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This paper deals with a new analytical method, the exponential matrix method EMM, for calculating the T-stress and the stress intensity factors SIFs under mixed mode loading. The linear, elastic, two-dimensional and stationary equations of the crack problem are transformed into a Hamiltonian system. This is solved by the proposed method involving eigensolutions which satisfy the adjoint symplectic orthogonality by means of performing an angular stress variation with respect to the radial stress. A good description of the expected solution of the studied problem is then obtained as a linear combination of these eigensolutions. To illustrate the validity of the present method, some numerical examples are used and the results obtained are compared with those of literature.

The purpose of this study was to establish a method based on an iterative scheme to approximate the numerical solution obtained from finite elements analysis for an RVE in two and three dimensions based on the homogenization concept for the assessment of the effective properties. The bounds of Hashin–Shtrikman and Voigt–Reuss were considered in the iterative process based on an updating of the constitutive relations of these models respectively. In this study, by assumption, we took the particular case of the heterogeneous materials with several elastic isotopic phases. The output variables considered using the iterative process are the bulk, shear modulus and the thermal conductivity. We have found a fast convergence of the iterative solution to the numerical result with a suitable concordance between the two solutions at the final step.

International audience; The main goal of this paper is to predict the elastic modulus of partially intercalated and exfoliated polymer-clay nano-composites using numerical homogenization techniques based on the finite element method. The representative volume element was employed here to capture nano-composites microstructure, where both intercalated exfoliated and clay platelets coexisted together. The effective macroscopic properties of the studied microstructure are obtained with two boundary conditions: periodic boundary conditions and kinematic uniform boundary conditions. The effect of particle volume fractions, aspect ratio, number and distribution of particles and the type of boundary conditions are numerically studied for different configurations. This paper investigate also the performance of several classical analytical models as Mori and Tanaka model, Halpin and Tsai model, generalized self consistent model through their ability to estimate the mechanical properties of nano-composites. A comparison between simulation results of polypropylene clay nano-composites, analytical methods and experimental data has confirmed the validity of the set results.

This paper aims at developing 3D numerical simulations of the mechanical properties of polymer composites based on the aggregates of argan shell. The microstructure is made up of two phases, corresponding to the Poly–Propylene PP matrix and the natural aggregates. Due to the grinding operation of agran shell during the manufacturing process, the aggregates shapes, crushed aggregates, greatly vary with their surfaces. The majority of published works used the spherical or ellipsoidal forms in order to study numerically the mechanical behavior of such composites, because of the inherent simplification in algorithm formulations. However, real microstructures of these composites based simple microscopic, show that the shape of aggregates does not takes a spherical form, but a polyhedral form. In this study, the microstructure is described and modeled as a combination of Poisson polyhedral and PP matrix. In the numerical model, the obtained aggregate morphology is similar to that of many argan shell powders often used as reinforcement of the PP matrix. This technique allows generating models with different reinforcement volume fractions up to 28%. The numerical homogenization technique is used to estimate the mechanical properties of these composites. The set obtained numerical results with 3D polyhedral model are compared with the pertinent experimental data and analytical models reported in the literature. The performance of the most used micromechanical schemes used in predicting the effective elastic properties of biocomposites was discussed.

Throughout this work, the influence of microstructures of non-overlapping aligned fiber reinforced composites on macroscopic elastic properties has been quantified with numerical homogenization on FEM simulations. New bounds that frame bulk and shear moduli of any equilibrium system were established. The corresponding microstructures for lower and upper bounds were found to be respectively a Percus-Yevick distribution of fibers and specific configurations of packed fibers. The radial distribution function has proven to be the best second order correlation to describe these fiber spatial distributions that were built with simulated annealing. The new numerical bounds established in this paper are tighter than existing third order ones.

In this study, we have explored the numerical modelling of the thermoforming of high-density polyethylene wood particle composites (WPC) into a formwork intended for construction applications. By using the parameters identified from oscillatory shear test, the Lodge model is used to describe the viscoelastic behavior of the WPC sheet. The forming stage of the WPC sheet is performed under the action of gas flow governed by the van der Waals equation of state. The thermoformability is firstly determined by simulating a free blowing of HDPE and highly charged WPC. Then, the numerical simulation of the formwork thermoforming is carried out on four types of WPC. The results have shown that the structure is subjected to increasing stress as the wood particle content increases, which consequently increases the risk of failure. Nevertheless, thermoforming is possible for WPC sheets with less than 40 % wood content. Simulations of the formwork under loadings have also shown good mechanical resistance at low thicknesses.

International audience; Wood polymer composites (WPC) have well proven their applicability in several fields of the plasturgy sector, due to their aesthetics and low maintenance costs. However, for plasturgy applications, the characterization of viscoelastic behavior and thermomechanical and thermophysical properties of WPC with the temperature and wood filler contents is essential. Therefore, the processability of polymer composites made up with different percentage of wood particles needs a better understanding of materials behaviors in accordance with temperature and wood particles contents. To this end, a numerical analysis of the viscoelastic, mechanical, and thermophysical properties of composite composed of high density polyethylene (HDPE) reinforced with soft wood particles is evaluated.

