Collapse criteria of foam cells under various loading

Recently porous materials are widely used in civil and mechanical engineering. In particular, such porous materials as metal and polymer foams have applications in lightweight structures. From mechanics point of view foams can demonstrate unusual behavior such as strain localization related to foam cells buckling under certain loads. The aim of this work is the elaboration of the model of foam material taking into account the cell collapse. We consider the cell collapse initiation during the elastic instability and its further evolution under loading. The geometrical structure of foam is generated with the use of the Voronoi algorithm. Based on stochastic distributions of cells we create various geometrical models of foams. The influence of the cell volume, wall thicknesses and material properties of the foam material on critical loads is obtained. The calculations are performed with the use of Abaqus CAD/CAE system. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transport of Mass,Momentum and Energy through Periodic Open Cell Metal Foams Applied in Catalysis

An ODE model to predict the temperature field of periodic open cell metal foams applied in catalysis as carrier structures is presented. The catalytic and highly endothermic reaction takes place in a porous layer which surround the struts of the foam and releases gas from a fluid. The one-dimensional model includes dependencies of the foam structure (strut radius, shape of strut), process conditions (surrounding velocity, surrounding fluid: liquid and/or gas), chemical conditions (reaction enthalpy, activation energy) and material parameters (thermal conductivity, density, viscosity). This makes it possible to estimate optimal parameters, that are able to provide sufficient heat to the reaction. The advantage of this model is the substantial time saving in contrary to three dimensional finite volume simulations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimation of large domain Al foam permeability by Finite Difference methods

Classical methods to calculate permeability of porous media have been proposed mainly for high density (e.g. granular) materials. These methods present shortcomings in high porosity, i.e. high permeability media (e.g. metallic foams). While for dense materials permeability seems to be a function of bulk properties and occupancy averaged over the volume, for highly porous materials these parameters fail to predict it. Several authors have attacked the problem by solving the Navier-Stokes equations for the pressure and velocity of a liquid flowing through a small domain (Ω_s) of aluminium foam and by comparing the numerical results with experimental values (prediction error approx. 9%). In this article, we present calculations for much larger domains (Ω_L) using the Finite Difference (FD) method, solving also for the pressure and velocity of a viscous liquid flowing through the Packed Spheres scenario. The ratio Vol(Ω_L)/Vol(Ω_s) is around 10³. The comparison of our results with the Packed Spheres example yields a prediction error of 5% for the intrinsic permeability. Additionally, numerical permeability calculations have been performed for Al foam samples. Our geometric modelling of the porous domain stems from 3D X-ray tomography, yielding voxel information, which is particularly appropriate for FD. Ongoing work concerns the reduction in computing times of the FD method, consideration of other materials and fluids, and comparison with experimental data. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and numerical investigation of metal foams undergoing large deformations

Open cell aluminum metal foams are a new kind of material that are used in composite structures to reduce their weight, to increase their sound or energy absorption capability or to decrease their thermal conductivity. The design and analysis of such structures requires a macroscopic constitutive model of the foam that has to be determined by various experiments under different loading conditions. We support this procedure by analyzing the microstructure of the metal foam numerically under large deformations. To this end, we employ the finite cell method that can deal with large deformations and allows for an automatic and efficient discretization of the CT-image of the foam. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and numerical investigation of PUR foam under dynamic loading

Various factors may subject buildings to shock which continues in their structure and is perceived by the people living in them as noticeable vibrations or noise. In this context, polyurethane (PUR) foams, which have been developed to isolate vibrations, have shown to be very effective in practical use. However, whereas static properties of open-cell structures have already been determined numerically in good agreement to experimental results, cf. [1], there are hardly any investigations on the dynamical properties characterizing acoustic damping. In order to validate experimental measurements of eigenfrequencies for different PUR foam specimen we present here a strategy to reproduce the foam behavior numerically. In doing so, PUR foams are modeled using a three dimensional Voronoi-tessellation technique. The resulting Voronoi cells correspond to open pores and are scaled in such a way that the volume ratio between the pores and material matches the given PUR foam. For finite element analysis the connections between the cells are modeled as beam elements, the beam shape follows Bezièr curves. The generated model is analyzed with a finite element software and the dynamical parameters are determined. The numerical results are compared to our experimental data. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and Simulation of the Transport of Protein Foams

The behaviour of foams at rest, but particularly during fluid mechanical transport is not sufficiently investigated yet. The present article deals with protein foams as they have a great importance in food production. In the first part, the foaming process of a highly viscous liquid due to gaseous materials dispersed under pressure in the liquid and mass transport of volatile components dissolved in the liquid is considered. The aim is to calculate the foam volume and the concentration of the dissolved, volatile components as a function of the material and process parameters. In the second part, material equations for bubble suspensions with gas volume fractions ϕ ≤ 0.6 and small bubble deformations (i.e. N_Ca ≪ 1) are presented. The basics form two constitutive laws which are used for describing a steady shear flow. If the rates of work of the two models are compared, material equations for the shear viscosity and the normal stress differences can be derived. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A contribution to the modeling of metal foams on the mesoscale

