On the stability of totally upwind schemes for the hyperbolic initial boundary value problem

In this paper, we present a numerical strategy to check the strong stability (or GKS-stability) of one-step explicit totally upwind scheme in 1D with numerical boundary conditions. The underlying approximated continuous problem is a hyperbolic partial differential equation. Our approach is based on the Uniform Kreiss-Lopatinskii Condition, using linear algebra and complex analysis to count the number of zeros of the associated determinant. The study is illustrated with the Beam-Warming scheme together with the simplified inverse Lax-Wendroff procedure at the boundary

Influence of the loading regime on the uniaxial compressive behaviour of density graded Citrus Maxima peel

To conceive more efficient protective structures, it is possible to draw inspiration from natural structures. However, the origin of the mechanical absorption properties of natural structures is not always clear. Among the multitude of existing natural structures, the density graded peel of the Citrus Maxima was studied in this work to characterize its mechanical behaviour under uniaxial compression, from the quasi-static regime to the dynamic regime. The resulting behaviour is very different from a classical foam behaviour as no linear part is observed for small strains. Furthermore, the mechanical behaviour is deeply influenced by the loading regime: a stair-case response appears under dynamic loading

From bio-sourced to bio-inspired cellular materials: A review on their mechanical behavior under dynamic loadings

Natural cellular materials can be used directly or as a constituent of bio-sourced composites for industrial applications involving dynamic loadings, usually for the purpose of absorbing mechanical energy. These biological materials can also be used as an inspiration to conceive more efficient heterogeneous structures for impact mitigation. In this review letter, we present two natural materials for which the properties have been studied dynamically: balsa wood and corkbased agglomerates. Both display an important strain-rate dependence but because of their different microstructure, this dependence is not the same. Consequently, a better understanding of the relationship between the hierarchical structure of natural cellular materials and their mechanical behavior, from quasi-static to dynamic, would be beneficial for the conception of new bio-inspired architected structures. We then focus on two types of bio-inspired architected structures: the functionally density graded cellular structures and the multi-layered architected structures. These two types of structures are gaining interest, but it appears that their dynamic behavior still lacks studying and understanding. More research linking the local strain mechanisms to their macroscopic mechanical behavior in quasistatic and dynamic would allow further architected structure optimization for mechanical energy absorption

Influence de la vitesse de sollicitation sur le comportement en compression d'un liège aggloméré renforcé

International audienceThe demand for bio-sourced materials is currently increasing. Cork material because of its unique properties (fire resistant, energy absorbing, ...) is then an excellent candidate for a large set of applications. In order to widen its possible uses, cork agglomerates with reinforcements at a 0.48 density were studied to compare their mechanical performances with classical cork agglomerates. This paper investigates the effect of these foreign reinforcements on the properties of agglomerated cork under a compressive loading. The material behavior has been determined as a function of the average strain rate and the direction of solicitation. The microstructure was first observed through optical and scanning electronic microscopy, spotting charges between each cork bead. The characterisation of cork at different strain rates was then carried out. An electromechanical testing machine was used to apply an uniaxial compression at quasi-static strain rates. Reinforced agglomerated cork was found to be anisotropic and strain-rate dependant. Its micro-structure reveals at complex composite material influencing strongly mechanical properties. Both Young's modulus and absorbed energy density at 0.6 strain increase with the cross-head speed displacement. From 12.7 MPa and 0.77 J · mm −3 when compressed at 0.05 mm · min −1 to 19.9 MPa and 1.44 J · mm −3 at 500 mm · min −1 in the Off-plane direction

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Elastically anisotropic architected metamaterials with enhanced energy absorption

Materials and structures featuring a combination of high stiffness, strength, and energy absorption are highly demanded. Current studies are focused on the improvement of these mechanical properties without considering their directional dependence. In practice, directional-dependent mechanical properties are crucial to structural integrity and performance, for instance, in the application of anisotropic bone scaffolds for load bearing and battery separators for ion conductivity. Recently, tunable anisotropic stiffness in mechanical metamaterials has been obtained by tailoring the microstructures using data-driven approaches. However, energy absorption behavior, which plays a critical role in the presence of large deformation, has largely been neglected. In this work, we propose a new type of elastically anisotropic architected metamaterials (AAMs) inspired by the current lithium-ion battery separator porous microstructure to acquire tunable anisotropy while exhibiting superior energy absorption. The integrated study presented herein, which combines an experimental investigation with numerical simulations, reveals that the anisotropy can be engineered across a broad range. Compared with two existing lattice and shell-based architected materials, it is shown that the energy absorption of the newly developed AAMs is increased by 120% and 13%. The findings in this work provide a new strategy to expand the existing metamaterial design space, with the potential to enable innovative solutions for applications where directional-dependent stiffness and energy absorption are needed

