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This paper aims at studying the damage evolution of a [0/90]3S cross-ply flax/epoxy laminate repeatedly impacted at three energy levels of 5, 6 and 7 J. Several specimen plates were prepared by the vacuum infusion technique and then subjected to repeated low-velocity impacts. To assess external damage mechanisms in the impacted plates, an inspection of the back and front faces damage was conducted by using a high-resolution digital reflex camera. Moreover, different techniques were used to evaluate the internal damage such as intensive light exposure, infrared thermal imaging, and computed X-ray tomography. The obtained results show that damage is visible even at low energy level and starts to appear from the first impacts, especially in the back face of the flax/epoxy samples. In addition, after front and back faces cracks appear, delamination is the most predominant damage mechanism that occurs during the different phases of impact fatigue loading. Its size is found to extend with the energy level and the multiplication of impacts.

2D and 3D finite element models of nonwoven flax/polypropylene composite are developed in this work to estimate its elastic and dynamic properties. These models are based on an in-plane random generation of the nonwoven flax fibres embedded in 2D and 3D networks of polypropylene (PP) matrix with porosities. First, the elastic properties of the flax/PP nonwoven composite are numerically predicted and a comparison with the experimental results from tensile tests is conducted. Second, the dynamic properties resulted from free vibration tests, at different fibre weight ratios and porosity contents, are numerically determined. Finally, the flax fibre damping is predicted using the strain energy method and the finite element results. This allows proposing a first estimation of the damping coefficient of this natural fibre.

International audience; Natural fibre-reinforced biopolymer composites are of special interest because they are entirely bioresourced, recyclable and biodegradable. Poly(lactic acid) (PLA), poly(hydroxybutyrate- co-hydroxyvalerate) (PHBV) and poly(butylene succinate) (PBS) are among the most known environment-friendly biodegradable thermoplastics. Unfortunately, they present unbalanced mechanical characteristics when they are taken separately. The aim of this work is to overcome this problem using a blending process accompanied with fibre reinforcement. For this purpose, entirely biodegradable composite materials were fabricated and characterized. These biocomposites are based on two different ternary PLA/PHBV/PBS blends reinforced with twill flax fabrics and fabricated using extrusion and film-stacking techniques. Monotonic and cyclic load–unload tensile tests followed by acoustic emission and scanning electron microscopy observations were performed. In particular, the obtained biocomposites present interesting mechanical properties with a tensile modulus of 20 GPa and an ultimate tensile strength of 110 MPa.

In this paper, an analysis of the hygroscopic and hygroelastic behaviours of unidirectional flax fibre-reinforced epoxy composite is presented. Samples of this composite material were elaborated by the vacuum infusion process, then cut and prepared to be aged in tap water until saturation. To describe their hygroscopic behaviour, Fick’s model is considered and an optimisation procedure is developed to identify their macroscopic water diffusion parameters. After that, a plane finite element modelling of the hygroscopic behaviour of the aged flax-epoxy samples is conducted to identify the flax fibre radial and longitudinal water diffusion parameters using an inverse approach. Finally, a plane finite element analysis of their hygroelastic behaviour is proposed allowing the estimation of the hygroscopic internal stress in flax fibres and epoxy matrix. In particular, the hygroscopic analysis reveals that water diffusion is more pronounced in the direction of flax fibres compared to the transverse and thickness directions. In addition, the hygroelastic finite element modelling highlights the high compressive and tensile stress subjected to flax fibres and epoxy matrix, respectively, due to water absorption.

This work aims at evaluating the transverse and longitudinal coefficients of linear thermal expansion (CLTE) of unidirectional (UD) flax fibres reinforced green epoxy composites. The determination was made by taking length measurements with a calliper and a three-dimensional measuring machine at three discrete temperatures. The longitudinal and transverse CLTE of flax fibre were then estimated from an inverse approach by using two micromechanical models. It was required to use an optimisation program based on the minimisation of the quadratic error. Finally, the internal stresses induced by the thermal expansion were estimated in a symmetric cross-ply laminate ([0/90]s) by a 2D and a 3D analytical model based on classical laminate theory. The thermo-mechanical behaviour of the composite was governed by a linear elastic constitutive law taking into account the expansion strains induced by thermal effects. This was defined firstly without and secondly with taking into account the layer thermal strain in the thickness of the laminate (case 2D and 3D, respectively). The results highlighted the highly anisotropic nature of flax fibres. Indeed, the transverse CLTE was positive and estimated at 75 × 10-6 /°C whereas the longitudinal CLTE was negative and equal to -1.2 × 10-6 /°C. This can be explained by the microstructure and anisotropic properties of wall components of the flax fibre. The results also show that, in the 2D case, externals 0° plies are subject only to a compressive stress of -13.81 MPa in the x-direction and to a tensile stress of 13.81 MPa in the y-direction. Due to the stacking sequence (i.e. symmetric cross-ply laminate), the opposite was expected and finally observed for the internal 90° plies. In the 3D case, the normal stresses increased compared to the 2D case (+17%) while the in-plane shear stress was no longer zero (± 6 MPa).

