentally and numerically the behavior of basalt fiber-reinforced polymer (BFRP) reinforcement exposed to a combination of ultraviolet rays, humidity, and rain. Specifically, the effects of the previously stated harsh exposure on the serviceability performance and flexural capacity of BFRP reinforced concrete beams was examined. Holding the exposure parameter constant, the study also evaluated the effects of reinforcement ratio and beam detailing on the flexural capacity and the bond-dependent coefficient (kb) of the beams. Seven beams were cast and tested, four of which were reinforced with exposed BFRP bars, two were reinforced with unexposed BFRP bars, and one specimen was cast and reinforced with steel bars to serve as a benchmark specimen. The results indicate that the kb factor was averaged to be 0.61 for all the beams. Test results also indicate that increasing the reinforcement ratio did not result in a directly proportional increase in the moment capacity. The period of exposure did not cause any significant impact on the behavior of the over-reinforced beams. Thus, a finite element model was created to simulate the impact of exposure on the behavior of under-reinforced BFRP reinforced concrete beams.