International audience; It is well known that in high cycle fatigue (HCF), macroscopically, structures undergo elastic shakedown and the stress level commonly determines the lifetime. In this domain, the fatigue phenomena is due to local plasticity at the grain scale. Therefore, some multiscale HCF multiaxial fatigue criteria were proposed, among them the well-known Dang Van criterion. This criterion supposes that in a polycrystal, some misoriented grains can undergo plastic shakedown which conducts to crack initiation. The objective of this work is to validate this assumption by conducting numerical simulations on polycrystalline aggregates. As it is necessary to estimate the stabilized state in each grain of the polycrystal, classical incremental simulations are not the best way as it will be highly time-consuming because of the size of the aggregate. In the recent years, Pommier proposed a method called Direct Cyclic Algorithm to obtain the stabilized response of a structure under cyclic periodic loading, which it is shown to be more efficient compared to an incremental analysis in such situation. However, errors can be obtained in certain case with respect to the incremental solution. In this work, a Crystal Plasticity FEM model, based on dislocation densities, was used. As a first step, an aggregate of 20 grains of AISI 316L stainless steel under strain controlled cyclic loading was studied. Precise comparisons were conducted with incremental analysis and the results show that DCA seems to be an efficient solution in order to estimate the shakedown state of polycrystalline aggregates.

During the ballistic impact process of fabrics, yarns are locally subjected to both longitudinal tensile and transverse compressive loading. This paper presents a microscopic numerical investigation of the transverse compressive behavior of a single and bulk aramid fibers. Interactions with friction between single fibers in a yarn have been taken into account. Numerical calculations were performed in the case of a transverse compression using the assumption of plane strain and validated by experimental data. Effects of friction and representative volume size were also discussed. It can be highlighted that using a numerical homogenization technique, the variation of the transverse mechanical effective property versus fiber volume fraction has been determined based on the microscopic transverse behavior of bulk aramid fibers. Finally, power relationships describing effective transverse Young's modulus E ¯ and apparent strain e ¯ versus the normalized fiber volume fraction have been proposed and discussed. This effective homogenized material allows the development of homogenized Kevlar yarns and fabrics in the further works of homogenized approaches.

The focus of this paper is on aligned fiber-reinforced composites, where fiber centers were randomly distributed in their cross-sections. The volume fractions of fibers were [Formula: see text]% and [Formula: see text]%. Samples were built with the help of the simulated annealing technique according to the chosen Radial Distribution Functions (RDFs). For each sample, the fields of local stresses and heat fluxes were simulated by finite element method. Then, homogenization by volume averaging was performed in order to investigate both the effective mechanical and thermal properties. The effect of RDF shape on elastic and thermal properties was quantified along with the influence of the probability of near neighbors of fibers on the physical properties. The more the fiber distributions deviate from Poisson’s Law, the higher the results compared to the lower bound of Hashin–Shtrikman.

In this study, an analytical model is developed for an investigation of ballistic impact behaviour of 2D plain-weave fabrics. This model is based on both energy conservation and strain wave theory. Also, reflections of deformation waves are considered. The model can predict the evolution of parameters during an impact event continuously in terms of time and particularly, the limit speed of fabric perforation. Different phases during an impact event are analysed and discussed. The effects of the size of the fabric and the distance between layers are also studied. The results of this new model have been compared with experimental data.

A numerical model of ballistic impact on a two-dimensional Kevlar KM2® plain-woven fabric has been validated by experiment. This paper shows that it is necessary to experimentally measure material constants of yarns for having good input parameters of the model. Effects of yarn Poisson’s ratio, transverse and shear modulus on impact behaviors of a simple crimped yarn and a complete fabric have been carried out. The effect of the Poisson’s ratio can be negligible in both impact cases: on a single crimped yarn and a complete fabric. The same conclusion has been proven for the effect of the transversal modulus except the cases of its so low values that can cause yarn early damage. The shear modulus of a yarn appears to be an important material parameter that mainly influences the ballistic performance of a two-dimensional plain-woven fabric. When using a very high value of a shear modulus of yarn, a crimped single yarn is broken immediately after contact with projectile in pure shearing mode.

International audience; 3D interlock woven fabrics are promising materials to replace the 2D structures in the field of ballistic protection. The structural complexity of this material caused many difficulties in numerical modeling. This paper presents a new tool that permits to generate a geometry model of any woven fabric, then, mesh this model in shell or solid elements, and apply the mechanical properties of yarns to them. The tool shows many advantages over existing software. It is very handy in use with an organization of the functions in menu and using a graphic interface. It can describe correctly the geometry of all textile woven fabrics. With this tool, the orientation of the local axes of finite elements following the yarn direction facilitates defining the yarn mechanical properties in a numerical model. This tool can be largely applied because it is compatible with popular finite element codes such as Abaqus, Ansys, Radioss etc. Thanks to this tool, a finite element model was carried out to describe a ballistic impact on a 3D warp interlock Kevlar KM2® fabric. This work focuses on studying the effect of friction onto the ballistic impact behavior of this textile interlock structure. Results showed that the friction among yarns affects considerably on the impact behavior of this fabric. The effect of the friction between projectile and yarn is less important. The friction plays an important role in keeping the fabric structural stability during the impact event. This phenomenon explained why the projectile is easier to penetrate this 3D warp interlock fabric in the no-friction case. This result also indicates that the ballistic performance of the interlock woven fabrics can be improved by using fibers with great friction coefficients.