The benefits of using materials from renewable resources are now well established. Plant fibre composites in particular are increasingly common in various industrial sectors, due to their attractive characteristics (specific strength and modulus, availability, cost) [1]. However, their development may be limited due to their high sensitivity to the moisture absorption. In addition, the low interfacial properties between hydrophilic reinforcement and hydrophobic matrix can result in delamination and thus lowering the mechanical properties. Although numerous works have studied the effect of water absorption on the mechanical properties of natural fibre composites, the study of their interlaminar properties in a wet environment remains limited [2]. It is within this context that Flax, Glass and Hybrid flax-glass Fibre Reinforced Epoxy (referenced by FFRE, GFRE and HFRE) laminates were investigated. Three twill weave fabric laminates were manufactured by a compression moulding process and subjected to ageing by immersion in 20°C water until saturation. Double cantilever beam test was performed to evaluate the mode I critical energy release rate as well as the corresponding resistance curve. Table 1 summarises the initiation fracture toughness GIc of the composites. For unaged composites, the results highlight that more energy is needed for the initiation of the cracks for FFRE, compared with HFRE and GFRE. After the water ageing, the drop of GIc is severe for the FFRE by about 60%. With the replacement of half flax layers with glass layers, the drop in HFRE become very lower (4% compared to its non-aged corresponding, 16% compared to unaged 100% flax). The reached value is comparable to the unaged 100% glass composite.

The aim of this work is to evaluate the dynamic properties of nonwoven flax, hemp, kenaf and glass fibre-reinforced polypropylene (PP) composites. Also, the influence of some parameters, such as the type of reinforcement, the fibre/matrix weight ratio, the fibre orientation and the porosity content, on the damping behaviour of these nonwoven composites is investigated. To this end, a free flexural vibrations analysis was conducted to experimentally identify their natural frequencies and their associated loss factors. The obtained results show that the nonwoven composites reinforced by natural fibres present higher loss factors compared with those of the glass-PP composite. These interesting damping properties make these nonwoven composites very attractive for automotive applications where the dissipation of vibrations is highly requested.

This contribution deals with the development of a four-node membrane composite finite element to analyse two-dimensional (2D) fibre-reinforced solids taking into account the local bending stiffness of fibres. This plane composite element is a combination of a four-node membrane element with rotational degrees of freedom (DOFs), modelling a unit of the matrix domain, and two-node Timoshenko beam elements that represent fibres crossing each matrix element. The so-called ’Projected Fibre Approach’ is then considered to express the beam elements variables in terms of their corresponding matrix elements. Accordingly, the obtained system of equations size is equivalent to that of a non-reinforced medium which considerably reduces the computing cost. To assess the accuracy of the proposed plane element, three examples are presented and the obtained results are found to agree well with the reference solutions.

International audience; This work aims at studying the effect of hygrothermal and UV cyclic aging on the tensile properties and esthetic characteristics of non-woven composites. The composite materials were thermo-compressed from non-woven mats made up of PP and flax or kenaf fibers. This works included evaluating the change in color appearance and analyzing the variations in tensile properties and damage mechanisms, depending on the aging time. The presence of the UV protection film on the composite surface showed its effectiveness against aging. From visual observations and measurement of colorimetric parameters, it has been proved effective in the reduction of the bleaching and yellowing of the composites. As regards the tensile tests, the UV protection film enabled to stabilize the Young's modulus after 1-week aging for Kenaf/PP and after 3- weeks for Flax/PP. After 4-weeks aging, it halved the number of acoustic emission events related to interfacial decohesion and fiber slippage/pull out for Flax/PP and Kenaf/PP composites.

