Analysis of the elastic properties of open-cell foams with tetrakaidecahedral cells

Zhu, Hanxing; Knott, J. F.; Mills, N. J.

doi:10.1016/s0022-5096(96)00090-7

Cited by 411 publications

(262 citation statements)

References 9 publications

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“…Results obtained with the ideal closed unit cell model developed by Simone and Gibson (1998a) and with the open cell model developed by Zhu et al (1997) are reported in Fig. 19 to verify the implemented computational approach.…”

Section: Ideal Unit Cell Modelmentioning

confidence: 88%

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Experimental and computational micro-mechanical investigations of compressive properties of polypropylene/multi-walled carbon nanotubes nanocomposite foams

Wan¹,

Tran

Leblanc

et al. 2015

Mechanics of Materials

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The compressive behavior of nanocomposite foams is studied by both experimental and computational micro-mechanics approaches with the aim of providing an efficient computational model for this kind of material.The nanocomposites based on polypropylene (PP) and different contents of multi-walled carbon nanotubes (CNTs) method. The nanocomposite samples are foamed using super-critical carbon dioxide (ScCO 2 ) as blowing agent at different soaking temperatures. The influence of this foaming parameter on the morphological characteristics of the foam micro-structure is discussed. Differential Scanning Calorimetry (DSC) measurements are used to quantify the crystallinity degree of both nanocomposites and foams showing that the crystallinity degree is reduced after the foaming process. This modification leads to mechanical properties of the foam cell walls that are different from the raw nanocomposite PP/CNTs material. Three-point bending tests are performed on the latter to measure the flexural modulus in terms of the crystallinity degree. Uniaxial compression tests are then performed on the foamed samples under quasi-static conditions in order to extract the macro-scale compressive response. Next, a two-level multi-scale approach is developed to model the behavior of the foamed nanocomposite material. On the one hand, the micromechanical properties of nanocomposite PP/CNTs cell walls are evaluated from a theoretical homogenization model accounting for the micro-structure of the semi-crystalline PP, for the degree of crystallinity, and for the CNT volume fraction. The applicability of this theoretical model is demonstrated via the comparison with experimental data from the described experimental measurements and from literature. On the other hand, the macroscopic behavior of the foamed material is evaluated using a computational micromechanics model using tetrakaidecahedron unit cells and periodic boundary conditions to estimate the homogenized properties. The unit cell is combined with several geometrical imperfections in order to capture the elastic collapse of the foamed material. The numerical results are compared to the experimental measurements and it is shown that the proposed unit cell computational micro-mechanics model can be used to estimate the homogenized behavior, including the linear and plateau regimes, of nanocomposite foams.

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Section: Ideal Unit Cell Modelmentioning

confidence: 88%

“…If a high value of Φ is used, e.g. Φ = 0.8, a large reduction Simone and Gibson (1998a) and the tetrakaidecahedron open cell model developed by Zhu et al (1997). The experimental Young's modulus measurements are also reported.…”

Section: Ideal Unit Cell Modelmentioning

confidence: 99%

Experimental and computational micro-mechanical investigations of compressive properties of polypropylene/multi-walled carbon nanotubes nanocomposite foams

Wan¹,

Tran

Leblanc

et al. 2015

Mechanics of Materials

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“…Analytical models for the description of the relation between relative density and effective stiffness properties are given by Gibson and Ashby [5]. Numerical approaches based on tetrakaidecahedron unit cells [6,7,8] and hollow-sphere arrangements [9] are reported.…”