Due to their useful properties in lightweight construction and due to their excellent behavior in energy absorption for example in crash mechanics, metal foams became an interesting, often utilized and investigated material. For the determination of the mechanical properties of foams without the help of expensive experiments, a way for computing these properties is searched. The problem in doing so is that foams can be composed out of randomly distributed edges and faces with varying thickness and of other inhomogeneities on the mesoscale like imperfections. The goal in this paper is, to investigate the influence of these irregularities on the mechanical, linear elastic properties of a metal foam on the macroscale and to determine the size of a representative volume element, for which the irregularities on the mesoscale do not have a great influence on the linear elastic properties. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation study on the formation and transition properties of cluster structures in liquid metals during rapid cooling processes

For the first time, a molecular dynamics simulation study has been performed for a liquid metal system consisting of 50000 atoms to deeply investigate the transitions of microstructure configurations dudng the rapid cooling processes. Especially, the cluster-type index method has been adopted to analyze the transforming and evolving processes of clusters and cluster configurations from liquid metal atoms. It has been found that the bigger cluster configurations in the system are formed by means of connecting some small clusters (they are combined by several smaller clusters), and not taken on the multi-shells configuration accumulated with an atom as the center and the surrounding atoms arranged according to some fixed pattern. With the decrease in temperature, the probability of repetitive appearance for clusters increases largely, which reveals that clusters are indeed possessing a certain relative stability and continuity (namely hereditary effect). These results will give us an important enlightenment to understand not only the forming mechanisms and microscopic processes of the short-order sections and disorder sparse sections in amorphous structures but also the freezing processes of liquid metals.``     

Free-surface instabilities during electromagnetic shaping of liquid metals

Electromagnetic shaping of free surfaces of liquid metals is a well-known EPM technology used in a couple of metallurgic processes like cold crucible melting, semi-levitation, and electromagnetic slit sealing, among others. However, the stability of such free surfaces is the most important problem and stability control is crucial for success. Within this context we investigate experimentally the stability behavior of liquid metal free surfaces submitted to a high-frequency magnetic field. In this case, the induced Lorentz forces act as an electromagnetic pressure directly on the free surface of the liquid met al. We consider three experimental model configurations: (i) Sessile liquid metal drop (ii) liquid metal ring, and (iii) liquid metal disc. In each model experiment, upon increasing the feeding current beyond a certain threshold value, I_C, we observe that the initial surface contour becomes unstable resulting in (i) drop oscillations (ii) electromagnetic pinching and (iii) static disc deformations. In each configuration the threshold value depends in a similar manner on the frequency of the applied magnetic field. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of the cellular structure on thermal conductivity of rigid closed-cell foam polymers during long-term aging

The thermal conductivity of rigid closed-cell polyurethane foams during long-term aging has been studied. The similarity between the kinetics of changes in the physical and mechanical characteristics of PU foams on progressive aging is established, which is attributed to the effect of matrix destruction. It is found that rigid foams have cell walls of various strength, whose impact on the kinetics of changes in the physical characteristics of the foams during long-term aging is ascertained. The results of predicting the thermal conductivity of PU foams by the method of temperature-time analogy and establishing the limits of its application are discussed. The research presented is of interest both in determining the foam durability and in replacing freons by alternative, ecologically less harmful blowing agents.     

Homogenisation of elasto-plastic open-celled foams

The effective yield behaviour of open-celled metal foams is studied by a micro-mechanical model. As a surrogate model for the sponge-like microstructure the simplified Kelvin foam is used. The yield loci in strain space and stress space are constructed by conducting numerical experiments. For the determination of the effective stresses a strain-energy based homogenisation procedure is adopted. The numerical examples show that the initial yield surface in the normal strain space is similar to a polyhedron with sharp corners. The further evolution of the yield surface is characterized by kinematic and isotropic hardening effects. In addition, the stress yield surface may rotate under certain loading conditions. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermo-mechanical modelling of cellular ceramic composites by a multiphase approach of porous media

Refractory materials have a wide range of applications in the steel-making industry for example as lining of furnaces, oxygen converters or for ladles. Often, magnesia carbon bricks (MgO-C) are used. These are made of a periclase phase (MgO) with carbon inclusions and pores. In their applications, refractories are subjected to thermal and mechanical loads causing damage. The thermo-mechanical behaviour of MgO-C composites and hence their thermal stability could be improved significantly using cellular MgO-C composites based on carbon foams [1, 2]. The present contribution focuses on the development of a fully coupled phenomenological thermo-mechanical continuum model based on the theory of porous media (TPM) with a new kinematic coupling of the displacement field of all constituents. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Local probabilistic homogenization schemes for assessment of material uncertainties in solid foams

