Representative volume element and effective elastic properties of open cell foam materials with random microstructures

Kanaun, S. K.; Tkachenko, Oleksandr

doi:10.2140/jomms.2007.2.1607

Cited by 23 publications

(12 citation statements)

References 15 publications

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“…Exemplary samples of both types are shown in Figure 1. Samples' dimensions were fit to satisfy the condition of the minimal number of cells for the specimen's volume to be representative [35]. e dimensions were on average (53.0 × 39.5 × 39.0) mm and (62.8 × 39.5 × 38.0) mm, respectively, for the "P" and "R" lots.…”

Section: Materials and Data From Uniaxial Compressionmentioning

confidence: 99%

ANN Architecture Specifications for Modelling of Open-Cell Aluminum under Compression

Dudzik

Stręk

2020

Mathematical Problems in Engineering

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e knowledge on strength properties of porous metals in compression is essential in tailored application design, as well as in elaboration of general material models. In this article, the authors propose specification details of the ANN architecture for adequate modelling of the phenomenon of compressive behaviour of open-cell aluminum. In the presented research, an algorithm was used to build different structures of artificial neural networks (ANNs), which approximated stress-strain relations of an aluminum sponge subjected to compression. Next, the quality of the built approximations was appraised. e mean absolute relative error (MARE), coefficient of determination between outputs and targets (R 2 ), root mean square error (RMSE), and mean square error (MSE) were assumed as criterial measures for the assessment of the fitting quality. e studied neural networks (NNs) were two-layer feedforward networks with different numbers of neurons in the hidden layer. A set of experimental stress-strain data from quasistatic uniaxial compression tests of open-cell aluminum of various apparent densities was used as data for training of neural networks. Analysis was performed in two modes: in the first one, all samples were taken for training, and in the second case, one sample was left out during training in order to play the role of external data for testing the trained network later. e taken out samples were maximum and minimum density samples (for extrapolation) and one random from within the density interval. e results showed that good approximation on the engineering level (MARE < 5%) was reached for teaching networks with ≥7 neurons in the hidden layer for the first studied case and with ≥8 neurons for the second. Calculations on external data proved that 8 neurons are enough to actually obtain MARE < 10%. Moreover, it was shown that the quality of approximation can be significantly improved to MARE ≈ 7% (tested on external data) if the initial region of the stress-strain relation is modelled by an additional network.

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Section: Materials and Data From Uniaxial Compressionmentioning

confidence: 99%

ANN Architecture Specifications for Modelling of Open-Cell Aluminum under Compression

Dudzik

Stręk

2020

Mathematical Problems in Engineering

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“…circular) in foam model. If the beams were modeled to have real hypocycloidal or plateauborder cross-section (e.g., Gong and Kyriakides, 2006;Kanaun and Tkachenko, 2007), the partition of total strain energy into stretch and bending components would not be straightforward due to the coupling terms. The elastic strain energy stored in stretch mode of deformation for each beam element, therefore, can be written as:…”

Section: Partition Of Elastic Strain Energymentioning

confidence: 99%

On the nature of pressure dependence in foams

Ayyagari

Vural

2016

International Journal of Solids and Structures

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a b s t r a c tPresent study explores the physical background of pressure dependence observed in the yield behavior of solid foams by analyzing the partition of strain energy and stress distribution in the struts that make up the foam. To this end, transversely isotropic Kelvin foam models of three different relative densities are utilized in FE analysis to probe the yield surface along various biaxial and triaxial stress paths for a wide range of mean stress. From a macroscopic viewpoint, it is observed that in addition to well-documented quadratic dependence of yielding on mean stress there also exists a linear pressure dependence, which has not been properly addressed in the literature. Partition of strain energy at the time of macroscopic yielding into bending and stretch modes of deformation within struts provides a unique tool with which the dominant deformation mode that drives yielding can be identified as a function of the stress path followed. Analysis of FE results indicates that positive mean stress, as compared to negative mean stress, provides a strong configurational stability in deformation kinematics that limits bending mode and promotes the stretch mode of deformation in struts. Increasing the fraction of strain energy stored in stretch mode effectively increases the critical strain energy of yielding and, thereby, delays the onset of microscopic yielding. Negative mean stress, on the other hand, results in a weak configurational stability where bending mode is more prominent. Furthermore, it seems that the degree of this already weak stability quickly decays with the magnitude of negative mean stress and completely disappears when (and if) the stabilizing effect of joint stiffness is exceeded. We conclude that this contrasting behavior is the main source of (i) linear pressure dependence observed in the yield behavior as well as (ii) the stronger effect of linear pressure in low-density foams.

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“…[7] Modeling approaches often start with a Voronoi or Laguerre tessalation of sphere packings [8][9][10] from which a foam skeleton can be derived. Those skeletons showing a lot of very short struts, a feature which is not observed for real foams.…”

Section: Introductionmentioning

confidence: 99%

An Approach Toward Numerical Investigation of the Mechanical Behavior of Ceramic Foams during Metal Melt Filtration Processes

et al. 2017

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This article demonstrates an approach for the numerical modeling of open cell ceramic foams, in order to investigate the thermo-mechanical behavior during metal melt filtration processes. The described methods include the creation of the geometric models, the fluid-dynamic simulations of the melt flow using the lattice boltzmann method, and finite element simulations of the ceramic foam under general loads. The paper mainly focuses on the representative geometry generation process, such that the modeled geometry replicates the real foam as far as possible, since high quality models are essential for the quantitative analyses to be reliable. The present parametric studies demonstrate the manner, in which the foam properties may be influenced by changing the geometric and the topological properties, in order to improve the behavior during filtration processes.

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Representative volume element and effective elastic properties of open cell foam materials with random microstructures

Cited by 23 publications

References 15 publications

ANN Architecture Specifications for Modelling of Open-Cell Aluminum under Compression

ANN Architecture Specifications for Modelling of Open-Cell Aluminum under Compression

On the nature of pressure dependence in foams

An Approach Toward Numerical Investigation of the Mechanical Behavior of Ceramic Foams during Metal Melt Filtration Processes

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