Section: Numerical Modelingmentioning

confidence: 99%

Regular, low density cellular structures - rapid prototyping, numerical simulation, mechanical testing

et al. 2004

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Cellular solids form the basis of many biological and engineering structures. Most models use the relative density and the mechanical properties of the bulk material as the main parameter for the prediction of the mechanical properties of such structures. In this work the influence of the architecture of periodic cellular solids on the mechanical properties is investigated numerically and experimentally.Using computer aided design, structures with 8x8x8 base cells are designed and fabricated. The physical prototypes which are tested experimentally are made from thermosetting and thermoplastic polymers by employing Rapid Prototyping (RP) techniques. Various RP techniques are compared regarding their suitability for the fabrication of cellular materials.For numerical simulation of the cellular structures, linear Finite Element analysis is employed. Three-dimensional models are set up using higher order beam elements. In a first step, the structure is treated as an infinite medium and homogenization via a 'periodic micro-field approach' is used. The entire elastic tensors for different relative densities are evaluated, from which the directional dependencies of the Young's moduli are derived. In a second step, simulations of finite structures are performed for direct comparison with experiments. Samples consisting of several basic cells are modeled which leads to a better correspondence to the experimental setup. Finite structures of different numbers of cells are modeled to study the influence of the sample size.The experimental and numerical results correspond very well and form a consistent picture of the problem. The multi-disciplinary approach leads to a comprehensive view of effects which govern the mechanical behaviour of the investigated cellular structures. RAPID PROTOTYPING OF CELLULAR MATERIALSRapid Prototyping (RP) offers the possibility to fabricate cellular structures with defined internal and external geometry [1]. Furthermore, recently developed techniques enable the fabrication of complex structures with very small feature resolution. Microstereolithography for instance enables the user to fabricate parts with feature resolutions in the range of 5-10 µm [2,3]. In the course of this work, RP techniques have been used to fabricate polymeric cellular structures whose mechanical properties (strength, stiffness) were investigated experimentally.Cellular structures exhibit multiple undercut features. The utilized process must be able to shape such features. In the course of this work, two RP processes were utilized: Stereolithography (SLA) and selective laser sintering (SLS) [4]. SLA offers excellent feature resolution. Problems might arise with structures which cannot be built without support. Due to the cellular structure of the fabricated parts, support structures cannot be removed mechanically. The unit cells of the Mat. Res. Soc. Symp. Proc. Vol. 823

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“…Young's modulus and Poisson's ratio, is a more complex process. Extensive research performed in recent years in this area includes experimental [12,13], analytical [14] and numerical [15,16] approaches. Numerical analysis uses both simplified model structures, and calculation models derived from X-ray micro-computed tomography (μCT) data [17].…”

Section: Introductionmentioning

confidence: 99%

“…Most of geometrical models proposed in literature base on the assumption of equal volume of pores of different shapes [18][19][20][21][22][23]. In commercial practice foams are very frequently manufactured with narrow pore size distributions, which was confirmed by experimental observations [24].…”

Section: Introductionmentioning

confidence: 99%

Design of Mechanical Properties of Open-Cell Porous Materials Based on μCT Study of Commercial Foams

Skibiński

Ćwieka

Wejrzanowski

et al. 2015

MATEC Web of Conferences

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Abstract. In the present paper numerical design of mechanical properties of open-cell porous materials is addressed. A detailed knowledge of mechanisms and parameters determining mechanical properties (i.e. Young's Modulus, Poisson's Ratio) of foams is essential for applications such as energy absorbers or lightweight construction materials. The foam structures were designed using procedure based on Laguerre-Voronoi tessellations (LVT) with microcomputed tomography of commercial foams used as reference. Foam morphology was studied on post-processed computed tomography images and the parameters of LVT structures were compared with commercial materials. Subsequently finite element method (FEM) calculations were performed on both types of structures to validate the LVT design algorithm. The results show that the described design procedure can be successfully used for modeling mechanical properties of open-cell foam structures.

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Analysis of the elastic properties of open-cell foams with tetrakaidecahedral cells

Cited by 411 publications

References 9 publications

Experimental and computational micro-mechanical investigations of compressive properties of polypropylene/multi-walled carbon nanotubes nanocomposite foams

Experimental and computational micro-mechanical investigations of compressive properties of polypropylene/multi-walled carbon nanotubes nanocomposite foams

Regular, low density cellular structures - rapid prototyping, numerical simulation, mechanical testing

Design of Mechanical Properties of Open-Cell Porous Materials Based on μCT Study of Commercial Foams

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