Mechanical Behavior Of Cellular Materials Research Articles

A Novel Equivalent Method for Computing Mechanical Properties of Random and Ordered Hyperelastic Cellular Materials.

Simulating the mechanical behavior of cellular materials stands as a pivotal step in their practical application. Nonetheless, the substantial multitude of unit cells within these materials necessitates a considerable finite element mesh, thereby leading to elevated computational expenses and requisites for formidable computer configurations. In order to surmount this predicament, a novel and straightforward equivalent calculation method is proposed for the computation of mechanical properties concerning both random and ordered hyper-elastic cellular materials. By amalgamating the classical finite element approach with the distribution attributes of cells, the proposed equivalent calculation method adeptly captures the deformation modes and force-displacement responses exhibited by cell materials under tensile and shear loads, as predicted through direct numerical simulation. This approach reflects the deformation characteristics induced by micro-unit cells, elucidates an equivalent principle bridging cellular materials and equivalent materials, and substantially curtails exhaustive computational burdens. Ultimately, this method furnishes an equivalent computational strategy tailored for the engineering applications of cellular materials.

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 mechanisms, 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.

Stiffness of bi-modulus hexagonal and diamond honeycombs

Cellular materials are widely used in various applications because of their low density and high strength. The mechanical behavior of cellular materials under various loading conditions has been investigated. Nevertheless, many of these previous studies assume that the Young’s modulus of constituting struts is the same in tension and compression. The present work first derives analytical expressions for the effective Young’s moduli of hexagonal and diamond lattices composed of struts with different tension and compression moduli under the assumption of small strain deformation. It also uses the finite element method to further investigate the mechanical responses of these lattices. The macroscopic Young’s moduli under both compressive and tensile loads are reported as a function of the ratio of compression and tension moduli of constituting struts. The numerical finite element models are implemented by a user defined material subroutine in ABAQUS. Results reveal that the effective Young’s moduli of periodic hexagonal and diamond lattices significantly decrease with decreasing ratio of compression and tension moduli of the struts. Furthermore, the mechanical behavior of hexagonal lattices composed of struts with different tension-compression moduli is dependent on the loading direction and whether they are compressed or stretched. The unique mechanical properties of bi-modulus cellular materials could find important applications in the automotive and construction industries.

Experimental and multi-scale analyses of open-celled aluminum foam with hole under compressive quasi-static loading

Compressive stress-strain behavior of open cell aluminum foam has been investigated using experimental and multiscale modeling methods. Mechanical behavior of cellular materials intensively depends on their microscopic structure and architecture which may degrade under loadings. To analyze the mechanical response of a full scale and complex aluminum foam component, one may develop multiscale modeling. In this way the degraded material properties are calculated through the analyses of a representative volume element (RVE) considering the micro-structural characteristic, architectural parameters and loading. In this study, open-celled AA6101-T6 aluminum foam is considered for the analyses. Geometrical characteristics of the foam using microscopic images are extracted, including thickness of cell walls, cell size, relative density and cross section of cell walls. The micro model is defined as RVE with nonlinear geometric and material behaviors considering the possible contacts between struts and it is conditioned on macroscopic quantity using appropriate boundary conditions. To validate the proposed model, different experiments have been performed for foam specimens with and without circular hole under compressive quasi-static loading. Finally, multiscale modeling has been proposed to analyze the foam components with complex and irregular shapes. It is shown that in order to model foams considering all the heterogeneities, even with larger size and having non-uniform stress field the use of currently existed finite-element and micro-structural models are not sufficient and the proposed multi-scale modeling which leads to acceptable results can be used for such analyses.

High temperature mechanical behavior of tube stackings – Part II: Comparison between experiment and modeling

This paper is the second part of a set of two papers dedicated to the mechanical behavior of cellular materials from room temperature to high temperatures. For that purpose, some monotonic and creep compression tests have been performed on a small tube stacking structure. In parallel, a finite-element model of these experiments has been proposed, using the constitutive elasto-viscoplastic behavior identified for the tube material in Part I [1] as input data. The comparison between the experiment and the modeling has provided many items of information regarding the collapse mechanisms of this kind of cellular structure at high temperatures and the role of the contacts created between the tube walls at large deformations. Especially, a competition between both relaxation and hardening phenomena locally has been revealed at high temperatures, resulting in some softening of the stacking effective behavior.

The in-plane elastic properties of hierarchical composite cellular materials: Synergy of hierarchy, material heterogeneity and cell topologies at different levels

The hierarchical organization of many biological materials plays a key role in their exceptional mechanical properties. Existing studies investigate how hierarchy affects the mechanical behavior of cellular materials and the vast majority of them assume empty cells. In reality, in numerous natural systems the cells are filled with fluids, fibers or other bulk materials to better resist external stimuli. Inspired by the highly efficiency of nature, this paper investigates the effects of adding hierarchy into a composite cellular material. Initially, the analytical expressions for the effective elastic moduli derived in the case of self-similarity reveal the system isotropy as for the not filled configuration. Then, from parametric analysis emerges a strong influence of the microstructure on the overall properties. We discovered that adding hierarchical levels to a filled cellular material can lead to a higher material specific stiffness only if the filler is stiffer than a critical value. Thus for classical cellular materials hierarchy is detrimental for the specific stiffness. In spite of this, for composite cellular solids an optimal number of hierarchical levels naturally emerges. In addition, numerical homogenization validates the analytical approach. Finally, the example of a hierarchical composite cellular material having different levels with different cell topologies is also considered. The present analysis provides an insight into the role of structural hierarchy on the in-plane elastic properties of composite cellular materials, as well as some possible ways to improve low-weight cellular structures by mixing different materials and varying the cell topology.

