Angles in Laguerre tessellation models for solid foams (original) (raw)
Related papers
Model Based Estimation of Geometric Characteristics of Open Foams
Methodology and Computing in Applied Probability, 2012
Open cell foams are a class of modern materials which is interesting for a wide variety of applications and which is not accessible to classical materialography based on 2d images. d imaging by micro computed tomography is a practicable alternative. Analysis of the resulting volume images is either based on a simple binarisation of the image or on so-called cell reconstruction by image processing. The first approach allows to estimate mean characteristics like the mean cell volume using the typical cell of a random spatial tessellation as model for the cell shape. The cell reconstruction allows estimation of empirical distributions of cell characteristics. This paper summarises the theoretical background for the first method, in particular estimation of the intrinsic volumes and their densities from discretized data and models for random spatial tessellations. The accuracy of the estimation method is assessed using the dilated edge systems of simulated random spatial tessellations.
Microstructure models for cellular materials
Computational Materials Science, 2009
Laguerre tessellations generated by random sphere packings are promising models for the microstructure of cellular or polycrystalline materials. In this paper, the case of hard sphere packings with lognormal or gamma distributed volumes is investigated. The dependence of the geometric characteristics of the Laguerre cells on the volume fraction of the sphere packing and the coefficient of variation of the volume distribution is studied in detail. The moments of certain cell characteristics are described by polynomials, which allows to fit tessellation models to real materials without further simulations. The procedure is demonstrated by the examples of open polymer and aluminium foams.
International Journal of Engineering Science
The dependency of the elastic stiffness, i.e., Young's modulus, of isotropic closed-cell foams on the cell size variation is studied by microstructural simulation. For this purpose, we use random Laguerre tessellations which, unlike classical Voronoi models, allow to generate model foams with strongly varying cell sizes. The elastic stiffness of the model realizations is computed by micro finite element analysis using shell elements. The main result is a moderate decrease of the effective elastic stiffness for increasing cell size variations if the solid volume fraction is assumed to be constant.
Stochastic multiscale modeling of metal foams
Procedia IUTAM, 2013
A procedure for the computation of eigenfrequencies for structures made of metal foam is proposed. The heterogeneity of the foam geometry has an influence on these macroscopic properties and has to be taken into account. This is done by fitting a model of the microstructure based on Laguerre tessellations by means of statistical information obtained from CT image analysis. As the length scale of the representative volume element is nearly of the same order as the length scale of the structures under consideration, classical homogenization techniques for the computation of effective properties can not be applied. A stochastic homogenization method that necessitates the computation of empirical marginal distributions and correlation functions for apparent properties defined on the mesoscale is proposed. This information allows to define random fields for elastic properties and the density on the structure level. Statistical properties of the eigenfrequencies can then be inferred.
Materials, 2019
Ceramic foams are promising, highly porous materials, with a wide range of specific surface area and low fluid flow resistance, which are well-suited for filtering applications. They are comprised mainly of macrovoids that are interconnected with struts. A branch-shaped reconstruction algorithm is introduced in the present work to reconstruct various ceramic foams from electron microscopy images using the Laguerre tessellation method. Subsequently, the reconstructed samples are used for the numerical calculation of pore structure and transport properties, including specific surface area, tortuosity, effective diffusivity, and flow permeability. Following comparison with experimental data, this reconstruction method is shown to be more reliable than typical analytical expressions that are suggested in the literature for the aforementioned structural and transport properties. Extracting the equivalent pore radius of the reconstructed domains offers improved accuracy of the analytical ...
Size effects in foams: Experiments and modeling
Progress in Materials Science, 2011
Mechanical properties of cellular solids depend on the ratio of the sample size to the cell size at length scales where the two are of the same order of magnitude. Considering that the cell size of many cellular solids used in engineering applications is between 1 and 10 mm, it is not uncommon to have components with dimensions of only a few cell sizes. Therefore, both for mechanical testing and for design, it is important to understand the link between the cellular morphology and size effects, which is the aim of this study. In order to represent random foams, two-dimensional (2D) Voronoi tessellations are used, and four representative boundary value problems -compression, shear, indentation, and bending -are solved by the finite element (FE) method. Effective elastic and plastic mechanical properties of Voronoi samples are calculated as a function of the sample size, and deformation mechanisms triggering the size effects are traced through strain maps. The modeling results are systematically compared with experimental results from the literature. As a rule, with decreasing sample size, the effective macroscopic stiffness and strength of Voronoi samples decrease under compression and bending, and increase under shear and indentation. The physical mechanisms responsible for these trends are identified.
A probabilistic constitutive model for closed-cell foams
In the homogenization analysis of closed-cell foams for determination of their effective properties, the generation of numerical models which reproduce the real microstructure is very complex and time extensive. For this reason, the present study deals with the definition of a probabilistic constitutive model which makes it possible to compute the effective stiffness components and the corresponding scatter band widths without modeling the real microstructure. However, probability distributions of the relative density, the cell size, cell shape and orientation, as the most essential microstructural variables influencing the effective stiffness, are required as the input database. These material characteristics can be easily determined by computed tomography processes. Furthermore, the influence of these distributions for the input variables on the effective material properties is investigated by a systematic variation.
Morphology and Linear-Elastic Moduli of Random Network Solids
Advanced Materials, 2011
Disordered networks or open-cell spatial structures represent the spatial morphology of many micro-structured materials: [ 1 ] the spatial structure of open-cell metal foams is given by the edge network of the liquid foam template; [ 2 ] similar designs are fabricated from biodegradable materials by rapid prototyping methods as artifi cial bone scaffolds mimicking the natural morphology of highly porous bone; [ 3 , 4 ] network structure and connectivity are important in biological and synthetic random fi ber composites. [ 5 ] Softer network materials, where thermal fl uctuations are relevant, include hydro-gels, [ 6 ] and networks composed of bio-polymer fi bers such as collagen or actin. [ 7 , 8 ] Several interesting physical effects result from the disordered threedimensional network-like nature of such systems, such as auxetic behavior in polymeric foams, [ 9 ] strain-hardening in constrained metal foams, [ 10 ] shear-stiffening and other non-linear behavior in crosslinked bio-polymeric networks such as actin, [ 8 , 11 ] rigidity in string networks [ 12 ] and spring networks, [ 13 ] and fl oppy modes in fi ber networks and foam structures. [ 14 , 15 ] Given the widespread occurrence of network structures in physical systems, the range of geometric models used in physical analyses is rather limited. The most common model for disordered networks is the so-called Poisson-Voronoi process where the Voronoi diagram [ 16 ] of points with random uncorrelated coordinates is computed and the network is given by the Voronoi edges, see Figure 1 (a). In the strict mathematical model, [ 17 ] random uncorrelated points are placed with intensity λ , implying that the point density fl uctuates between different realizations around its average value λ. An advantage of the Poisson-Voronoi model is the availability of analytic expressions for fundamental morphological characteristics. Importantly, the probability of edges of length l in Poisson-Voronoi networks follows a broad distribution with large probabilities for both very small and very large edges (see e.g. the discussion of morphological properties of random Voronoi models in refs. [17-19]). Alternative random network models include foam structures that are obtained by evolving an initial cellular partition such that surface area is minimized while striving for equal cell volumes. [ 18 , 20 ] The definition of these models is algorithmic and analytic expressions for morphological quantities are not known. Somewhat similar are edge graphs of constrained Voronoi tessellations , obtained by Monte Carlo methods, with constraint distributions of e.g. the