The symmetric buckling mode in laminated elastoplastic micro-structures under plane strain

The present work considers lamellar (micro) structures of thin, elastic lamellae embedded in a yielding matrix as a stability problem in the context of the theory of stability and uniqueness of path-dependent systems. The volume ratio of the stiff lamellae to the relatively soft matrix is assumed low enough to initiate a symmetric buckling mode, which is investigated by analytical and numerical means. Using a highly abstracted, incompatible model, a first approach is made, and the principal features of the problem are highlighted. Assuming plane strain deformation, an analytic expression for the bifurcation load of a refined, compatible model is derived for the special case of ideal plasticity and verified by numerical results. The effect of lamella spacing and matrix hardening on the bifurcation load is studied by a finite element unit cell model. Some of the findings for the ideal plastic matrix are shown to also apply for a mildly hardening matrix material. Furthermore, the postbuckling behaviour and the limit load are investigated by simulating a bulk lamella array

Mechanical properties of epoxy/boehmite nanocomposites in dependency of mass fraction and surface modification - An experimental and numerical approach

Boehmite nanoparticles show great potential in improving the matrix dominated mechanical properties of fiber reinforced polymers. For the material design process and the prediction of the nanocomposite's properties, knowledge about the material behavior of the constituent phases and their interactions is crucial. Since the chemical composition of the particle surface can strongly affect the interaction between particle and matrix, the influence of particle surface modification and mass fraction on mechanical properties (tensile modulus, tensile strength, fracture toughness) and failure mechanisms of nanoparticle reinforced epoxy resins is investigated using experimental and numerical methods. In the present work, unmodified and thus chemically reactive boehmite particles are compared to acetic acid modified particles with supposedly lower chemical reactivity and thus worse particle-matrix bonding. A linear relationship between particle mass fraction and tensile modulus/fracture toughness is experimentally found with a maximum increase of 26% in tensile modulus and 62% in critical energy release rate for a particle content of 15 wt%. Furthermore, the experiments indicate that the acetic acid surface modification increases the tensile modulus (up to 6% compared to the unmodified boehmite particles), but at the same time not significantly affects the tensile strength or the fracture toughness. Molecular Dynamic Finite Element Method (MDFEM) simulations are conducted to identify and understand the mechanisms induced by nanoparticles. The material properties of both, modified and unmodified, nanoparticle systems are discussed in relation to the change of particle-matrix bonding strength and interphase morphology. While simulation results of the unmodified system show an outstanding agreement with the experiments, the acetic acid modified system deviates significantly. In conclusion, it seems that additional effects have to be considered to completely understand the material behavior

Etat de l'art de la modélisation de la rupture en compression des composites stratifiés

International audienceThis article reviews the last twenty years of academic research on the topic of modelling the compressive behavior andfailure of laminated composites in the fibers’ direction. This review is split into three chapters after a brief reminder of thefundamental theories explaining the main mechanism responsible for compressive failure – fibre kinking. The first chapterdeals with supplementary semi-analytical micromodels that take into account increasingly complex physics. The secondchapter deals with finite element analyses of various structure effects : size effects, edge effects, stress gradients, etc. Thethird and final chapter deals with finite element analyses of microbuckling interaction with other failure mechanisms,namely fibre failure, fibre-matrix debonding, intra-laminar cracking, and delamination. The conclusion offers an overviewof recent trends and expected progresses from an industrial perspective.Cet article propose la revue d’environ vingt années de travaux récents sur le modélisation du comportement et de la rupture des composites stratifiés sollicités en compression dans le sens des fibres. Après un bref rappel des théories fondamentales à l’origine de la compréhension du mécanisme principal responsable de la ruine, le micro flambage des fibres, la revue est divisée en trois partie. La première évoque les études supplémentaires menées sur les micro modèles semi-analytiques permettant la prise en compte de phénomènes de plus en plus complexes. La deuxième traite des calculs par éléments finis ayant étudié, par ailleurs, l’influence des effets de structure : effets de taille, de gradient, de bord, etc. La troisième et dernière partie traite enfin des calculs par éléments finis s’intéressant aux interactions entre micro flambage et d’autres mécanismes de ruine, tels que la rupture des fibres, la décohésion fibres-matrice, la fissuration intra-laminaire et le délaminage. La conclusion de cette revue brosse un aperçu des tendances récentes et des progrès attendus d’un point de vue industriel

Über die numerische Berechnung von Faserbeulen durch Mesoskalenansätze

The present treatise is concerned with the application of numerical models to the prediction of compressive strength and associated phenomena in fiber reinforced polymer matrix composites. This topic has received much attention by the scientific community, and the basic mechanisms at microscopic scale are well understood. Even so, microscale models and theories offer no predictive capability at scales relevant for practical application, and the problem of devising suitable approaches for this purpose is still wide open. The main obstacle in this endeavor is that relevant mechanisms are spread over several length scales, hindering their integration. To address this challenge, the topic is thoroughly reviewed and mesoscale approaches are identified as an essential stepping stone towards an eventual transfer of fundamental scientific research to engineering application. Subsequently, the mesoscopic approach based on a homogenized representation of the fiber/matrix composite is developed further and its application for the prediction of the aforementioned mechanisms is demonstrated: Random flaws in local fiber alignment are the main source of uncertainty with regard to compressive strength and introduce a dependence of compressive strength on domain size. Methods for the proper representation of these flaws and their effect on compressive strength are considered and extended. Compressive failure in the materials under consideration is caused by shear strain localization and features characteristic width and orientation. To make these phenomena amenable to mesoscale modelling as a homogenized solid, the application of an extended solid theory with additional rotational degrees of freedom is considered. The versatility of the approach is demonstrated by predicting phenomena ranging from very small sizes, i.e. the bandwidth, to large sizes via the predicted scale law for compressive strength. Hence, it is argued that the mesoscale approach provides an excellent platform for further work concerned with component scale applications

A Structural Design Concept for a Multi-Shell Blended Wing Body with Laminar Flow Control

Static and fatigue analyses are presented for a new blended wing body (BWB) fuselage concept considering laminar flow control (LFC) by boundary layer suction in order to reduce the aerodynamic drag. BWB aircraft design concepts profit from a structurally beneficial distribution of lift and weight and allow a better utilization of interior space over conventional layouts. A structurally efficient design concept for the pressurized BWB cabin is a vaulted layout that is, however, aerodynamically disadvantageous. A suitable remedy is a multi-shell design concept with a separate outer skin. The synergetic combination of such a multi-shell BWB fuselage with a LFC via perforation of the outer skin to attain a drag reduction appears promising. In this work, two relevant structural design aspects are considered. First, a numerical model for a ribbed double-shell design of a fuselage segment is analyzed. Second, fatigue aspects of the perforation in the outer skin are investigated. A design making use of controlled fiber orientation is proposed for the perforated skin. The fatigue behavior is compared to perforation methods with conventional fiber topologies and to configurations without perforations