Stochastic multiscale modeling of metal foams (original) (raw)
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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.
Angles in Laguerre tessellation models for solid foams
Computational Materials Science, 2014
ABSTRACT Geometric stochastic models proved to be very helpful to improve the understanding of how physical properties of materials depend on their microstructures. The microstructures of cellular materials are well modeled by random Laguerre tessellations generated by systems of non-overlapping spheres. We enrich the geometric characterization of Laguerre tessellations by computing angles between facets and angles between edges. Their distributions, which depend on the model parameters, are investigated in detail. To include angles in the model fit, we developed a method for estimating angles in 3D images of foams, e. g. obtained by micro-computed tomography. Furthermore, we analyzed the influence of different characteristics on the model’s fit to samples of closed and open foams.
Validation of a Probabilistic Model for Mesoscale Elasticity Tensor of Random Polycrystals
2013
In this paper, we present validation of a probabilistic model for mesoscale elastic behavior of materials with microstructure. The linear elastic constitutive matrix of this model is described mathematically as a bounded random matrix. The bounds reflect theoretical constraints consistent with the theory of elasticity. We first introduce a statistical characterization of an experimental database on morphology and crystallography of polycrystalline microstructures. The resulting statistical model is used as a surrogate to further experimental data, required for calibration and validation. We then recall the construction of a probabilistic model for the random matrix characterizing the apparent elasticity tensor of a heterogeneous random medium. The calibration of this coarse scale probabilistic model using an experimental database of microstructural measurements and utilizing the developed microstructural simulation tool is briefly discussed. Before using the model as a predictive tool in a system level simulation for the purpose of detection and prognosis, the credibility of the model must be established through evaluating the degree of agreement between the predictions of the model and the observations. As such, a procedure is presented to validate the probabilistic model from simulated data resulting from subscale simulations. Suitable quantities of interest are introduced and predictive accuracy of the model is studied by comparing probability density functions of response quantities of interest. The validation task is exercised under both static and dynamic loading condition. The results indicate that the probabilistic model of mesoscale elasticity tensor is adequate to predict the response quantity of interest in the elastostatic regime. The scatter in the model predictions is found to be consistent with the fine scale response. In the case of elastodynamic, the model predicts the mean behavior for lower frequency for which we have a quasistatic regime.
Multiscale characterisation and simulation of open cell metal foams
PAMM, 2018
The complex microstructure of open cell metal foams results in beneficial global material properties like a good weight to stiffness ratio, which makes this special group of cellular materials interesting for several applications. Open cell metal foams are suitable for lightweight applications as well as for energy absorbing systems. The dependency of the entire samples' mechanical behaviour on their microstructure induces the demand of experiments and simulations on different scales. Hence, a couple of experiments are necessary to specify the material properties of open cell aluminium foams. On the macroscopic level, several tests with different load cases such as pure tension, pure compression or pure torsion and the superposition of these loading conditions are needed to obtain the yield surface for the different types of foams. The material parameters on the microscopic level can be identified by microtensile tests and inverse calculations using a 3D model of the strut. The deviation of the simulation results from the experimental data is minimised by an optimisation. Thus, the used material parameters in the simulations are changed until the numerical results match the experiments. This contribution focuses on the characterisation of open cell metal foams on different hierarchical levels. It introduces an approach to describe the macroscopic material behaviour with a homogeneous material model based on micromechanical experiments and material parameters.
Multiscale thermoelastic analysis of random heterogeneous materials
Computational Materials Science, 2010
This study is concerned with the modeling of heterogeneous materials with random microstructure and understanding their thermomechanical properties. Realistic random microstructures are generated for computational analyses using random morphology description functions (RMDFs). The simulated microstructures closely resemble actual micrographs of random heterogeneous materials. It is possible to simulate a wide range of random microstructures using this method, including: (a) particles of irregular shapes and sizes embedded in a matrix phase and (b) interpenetrating phase composite microstructures in which each material phase forms an interconnected network. In this first part of the work, the simulated RMDF microstructures are characterized using statistical techniques and their homogenized material properties computed using the asymptotic expansion homogenization (AEH) method. The material properties thus obtained are compared with analytical homogenization schemes and experimental data for several different material combinations and constituent volume fractions.
Mechanics of Materials, 2013
A numerical investigation has been conducted to determine the influence of Representative Volume Element (RVE) size and degree of irregularity of polymer foam microstructure on its compressive mechanical properties, including stiffness, plateau stress and onset strain of densification. Periodic two-dimensional RVEs have been generated using a Voronoibased numerical algorithm and compressed. Importantly, self-contact of the foam's internal microstructure has been incorporated through the use of shell elements, allowing simulation of the foam well into the densification stage of compression; strains of up to 80% are applied. Results suggest that the stiffness of the foam RVE is relatively insensitive to RVE size but tends to soften as the degree of irregularity increases. Both the shape of the plateau stress and the onset strain of densification are sensitive to both the RVE size and degree of irregularity. Increasing the RVE size and decreasing the degree of irregularity both tend to result in a decrease of the gradient of the plateau region, while increasing the RVE size and degree of irregularity both tend to decrease the onset strain of densification. Finally, a method of predicting the onset strain of densification to an accuracy of about 10%, while reducing the computational cost by two orders of magnitude is suggested.
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.
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.
On the Linear Elastic Properties of Regular and Random Open-Cell Foam Models
Journal of Cellular Plastics, 1997
Foams can be created from coagulation of gas bubbles in liquid. After removal of cell faces, an open-cell foam remains consisting of a strut framework. In the past, mechanical properties were estimated by a small unit cell consisting of only a few struts. However, the random geometry of the foam can be of importance for the linear elastic properties. Here,
Material spatial randomness: From statistical to representative volume element
2006
The material spatial randomness forces one to re-examine various basic concepts of continuum solid mechanics. In this paper we focus on the Representative Volume Element (RVE) that is commonly taken for granted in most of deterministic as well as in stochastic solid mechanics, although in the latter case it is called the Statistical Volume Element (SVE). The key issue is the scale over which homogenization is being carried out-it is called the mesoscale, separating the microscale (level of microheterogeneities) from the macroscale (level of RVE). As the mesoscale grows, the SVE tends to become the RVE. This occurs in terms of two hierarchies of bounds stemming from Dirichlet and Neumann boundary value problems on the mesoscale, respectively. Since generally there is no periodicity in real random media, the RVE can only be approached approximately on finite scales. We review results on this subject in the settings of linear elasticity, finite elasticity, plasticity, viscoelasticity, thermoelasticity, and permeability. q