High temperature mechanical behavior of tube stackings – Part I: Microstructural and mechanical characterization of Inconel® 600 constitutive material

This paper is the first part of a set of two papers dedicated to the mechanical behavior of cellular materials at high temperatures. For that purpose, cellular materials made of brazed tube stacking cores have been considered here. This paper addresses the characterization of the elasto-viscoplastic properties of the constitutive material of the tubes, Inconel®600, by means of tensile tests. Various temperatures and strain rates were investigated, from room temperature to 800°C, in order to study the influence of both the brazing heat treatment and the test temperature on the mechanical properties of Inconel®600. Whereas the heat treatment drastically decreases the strength of the tubes, a significant viscous effect is revealed at 800°C. Electron backscattered diffraction analyses carried out post-mortem on samples showed that both dynamic recrystallization and recovery occurred during tensile tests performed at 800°C, especially at lower strain rates. In contrast, a highly deformed and textured microstructure was observed for the tubes loaded at lower temperatures.

Phononic Band Gaps in 2D Quadratic and 3D Cubic Cellular Structures.

The static and dynamic mechanical behaviour of cellular materials can be designed by the architecture of the underlying unit cell. In this paper, the phononic band structure of 2D and 3D cellular structures is investigated. It is shown how the geometry of the unit cell influences the band structure and eventually leads to full band gaps. The mechanism leading to full band gaps is elucidated. Based on this knowledge, a 3D cellular structure with a broad full band gap is identified. Furthermore, the dependence of the width of the gap on the geometry parameters of the unit cell is presented.

Strain-rate dependence for Ni/Al hybrid foams

Shock absorption often needs stiff but lightweight materials that exhibit a large kinetic energy absorption capability. Open-cell metal foams are artificial structures, which due to their plateau stress, including a strong hysteresis, can in principle absorb large amounts of energy. However, their plateau stress is too low for many applications. In this study, we use highly novel and promising Ni/Al hybrid foams which consist of standard, open-cell aluminium foams, where nanocrystalline nickel is deposited by electrodeposition as coating on the strut surface. The mechanical behaviour of cellular materials, including their behaviour under higher strain-rates, is governed by their microstructure due to the properties of the strut material, pore/strut geometry and mass distribution over the struts. Micro-inertia effects are strongly related to the microstructure. For a conclusive model, the exact real microstructure is needed. In this study a micro-focus computer tomography (μCT) system has been used for the analysis of the microstructure of the foam samples and for the development of a microstructural Finite Element (micro-FE) mesh. The microstructural FE models have been used to model the mechanical behaviour of the Ni/Al hybrid foams under dynamic loading conditions. The simulations are validated by quasi-static compression tests and dynamic split Hopkinson pressure bar tests.

Comparison of the Mechanical Behaviour of Standard and Auxetic Foams by X‐ray Computed Tomography and Digital Volume Correlation

ABSTRACTThe tensile behaviour of standard and auxetic polyurethane foams are contrasted by digital volume correlation of 3D images collected by in situ X‐ray computed tomography (CT). It was found that subset sizes of 32 and 64 voxels for the auxetic and standard foams were optimal for strain resolutions in the order of 0.1%. For the standard foam, good uniformity of strain was observed at low strains giving a tangent Poisson's ratio of 0.5. Some heterogeneity of strain was observed at higher strains, which may be related to the fixtures. The behaviour of the auxetic foam was totally different, with strain being spatially heterogeneous with transverse strains both positive and negative but giving a negative Poisson's ratio on average. This suggests that the unfolding tendency of some groups of cells was higher than others because of the complex frozen starting microstructure. Further different methods of deriving Poisson's ratio gave different results. Besides revealing interesting microstuctural mechanisms of transverse straining, the study also shows digital volume correlation of tomography sequences to be the perfect tool to study complex mechanical behaviour of cellular materials.

Micromechanical and macromechanical modelling of foams: Identification of Cosserat parameters

AbstractThe classical continuum model does not describe the mechanical behaviour of cellular materials. To model the size‐dependent mechanical properties of these materials, the extended continuum models such as the micropolar approach can be used. The reference data is extracted from the virtual experiments performed on an artificial open‐cell foam specimens. With the proper set of the Cosserat parameters the detailed microstructural model can be described on the macroscopic level using the extended continuum approach. The parameter identification task is defined as a minimisation task, which is solved using the evolutionary computational framework.