In the present work, we propose to confront two modeling techniques for predicting the macroscopic properties of short alfa fiber-reinforced polypropylene composites. The first modeling was a micromechanical analysis using the Mori-Tanaka, Self-consistent, Diluted, Voigt, Reuss, and Neerfeld-Hill models. The second modeling was digital, using a specific finite element technique called the Projected Fiber (PF) approach. In the framework of this study, both 2D and 3D finite element analyses based on the PF approach were used. First, we proposed an inverse approach using these analytical and finite element models to predict the Young’s modulus of alfa fiber. Then, we compared the obtained results with the experiment values available in the literature. This comparison showed that the micromechanical models underestimated the alfa fiber’s Young’s modulus, while the finite element approach, PF, allowed for good framing of the experimental values. Moreover, we investigated the effect of fiber content on the predicted elastic properties of a polypropylene (PP) matrix reinforced with randomly distributed short alfa fibers. We noticed that the Diluted model was more accurate than the Mori-Tanaka and Self-consistent methods. As for the PF approach, its estimations were close to the experimental values. For example, the Young’s modulus for the PP/alfa with a 30 wt% of fiber content was underestimated with an error of 4.3%. It is shown that the 2D PF approach can provide calculated results with sufficient prediction accuracy.

The purpose of this paper is to investigate how the damping properties of structures made of carbon laminates can be increased when flax and viscoelastic layers are interleaved into the carbon laminates. The viscoelastic layers are constituted of Vinyl Ethylene Acetate (EVA) and are considered to take advantage of their high vibration damping. Their dynamic properties are very dependent on the frequency and accordingly a fundamental and extensive analysis was implemented. This dependency was identified from free vibrations of aluminium–EVA–aluminium sandwich beams. In a similar way, the damping coefficients of carbon and flax laminates were determined from flexural vibrations of test beam specimens. Next, a parametric analysis based on the finite element method is proposed to show how the flax and EVA layers could be arranged to improve the damping properties of carbon laminates. Finally, the study of a carbon structure permits to highlight the interest of flax-viscoelastic association to enhance its damping by 25–45% without affecting its dynamic behaviour.

International audience; This work aims at studying the low velocity impact and post-impact behaviour of flax/epoxy composites. The samples were composed of 8 plies of 2/2 twill weave fabric. The experimental device used for impact tests was a drop tower with impact energies varying from 5 to 34 J (perforation). Pictures of the sample were captured during the test with two high-speed cameras in order to perform high-speed imaging and Stereo Image Correlation (SIC) analysis. Residual properties have been assessed by bending after impact tests. High-speed imaging easily detected the back face cracks at maximum deflection while some were almost invisible after impact. The results also highlighted the material’s behaviour in three-stages. At low energy, no damage was observed. The cracks and the recovered energy evolved proportionally with the impact energy between 5 and 25 J, and then reached a threshold. The post-impact tests showed that even a 5 J impact resulted in a degradation of composite performance, with a loss of approximately 10% in stiffness and 21% in strength.

Flax-fibre composites are increasingly used as a replacement of classical synthetic composite materials. Due to the good energy absorption properties of flax fibres, they represent a promising alternative in structures susceptible to low velocity impact (LVI) damage. However, this type of dynamic loading is complex, expensive to perform and not necessarily easy to fully investigate. A simpler way to tackle this problem consists in investigating quasi-static indentation (QSI) tests, but this alternative remains relatively under-researched for natural fibre composites. Thus, this paper aims at providing a comparison between both types of loading to facilitate the later analysis and modelling of flax fabric laminates submitted to LVI. Six layers of a flax 2/2 twill fabric were used as reinforcement for epoxy laminates made through vacuum infusion. Specimens were then submitted to instrumented LVI and QSI tests at comparable energy levels, with a 1.5 %–3.9 % difference only. Load-displacement curves and visible damage were first analysed and compared between both test types. Then, the internal damage within QSI specimens were investigated using acoustic emission (AE). Our findings showed good analogies between both testing methods in all the stages of damage development. Great similarities were found in load-displacement curves (in shape, stiffness and peak load), in energy absorption capacity (at 5 and 10 J) and in visible damage. Actually, the differences between QSI and LVI remain low, i.e. 2.1 % for linear stiffness, from 0.2 to 5.6 % for peak load and less than 7% for the proportions of absorbed energy. Comparison of the QSI damage analysed from the AE data with LVI results from literature suggested similar mechanisms and onset sequences. These results revealed that QSI monitoring could provide characteristic indications on the damage evolution of flax-fibre woven composites during an LVI test.