Energy Absorption Capacity of Agglomerated Cork Under Severe Loading Conditions

Understanding the mechanical behavior of materials in working conditions is a current problem in transport industries. In this article, we demonstrate why the temperature and the strain-rate are first-order parameters when studying the mechanical behavior of polymeric cellular materials with a glass transition temperature Tg in working temperatures. Compressive tests in quasi-static until a 0.5 hencky strain were conducted at several temperatures on agglomerated cork. Compressive tests were then conduted along a large range of strain rates, from 4.2 10−5 s−1 to 250 s−1 at room temperature (24 °C). Both parameters influence strongly the overall mechanical behavior with an opposite effect because of the polymeric nature of the constitutive materials. However discrepencies in the variation were observed between materials parameters of the two conditions (temperature and strain rate). In order to separate the dynamic effects from the modification of the stiffness of the constitutive materials with temperature or strain rate, a specific apparatus was designed to achieve high-strain rate tests in temperature. Compressive tests in dynamic regime were then conducted at −20 °C on agglomerated cork as a proof-of-concept. The experimental results (stress/strain curves and materials parameters) showed a great influence of the strain-rate and the temperature combined. Such apparatus will provide results allowing a more in-depth characterisation of the local mechanisms that will be precious for future simulations

Multi-scale foam : 3D structure/compressive behaviour relationship of agglomerated cork

This study focuses on the microstructural aspects of a cork-based by-product known as agglomerated cork and its influence on the compressive mechanical behaviour. The material consists in granulates of a natural polymeric foam - cork - mixed together with a small quantity of a bio-sourced resin. Optical and scanning electron microscopy (SEM) are first used to investigate on the bead geometry and placement and interfaces arrangement. Then X-ray computed tomography allows to study the spatial arrangement of agglomerated cork microstructure and hence to complete and confirm 2D observations. 2D and 3D observations show a transverse anisotropic material which is confirmed by the mechanical tests. SEM pictures demonstrate an intricate and heterogeneous material. Microtomography confirms the presence of macroporosities between cork granulates having a mean volume around 0.1 mm 3 . Cork cell specific geometry is also confirmed. The volume of those cells lies around 10 −5 mm 3 . Finally quasi-static compression tests are run to establish a link between microstructure and mechanical behaviour thanks to digital image correlation (DIC). Cork agglomerate demonstrates strong strain localisation at its surface caused by its multi-scale structure

Reinforcement of cellular materials with short fibres: Application to a bio-based cork multi-scale foam

A bio-sourced foam, agglomerated cork, was chosen to evaluate the influence of short fibres on the mechanical behaviour of cellular materials. The final material was obtained by mixing cork particles with a thermoset resin. Rigid short fibres were then added before uni-axial compression. Enhancing the foam’s mechanical properties without increasing the density is a current problem in transport industries. In this article, we demonstrate how the addition of short fibres strongly modifies the mechanical behaviour of agglomerated foam materials. Dynamic Mechanical Analysis technique revealed that the glass temperature was greater for reinforced foams and more energy loss by heat in visco-elasticity was also noticed for this material. In quasi-static compression, rigidity was strongly enhanced, causing absorbed energy before densification to increase. Maximal force and displacement before fracture were studied by applying Mode I fracture tests, and both were improved by the addition of short fibres. The mesoscopic and microscopic observations revealed it was linked to fracture me- chanisms, most of which happen inside cork beads for the reinforced cellular material. The properties of agglomerated foams may then be improved and tailored by the addtion of short fibres and make weight saving possible in several industrial applications.Projet LIAM

A thick cellular structural adhesive: Identification of its behavior under shear loading

This study focuses on the link between the microstructure and the mechanical behavior under shear loading of a thick cellular structural adhesive (TCSA). X-ray microtomography and image post-processing were first used to perform 3D-quantitative microstructure analysis. The cells morphometric parameters and their orientations were studied. The foaming process boundary conditions seems to create local density gradients changing the cells dimensions and shape. The cells are more spherical in the core of the material whereas being more ellipsoidal close to the upper and lower faces of the samples creating a skin layer. The effect on the strain field of this skin layer has then been highlighted. Secondly, a shear test method using an Arcan setup coupled with digital image correlation was used and allowed to observe the mechanical behavior of the material under shear loadings. Instead of the material being cellular and heterogenous, it has been found that the strain field can be considered homogeneous at macroscopic scale to extract the properties on a homogeneous equivalent material. Shear test on samples with different densities were performed. Using the relation developed by Gibson and Ashby linking the shear modulus to the density squared is a first approximation, at this scale, to predict and describe the mechanical behavior under shear loading