Modeling the compressive stress–strain response of polymeric foams

AbstractThe mechanical behavior of cellular materials appears to have, for both open and closed cells, similar characteristics. The compressive stress–strain diagram contains a nearly elastic regime; this leads to a limit load, followed by a plateau extending to a strain of about 50% on average. All of the main features of this curve are related to the material's microstructure. In this study, taking into account the complex deformation mechanisms occurring in a cellular material under external loading, we introduced a statistical micromechanics model. The geometry of our analysis was based on a previous study, where the deformation of the individual struts was connected to the macroscopic deformation tensor. Assuming further that deformation was separated into elastic and viscoplastic parts and following a specific kinematic procedure, we simulated the compressive stress–strain response, the rate dependence, and the loading–unloading behavior of polymeric foam materials. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Investigations on an elastic micropolar continuum model for large deformations

AbstractThe mechanical behaviour of cellular materials is dominated by the influence of the microtopology. If the characteristic microstructural length scale becomes comparable to the macroscopical length scale, classical homogenisation strategies fail and have to be replaced by extended approaches. In the present contribution, we present a micropolar continuum model for large deformations introducing the microrotation as an additional degree of freedom. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Multiaxial Characterization Of The MechanicalBehaviour Of Aluminium Foam

In the past ten years many new processes for making foamed metals, mostly aluminium or aluminium alloys, have been developed. As a matter of fact, closed-cell aluminium foam offers a unique combination of properties such as low density, high stiffness, strength, and energy absorption capability. One of the main differences in the mechanical behaviour of cellular materials with respect to classical homogeneous materials such as solid metals is that foam failure is not independent from a hydrostatic state of stress. Therefore, it is not possible to describe the failure surface from a single, usually uniaxial, test but it is necessary to perform tests with different combination of deviatoric and hydrostatic stress components. Within the European Project APROSYS, whose main objective is increasing the safety of all road-users, the mechanical behaviour of aluminium foam, under multiaxial loading, was investigated by the authors. In this paper the results of the hydrostatic and hydro-compression experimental tests are reported. From the results of these tests, it has been possible to obtain the yield locus of the aluminium foam in the deviatoric-hydrostatic stress components space.

Size effects in the mechanical behavior of cellular materials

Effective mechanical properties of cellular materials depend strongly on the specimen size to the cell size ratio. Experimental studies performed on aluminium foams show that under uniaxial compression, the stiffness of these materials falls below the corresponding bulk value, when the ratio of the specimen size to the cell size is small. Conversely, in the case of simple shear and indentation, the overall stiffness rises above the bulk value. Classical continuum theory, lacking a length scale, cannot explain this size dependent mechanical behaviour. One way to account for these size effects is to explicitly model the discrete cellular morphology. We performed shear, compression and bending tests using discrete models, for hexagonal (regular and irregular) microstructures. Even though discrete models give a very good agreement with the experiments, they are computationally expensive for complex microstructures, especially in three dimensions. To overcome this, one can use a generalized continuum theory, such as Cosserat continuum theory, which incorporates a material length scale. We fit the Cosserat elastic constants of the models by comparing the discrete calculations with the analytical Cosserat continuum solutions in terms of macroscopic properties. We critically address the limitations of the Cosserat continuum theory.

Finite element modelling of the actual structure of cellular materials determined by X-ray tomography

The initial microstructure and local deformation mechanisms of a polyurethane foam during a compression test are investigated by means of X-ray microtomography. A methodology to mesh the actual solid volume is described. The polymer material behaviour is assumed to be elastoplastic. A predictive finite element modelling of the mechanical behaviour of cellular materials is then implemented. The validation of the modelling procedure is performed in relation to the macroscopic mechanical response as well as to the local deformation mechanisms observed during the experiments.

The effect of cell size on the mechanical behavior of cellular materials

The Young's modulus, strength and fracture toughness, of a brittle reticulated vitreous carbon foam, was measured as a function of cell size at a constant density and compared to a theoretical model. Image analysis was used to characterize the macrostructure of the samples and provided a basis for evaluating the mechanical behavior. It was determined that both the compressive and bend strength scale inversely with cell size. The change in compressive strength is due to a change in the strut strength with cell size. The bend strength behavior may be due to a reduction in the critical flaw size, as well as the increasing strut strength at smaller cell sizes. The fracture toughness and elastic modulus were found to be independent of cell size. Comparison of these results with previous work on open cell alumina clearly indicates a very different behavior and is attributed to a change in the microstructure of the solid phase with cell size in the alumina materials.

Modelling the mechanical behavior of cellular materials

Materials with a cellular structure are widespread; they include natural materials such as wood and cork as well as man-made honeycombs and foams. Their cellular structure gives rise to unique properties which can be exploited in engineering design. The selection of a specific honeycomb or foam for a particular engineering application is guided by models which describe their mechanical behavior in terms of the cell geometry and the mechanisms of deformation and failure. In this review, models for the mechanical behavior of cellular materials are first described and then used to select the optimum foam for two engineering applications, the design of packaging and of light-weight structural sandwich panels.