International audience; This work presents an assessment of the damage mechanisms occurring during tensile tests in hybrid flax-glass fibres reinforced epoxy composites. The samples were composed of twill flax and glass fibre laminate plies with different stacking sequences and subjected to water immersion at 55 °C. The Acoustic Emission (AE) technique combined with scanning electron microscopy observations was used to identify the typical damage mechanisms and to follow their evolution. This identification was made with a statistical multivariable analysis in which the number of parameters and classes was optimised. Finally, the participation of each damage mechanism to the global failure was evaluated from the hits number and AE energy. The AE results showed that, although the hits number associated with the fibre failure was the lowest, their contribution to the overall failure of composites became predominant regarding the cumulative of AE energy. Furthermore, an additional group of AE signals induced by the delamination between flax and glass fibre layers was detected for the aged hybrid laminates.

The automotive and aeronautic industries have become strategic sectors for North African countries. However, the future growth of these sectors will likely depend on the availability of raw materials such as plant fibres to reinforce polymers. In the framework of this paper, we reviewed the research that focused on alfa fibres, which are deemed to be one of the most available fibres in the Mediterranean area. This plant also plays an essential role in protecting the Mediterranean countries from desertification and desert encroachment. Throughout this review, we discussed and expounded the morphological, chemical compositions and the mechanical properties of the alfa fibres and we compared them to other plants fibres. Moreover, we surveyed several academic research works that used different alfa fibres as reinforcement of thermoset and thermoplastic matrices. In particular, we outlined that alfa fibre can constitute a potential reinforcement of polymer matrices in the North Africa countries.

International audience; The hybrid solution of natural-synthetic fibres can be an effective option to enhance the moisture resistance of natural fibre reinforced polymer composites. This work aims at studying the effect of long-term water immersion of hybrid composites on their mechanical and damping properties. These properties were investigated using free vibrations from samples composed of quasi-unidirectional flax and glass layers and epoxy resin. The results showed that the saturation mass uptake and the diffusion coefficient of the composites were strongly dependent on the stacking sequence between the flax and glass layers. For instance, less than 25 days were necessary to reach the water saturation when flax fibre reinforcements were in the outer layers, whereas it took over 10 months when these reinforcements were in the inner layers. Compared to the flax fibre reinforced composite, the flax-glass hybrid laminate with two inner flax layers and two outer glass layers was the most efficient for a specification where damping and bending modulus are the main criteria. This one enabled a significant increase in bending and specific bending moduli (+38 % and +79 % respectively compared to the unaged flax laminate), a considerable slowing down of the diffusion phenomenon, while limiting the decrease in damping property with ageing (−20 %).

International audience; The mode-I interlaminar fracture toughness of flax, glass and hybrid flax-glass fibre woven composites was studied by using a DCB test. The acoustic emission signals recorded during the tests and scanning electron microscope images were used to analyse the damage mechanism of each composite. The crack initiation for the flax-fibre laminate needs the highest energy (1079 versus 945 for hybrid flax-glass fibre and 923 J/m2 for glass-fibre laminates). The morphology of the flax fibres, short and bonded together in bundles to manufacture the twill fabric, allows the creation of a larger amount of fibre bridging as the origin of this highest energy. Furthermore, hybridisation of glass fibres with flax fibres in an appropriate combination offers an interesting solution when the toughness of glass fibre composites needs to be increased. More interesting is the considerable advantage of the composite structure weight reduction due to the low flax fibre density.

International audience; This paper aims at investigating the hybridisation effect on the diffusion kinetic and the tensile mechanical behaviour of flax–glass fibres reinforced epoxy composites. For this purpose, hybrid composites composed of flax and glass fibre laminates with different stacking sequences were consolidated by compression moulding and subjected to environment ageing. The obtained results show that the water uptake and the diffusion coefficient are clearly reduced by the addition of glass fibre layers in flax laminate. The ageing conditions performed show that the flax–glass hybridisation presents a positive effect in a wet environment at low temperatures (∼20 °C) in the Young’s modulus and the tensile strength. For example, the Young’s modulus fell by 50% and 41% for hybrid laminates with 6% and 11% of glass fibres, and by 67% for the Flax laminate. However, the flax–glass hybridisation was not necessarily a relevant choice when the hybrid laminates were exposed in a wet environment at high temperatures. Indeed, at 55 °C, this hybridisation had a negative effect on the tensile strength and on the specific tensile strength.