The present study is concerned with a numerical scheme for prediction of the effective properties of solid foams considering their uncertainty. The approach is based on an analysis of a large-scale, statistically representative volume element which is subdivided into small-scale testing volume elements. Application of a standard homogenization scheme to the testing volume elements together with a stochastic evaluation yields a complete probabilistic characterization of the material which may be used for a random field definition of the material behaviour in a macroscopic effective field analysis of foam structures. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of the cellular structure on thermal conductivity of rigid closed-cell foam polymers during long-term aging

The thermal conductivity of rigid closed-cell polyurethane foams during long-term aging has been studied. The similarity between the kinetics of changes in the physical and mechanical characteristics of PU foams on progressive aging is established, which is attributed to the effect of matrix destruction. It is found that rigid foams have cell walls of various strength, whose impact on the kinetics of changes in the physical characteristics of the foams during long-term aging is ascertained. The results of predicting the thermal conductivity of PU foams by the method of temperature-time analogy and establishing the limits of its application are discussed. The research presented is of interest both in determining the foam durability and in replacing freons by alternative, ecologically less harmful blowing agents.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 187–198, March–April, 1999.     

Macroscopic mechanical properties of metal foam in dependence on the inhomogenities of the mesoscale

In this contribution, a way of simulating the influence of the mesoscopic irregular structure of metal foams on the macroscale is shown. To this end, mesoscopic periodic volume elements of a foam are derived in order to compute the mechanical properties including the effects of inhomogenities like imperfections, irregular structure and varying cell wall thicknesses. With the help of these volume elements, which are analysed via the finite element method, and their varying mechanical properties, a local varying stiffness can be computed and inserted into the macromechanical model. In this way the propagation of uncertainities from the mesoscale to the macroscale can be assessed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于微观方法对液态铝泡沫宏观析液过程的数值模拟研究

通过微元管内流动模型,研究了液态金属熔体泡沫体内单条Plateau边界内析液过程中的速度场.分析了不同Newton表面粘度,即不同的气液界面运动能力(无量纲参数M)下,Plateau边界内速度的分布.结果显示:在相同的气液界面运动能力和曲率半径条件下,泡沫体内固壁处Plateau边界内速度约是内部Plateau边界内速度的6～8倍,从而解释了不同容器内泡沫体析液速率的差异现象;发现M存在1个临界值,在此值的两边,液膜厚度与曲率半径的比值对Plateau边界内速度的影响呈现出相反的趋势.结合多尺度方法,进而利用微观计算结果建立了泡沫体的整体宏观析液模型,将模型计算结果和经典析液方程计算结果及实验值作了比较,结果表明:该文模型计算结果与实验值在泡沫层上部、中部吻合较好,M值和气泡大小对析液过程有显著影响.     

Model of Deformation of Monotropic Plastic Foams Parallel to the Foam Rise Direction Based on the Volume-Deformation Hypothesis

The deformation properties of monotropic plastic foams under uniaxial deformation (compression or tension) parallel to the foam rise direction is considered. The theoretical results are obtained in the case where the volume-deformation hypothesis is assumed. The validity of neglecting the fluctuation component in calculations of the effective volume strains of foams is substantiated. A tie condition permitting the sought-for semiaxes to vary not obligatorily equally is derived. The values of Young's modulus and Poisson coefficients are obtained for a wide range of model cell stretch ratios and foam space-filling coefficients. A comparison of the theoretical results with the experimental data available is performed.     

Numerical assessment of disorder effects in metal foam core sandwich beams based on a local homogenization procedure

The present study is concerned with a numerical procedure for prediction of uncertainty effects in sandwich structures with disordered cores. The approach is based on probability distributions of different material properties and their spatial correlation which are the results of the multiple homogenization analysis of testing volume elements. In order to illustrate the essential difference in the results of material uncertainties between computations using random fields and a deterministic approach both methods are applied to a single edge clamped sandwich beam with a metal foam core which is loaded by a force at the free end. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of Ni/Al hybrid metal foams using the finite cell method

Aluminium metal foams are a new type of material that can be used in many lightweight applications. One method to improve their mechanical properties is to coat them with a thin layer of nickel by electrodeposition. A voxel representation of this hybrid foam can be obtained in a straightforward way using a CT scanner. The voxel-based geometry can then be processed and modified with respect to the thickness of the nickel layer in order to investigate its influence on the effective properties. By employing the finite cell method (FCM) we are able to automatically convert the voxel-based geometry into a finite cell grid and to directly perform a homogenization procedure. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)