A micro-model of the intra-laminar fracture in fiber-reinforced composites based on a discontinuous Galerkin/extrinsic cohesive law method

The hybrid discontinuous Galerkin (DG)/extrinsic cohesive law (ECL) method was recently proposed [1] to circumvent the drawbacks of the cohesive element methods. With the DG/ECL method, prior to fracture, the flux and stabilization terms arising from the DG formulation at interelement boundaries are enforced via interface elements in a way that guarantees consistency and stability, contrarily to traditional extrinsic cohesive zone methods. At the onset of fracture, the traction–separation law (TSL) governing the fracture process becomes operative without the need to modify the mesh topology since the cohesive elements required to integrate the TSL are already present. This DG/ECL method has been shown to be an efficient numerical framework that can easily be implement in parallel with excellent scalability properties to model fragmentation, dynamic crack propagation in brittle and small-scale yielding materials, both for 3D problems and for thin structures [1, 2]. In this work, following the developments in [3], the DG/ECL method is extended to the study of composite materials failures at the micro-scale. The method is applied to study the transverse traction of composite materials in characteristic micro-volumes of different sizes. The method captures the debonding process, assimilated to a damaging process before the strain softening onset. It is shown that the density of dissipated energy resulting from the damage (debonding) remains the same for the different studied cell sizes. During the strain softening phase, a micro-crack initiates and propagates, in agreement with experimental observations. After strain softening onset, the extracted macroscale cohesive law, obtained by the method proposed in [4], is ultimately shown to converge for the different cell sizes. The predicted behaviors are then compared to experimental results obtained from laminate tests, and are found to be in good agreement.SIMUCOMP The research has been funded by the Walloon Region under the agreement no 1017232 (CT-EUC 2010-10-12) in the context of the ERA-NET +, Matera + framework

An XFEM/CZM implementation for massively parallel simulations of composites fracture

Because of their widely generalized use in many industries, composites are the subject of many research campaigns. More particularly, the development of both accurate and flexible numerical models able to capture their intrinsically multiscale modes of failure is still a challenge. The standard finite element method typically requires intensive remeshing to adequately capture the geometry of the cracks and high accuracy is thus often sacrificed in favor of scalability, and vice versa. In an effort to preserve both properties, we present here an extended finite element method (XFEM) for large scale composite fracture simulations. In this formulation, the standard FEM formulation is partially enriched by use of shifted Heaviside functions with special attention paid to the scalability of the scheme. This enrichment technique offers several benefits since the interpolation property of the standard shape function still holds at the nodes. Those benefits include (i) no extra boundary condition for the enrichment degree of freedom, and (ii) no need for transition/blending regions; both of which contribute to maintaining the scalability of the code. Two different cohesive zone models (CZM) are then adopted to capture the physics of the crack propagation mechanisms. At the intralaminar level, an extrinsic CZM embedded in the XFEM formulation is used. At the interlaminar level, an intrinsic CZM is adopted for predicting the failure. The overall framework is implemented in ALYA, a mechanics code specifically developed for large scale, massively parallel simulations of coupled multi-physics problems. The implementation of both intrinsic and extrinsic CZM models within the code is such that it conserves the extremely efficient scalability of ALYA while providing accurate physical simulations of computationally expensive phenomena. The strong scalability provided by the proposed implementation is demonstrated. The model is ultimately validated against a full experimental campaign of loading tests and X-ray tomography analyzes.A.J., A.M., D.T., L.N. and L.W. acknowledge funding through the SIMUCOMP ERA-NET MATERA + project financed by the Fonds National de la Recherche (FNR) of Luxembourg, the Consejería de Educación y Empleo of the Comunidad de Madrid, the Walloon region (agreement no 1017232, CT-EUC 2010–10-12), and by the European Unions Seventh Framework Programme (FP7/2007–2013).Peer ReviewedPostprint (author's final draft

Potentiels de muffin tin, déphasages et structure électronique pour l'interprétation de nos mesures de transport électronique dans les alliages métalliques liquides à base de germanium (Ge-Ag ; Ge-Zn ; Ge-Cd)

This work was devoted to the experimental measurement of electron transport properties of binary liquid metals alloys with germanium (Ge-Ag ; Ge-Zn ; Ge-Cd). One of the originality of this study is the difficulty to control the measurements on these alloys because of their high vapor pressure. The experimental results are interpreted and discussed in term of Faber Ziman extended formula depending on the phase shifts due to diffusion by the muffin-tin potential for pure metals. We made a critical analysis for different construction methods of the muffin-tin potentials. In these methods we proceed by a construction of an atomic potential using Herman-Skilman-Slater approach or an ionic screened potential using Ratti approach. We introduced in both the exchange correction of Robinson, and we use an self consistent determination of the Fermi energy by adjusting the muffin-tin zero potential on the conduction band energy bottom. The differents improvements of the theory led us to a satisfactory interpretation of the alloys studied in this workCe travail a été consacré à l'étude expérimentale des propriétés de transport électronique d'alliages métalliques liquides binaires à base de germanium (Ge-Ag ; Ge-Zn ; Ge-Cd). Il s'agit d'un ensemble de mesures originales sur des alliages difficiles à mesurer en raison de leur tension de vapeur élevée. Nous avons interprété théoriquement la résistivité et le pouvoir thermoélectrique absolu des métaux purs par la formule de Ziman étendu exprimée en fonction des déphasages dus à la diffusion par des potentiels muffin tin sur les métaux purs. Nous avons effectué une analyse critique sur les métaux purs par différentes méthode de construction des potentiels de muffin tin. Ceux-ci font intervenir la construction du potentiel atomique suivant l'approche de Herman-Skilmann-Slater ou celle d'un potentiel ionique écranté suivant l'approche de Ratti, en incluant dans les deux cas la corrélation de robinson. Nous avons introduit une détermination autocohérente de l'énergie de fermi en ajustant le potentiel de muffin tin zéro sur le fond de la bande de conduction. Les perfectionnements proposés permettent d'améliorer de manière satisfaisante les interprétations des systèmes étudié

A Reference Benchmark Solution for Free Convection in A Square Cavity Filled with A Heterogeneous Porous Medium

International audienceThe Fourier-Galerkin (FG) method is used to produce a highly accurate solution for free convection in a square cavity filled with heterogeneous porous medium. To this end, the governing equations are reformulated in terms of the temperature and the stream function. These unknowns are then expanded in infinite Fourier series truncated at given orders. The accuracy of the FG solution is investigated for different truncation orders and compared to the results of an advanced finite-element numerical model using fine-mesh discretization. The obtained results represent a set of high-quality data that can be used for benchmarking numerical models

Global sensitivity analysis of solid oxide fuel cells with Bayesian sparse polynomial chaos expansions

International audienc

A new benchmark reference solution for double-diffusive convection in heterogeneous porous medium

International audienceA new benchmark with a high accurate solution is proposed for the verification of numerical codes dealing with double-diffusive convection in a heterogeneous porous medium. The new benchmark is inspired by the popular problem of square porous cavity by assuming a stratified porous medium. A high accurate steady state solution is developed using the Fourier–Galerkin method. To this aim, the unknowns are expanded in double infinite Fourier series. The accuracy of the developed solution is assessed in terms of the truncation orders of the Fourier series. Comparison against finite element solutions highlights the worthiness of the proposed benchmark for numerical code validation