International audience; The aim of this study is to show the interest of the mechanical and dynamical properties of glass-flax hybrid composites. Therefore, various staking sequences of glass-flax hybrid composites were manufactured and tested in free vibrations. The damping coefficients were identified by fitting the experimental responses of free-free bending vibrations. The obtained results show that the staking sequences and the position of flax fiber layers in the hybrid composites changed the properties, so a classification of different stacking sequences was established. In fact, the hybrid laminate made of two glass external layers placed on both sides of four flax layers is very interesting in term of its mechanical and damping properties. Indeed, it showed better specific bending modulus and loss factor than glass composites with proportions of 31 and 39%, respectively. A study of a structure of this composite has been made to validate the obtained results.

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Supplemental Material, Experimental_results_proof for Mechanical characterization and damage events of flax fabric-reinforced biopolymer composites by Abderrazak Chilali, Mustapha Assarar, Wajdi Zouari, Hocine Kebir and Rezak Ayad in Polymers and Polymer Composites

The present work aims at modelling the hydro-elastic behaviour of twill flax fabric-reinforced epoxy composites . These latter were manufactured using the vacuum infusion technique and aged into tap water until saturation. Their heterogeneity is taken into consideration by modelling the twill weave fabrics with two geometric paths: [0/90] and elliptical undulation. Moreover, the water diffusion coefficient and the hygroscopic expansion parameter of the flax fibre are estimated by an inverse approach exploiting the experimental results. In particular, the finite element simulations reveal high mechanical stress concentrations especially at the fibre-matrix interface caused by the differential swelling between the flax fabrics and the epoxy resin. This water absorption-induced internal stress is the main cause of damage initiation in the flax-epoxy composites, which leads to high variations of their mechanical properties and reduces their long-term sustainability.

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Updated Lagrangian formulations of two eight-node hexahedral solid elements with rotational degrees of freedom (DOFs) are developed to analyse geometrically nonlinear large deflection problems. These two elements are based on the so-called Space Fibre Rotation (SFR) concept that considers fictive small rotations of a nodal fibre within the element to enrich the displacement vector approximation of low-order finite elements. The validity and efficiency of the proposed formulations are demonstrated by solving several nonlinear large deflection benchmarks and the obtained results show a much better accuracy than those based on the total Lagrangian approach.

This paper aims at investigating the effect of alkali treatment and water ageing on several short Alfa fibre reinforced polypropylene composites. For this purpose, different composites with untreated and treated fibres were elaborated by extrusion and injection moulding processes and subjected to water ageing. The obtained results showed that the alkali treatment enhances significantly the Young’s modulus and tensile strength of the Alfa fibre reinforced polypropylene composites and reduces their loss during water ageing. The acoustic emission analysis showed that the use of alkali treatment plays a major role in the improvement of the fibre-matrix interface of both unaged and aged composites.

A finite degenerated shell element based on Mindlin discrete approach is presented for nonlinear geometric analysis in large displacements and small deformations. The element, called DMQS (Discrete Mindlin Quadrilateral Shell) with four-nodes and 6 dof/node, includes a constant transverse displacement and rich quadratic rotations. Since the global kinematics of shell is dominated by a rigid body rotation and motion involving small displacements and rotations, an Updated Lagrangian Formulation at each Iteration is used. The tangent stiffness matrix has been treated as a sum of two parts: linear part related to the degenerated shell model (DMQS) as well as the initial stress part associated with the well-known membrane standard element. Some standard nonlinear benchmarks are presented herein, where very good results have been obtained and show better accuracy than similar quadrilateral elements.

In the present work, twill flax fabrics-reinforced thermoplastic and thermosetting composites were subjected to water ageing in order to study its effect on their mechanical properties. Water ageing was conducted by immersing composite specimens into tap water at room temperature until saturation. To assess their mechanical behaviour, the aged composites were subjected to monotonic and load-unload tensile tests completed by Acoustic Emission (AE) recording. The AE records were analysed by the k-means unsupervised pattern recognition algorithm associated with the Principal Components Analysis (PCA) and the Silhouette index. In particular, the load-unload tensile tests highlighted a decrease of about 10% of the aged composites stiffness with respect to unaged ones at high loads. Besides, three classes of damage events were identified and assigned to the damage mechanisms. Finally, the mechanical behaviour of the aged composites is found to exhibit a significant Felicity effect synonymous of a substantial damage induced by water ageing.

In this work, we investigate the diffusion behaviour of twill flax fabrics reinforced thermoplastic and thermosetting composites elaborated by the vacuum infusion technique. Water absorption tests were conducted by immersing composite specimens into tap and salt water at room temperature. In particular, the effects of aspect ratio, thickness and fibre orientation are considered. The principal three-dimensional (3D) diffusion parameters are identified by 3D Fick’s and Langmuir’s models using an optimization algorithm. It is found that the flax reinforced thermoplastic composite absorbs less water than the flax thermoset composite. In addition, the obtained absorption curves indicate that the equilibrium mass gain linearly increases with fibre orientation, decreases with thickness and strongly related to the diffusion rate. Furthermore, 3D water diffusion kinetics are shown to depend on the samples aspect ratio and governed by a privileged direction.

Motivated by computing elastic properties of reinforced natural fibre composites, a multi-scale numerical model, named ‘the Projected Fibre approach (PF)’, is proposed. It uses a specific finite element procedure which is associated with a random distribution of short fibres. It takes into account of the geometry and the mechanical properties of composite’s components. A microscopic truss finite element is used to model the short fibre reinforcements. The corresponding degrees of freedom are projected on those of the resin matrix. Numerical results of the elastic properties of a reinforced hemp fibre polypropylene composite are compared to those obtained from the experiment.

This article aims at investigating the effects of hygrothermal aging on the damage mechanisms of short white Hemp Fiber Reinforced Polypropylene (HFRP) composites with various fiber contents (10, 20, 30, and 40 wt%). Injected molded specimens were subjected to hygrothermal aging with a relative humidity of 80% and two temperatures, 25 and 50°C. The water absorption and its effect on tensile properties of HFRP composites were investigated. The Acoustic Emission (AE) technique combined with scanning electron microscopy observations was used to identify microstructural damage events leading to overall failure of the HFRP composites. This identification according to hemp-fiber content and hygrothermal aging was made with an unsupervised method based on a statistical multi-variable analysis (k-means algorithm). The AE results indicate that the quality of fiber-matrix interface plays a major role in the damage process of HFRP composites, shown by the number of AE signals induced by the interface failure and their amplitude ranges. POLYM. COMPOS. 37:1101–1112, 2016. © 2014 Society of Plastics Engineers

SUMMARY The present paper deals with the enrichment of 3D low-order finite elements. The used concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. A consistent stiffness matrix is obtained, allowing a better approximation of the actual solution compared with that resulting from low-order finite elements. Implemented for two eight-node hexahedral elements, the performance of the space fiber rotation concept is assessed by running some classical beam, plate, and shell benchmarks, and the obtained results are compared especially with those given by linear eight-node and quadratic 20-node hexahedral elements. In particular, it is shown that the developed elements accuracy is significantly superior to that of the classical eight-node hexahedral element and close to that of the classical 20-node hexahedral element. Copyright © 2013 John Wiley & Sons, Ltd.

The model DDM (Discrete Displacement Mindlin), leads to a finite element which is geometrically simple: 4-node quadrilateral with 5 doffs per node for a shell and efficient. The mid-side rotational nodes, derived from a quadratic interpolation of normal rotations, are eliminated using a combination of local discrete kinematic and constitutive Mindlin hypotheses. The derived 4-node element is free of shear locking and passes all patch tests for thick and thin plates in arbitrary mesh. The applications concern the static and dynamic analysis of sandwich and multilayered shells.

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In this paper, we propose a finite element formulation based on a total Lagrangian approach to analyze two-dimensional (2D) fiber reinforced elastic solids undergoing large displacements. It allows the consideration of discrete short or long fibers embedded in a continuum matrix and the obtained system of equations size is equivalent to that of a non-reinforced medium. The matrix domain is discretized with four-node quadrilateral membrane elements while fibers crossing each matrix element are automatically detected and represented by two-node truss elements. A perfect bonding of fibers to the matrix is assumed and a projection technique is used to express the truss elements variables in terms of their corresponding matrix elements. Five nonlinear examples are presented to validate and demonstrate the capabilities of the proposed finite element formulation.

Two four-node quadrilateral membrane elements with rotational DOFs are proposed.They are based on the so-called Space Fiber Rotation (SFR) concept.An updated Lagrangian framework is chosen to describe large displacement kinematics.Several geometrically linear and nonlinear benchmarks are considered.The accuracy of the proposed elements is close to the eight-node quadrilateral element. In this paper, we present the formulations of two four-node quadrilateral membrane finite elements with rotational degrees of freedom to analyze geometric linear and nonlinear plane problems. They are based on a plane adaptation of the space fiber rotation concept that considers virtual rotations of a nodal fiber within the element enhancing the displacement vector approximation of low-order elements. An updated Lagrangian approach is chosen to describe large displacement with small strain kinematics. Several geometric linear and nonlinear benchmarks are presented to assess the performance of the proposed membrane elements and the obtained results demonstrate their efficiency.

International audience; The aim of this work is to study the effect of water ageing of quasi-Unidirectional Flax fibre Reinforced Epoxy (UFRE) composites on their mechanical and damping properties. The studied composites were manufactured by press platen process and subjected to water immersion at room temperature. Mechanical and damping properties of unaged and aged materials were investigated using free vibrations. Next, they were dried and tested to study the reversibility of the variation of those properties caused by water ageing. The results showed that water uptake induces a decrease in the bending moduli and an increase in loss factors compared in term of ageing time. It was also proven that those variations are practically reversible in the case of loss factors but irreversible in the case of bending moduli.

International audience; This paper aims at comparing the mechanical behaviour of different composite materials constituted of twill flax and glass fabrics-reinforced liquid thermoplastic and thermoset resins. The main objective is to study the possibility of thermoplastic to replace thermoset matrix, and flax fibre to replace glass fibre. For this purpose, the studied composites were fabricated using the vacuum infusion technique. Next, they were subjected to several monotonic and load-unload tensile tests in order to determine their mechanical properties and their evolution with damage. Two elastic damage and elastic-plastic damage models were also considered to predict their behaviour. The obtained results show that the used thermoplastic resin could constitute an interesting alternative to the thermoset resin for the vacuum infusion process. Furthermore, the flax fibre composites, in particular those based on the thermoplastic resin, present specific tensile moduli close to those of glass composites.

In this paper, we present two four-node multilayered hybrid-mixed shell elements for the static and free vibration analyses of plate and shell composite structures. Their formulation is based on the first shear deformation theory of Reissner/Mindlin without transverse shear correction factors. Linear and quadratic variations of the local in-plane and transverse shear stresses across the thickness, respectively, are supposed. To reduce the total number of variables in these models, transverse shear stresses are directly related to bending stresses by using two equilibrium equations. The performances of the proposed elements are assessed by means of two known numerical benchmarks and their results are found to agree globally well with the reference solutions.

This paper presents the development of a new 6-node solid wedge element with three translational and three rotational degrees of freedom per node. It is based on the model Space Fibre Rotation (SFR). Using the rotation of a material fibre in 3D space, the SFR approach allows to get a more accurate displacement field, which becomes quadratic without changing the number of nodes of the element. It is economical since only two integration points are used. In order to evaluate the usual element stiffness, a small penalty stiffness is introduced so that no zero energy modes appear while preserving the advantage of reduced integration. Several benchmark tests have demonstrated the improved performance of the present element.

International audience; Moisture absorption and durability in water environment are major concerns for natural fibres as reinforcement in composites. This paper presents a study on the influence of water ageing on mechanical properties and damage events of flax–fibre composites, compared with glass–fibre composites. The effects of the immersion treatment on the tensile characteristics, water absorption and acoustic emission (AE) recording were investigated. The water absorption results for the flax–fibre composites show that the evolution appears to be Fickian and the saturated weight gain is 12 times as high that the glass–fibre composites. Decreasing continuously with increasing water immersion time, the tensile modulus and the failure strain of flax–fibre composites are hardly affected by water ageing whereas only the tensile stress is reduced regarding the glass–fibre composites. AE indicate that matrix–fibres interface weakening is the main damage mechanism induced by water ageing for both composites.

A new hybrid-mixed variational approach for the linear analysis of laminated and sandwich plates, without transverse shear correction factors, is presented. It’s based on the first order theory of Reissner/Mindlin. A quadratic approximation through the thickness is proposed for transverse shear stresses (continuity C-1), and two equilibrium equations are used for their approximation. This reduces in consequence the number of interpolation parameters of bending stresses, which are eliminated using the static condensation technique. The proposed approach has been adapted to a quadrilateral 4-node finite element, free of locking, to which performances have been analyzed using some known problems of sandwich and laminated structures.

In this paper, an analytical homogenization model for corrugated cardboard and its numerical implementation in a shell element are presented. Taking into account the geometric and mechanical properties of the corrugated board components, this homogenization model leads to an elastic stiffness matrix relative to the generalized strains and internal efforts for an equivalent orthotropic plate. Special attentions are paid to the corrugated cardboard behaviours under the transverse shear efforts and torsion moments. Both laminated and sandwich plate theories are studied and some important improvements are proposed. This model is then implemented into a 3-node shell element called T3γ18 for the linear and buckling analyses. The results obtained by the present model are compared to those given by 3D shell simulations and experiments. The comparison shows the efficiency and accuracy of our homogenization model.

The present work deals with a procedure of defining discrete kinematic and mechanic hypothesises for Reissner-Mindlin plate finite elements. They are associated with the transverse shear strains for which the corresponding classical approximations caused the shear locking problem. Used in the past for isotropic homogeneous bending-shear plates, these hypothesises have been locally modified in order to be used for laminated composite plates. The derived plate finite element model, labelled DDM “Displacement Discrete Mindlin” has been applied to a 3-node triangular (DMTP: Discrete Mindlin Triangle for Plates) and validated on some standard problem tests, including one or several orthotropic layers.

International audience; This paper aims at assessing the experimental and analytical parameters of moisture diffusion of quasi-unidirectional and twill flax-fibres reinforced epoxy composites. The tested specimens of these composites were elaborated by hand lay-up technique at room temperature by using a vacuum moulding process. For several days, the samples were subjected to three ageing conditions, in order to evaluate the percentage of moisture uptake according to the ageing time. Next, the collected experimental data were analysed by using an optimisation program of Matlab software in order to identify the 3D diffusion parameters. The obtained results showed that the morphology and the anisotropy of flax fibres had a significant influence on the moisture diffusion. It also showed that moisture diffusion behaviour predicted by the 3D Fick model was in good agreement with the experimental results.

This paper presents an extension of two recently published conforming and non conforming eight-node hexahedral finite elements, presenting rotational degrees of freedom in addition to the classical displacement ones, to analyze geometric nonlinear problems. Their formulations are based on the so-called space fiber rotation concept that considers virtual rotations of a nodal fiber within the element which enhances the displacement vector approximation. To demonstrate the efficiency and accuracy of the proposed finite elements, several beam and shell nonlinear assessment tests are presented and the obtained results are principally compared with the classical first-order and second-order hexahedral elements responses as well as other advanced elements from the literature. In particular, it is shown that the proposed elements allow a correct prediction of the studied structures nonlinear behaviors including snap-through and snap-back instabilities and the accuracy of the non conforming element is close to the classical 20-node hexahedral element.

The object of the paper is to investigate the effects of staking sequences and hybridation on the damping properties of flax–carbon twill epoxy composites. Various staking sequences of these hybrid laminates were manufactured by platen press process. Next, dynamic properties were investigated using beam test specimens and an impulse technique. Damping modelling was implemented by using a finite element analysis to evaluate the dissipated energies in each layer of carbon–flax laminates. The obtained results show a good agreement between the experimental damping coefficients and those deduced from modelling. It is also shown that the position of flax layers within the hybrid composites plays a major role on their bending stiffness and damping properties.

The study presents a multilayer eight-node hexahedral finite element with rotational degree of freedom to model composite laminate structures. Its formulation is based on virtual rotations of a nodal fibre within the element that enriches the displacement vector approximation. A particular attention is made to the determination of transverse deflections as well as in-plane stresses. To assess the accuracy of the proposed element, several benchmarks are considered and the obtained results are compared with 3D elasticity solutions and other advanced finite elements from the literature.