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Modeling of rigid foams
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The morphology and elastic properties of foams are investigated using models accounting for the cellular structure. Different modeling approaches are evaluated and compared to the cellular structures of real foams. The aim is to find an approach that produces realistic models that can be adjusted to match morphology measures taken form real foams. The elastic properties are computed using finite element analysis and the results are compared with both experimental results from mechanical testing and existing analytical models. A generalization of the existing analytical models is suggested for better agreement with the modeling results.

In Paper A Voronoi and equilibrium foam models are generated and investigated. The Voronoi models are found to have a high content of short edges and small faces while conversion into equilibrium foams eliminates such small geometrical features. It is also seen that different seed point distribution algorithms generally result in different model topologies.

In Paper B the relations between the sphere packing fraction and the resulting degree of volumetric polydispersity are studied as well as the relations between polydispersity and a number of morphology parameters. Both Voronoi and equilibrium foams are investigated and compared with data from real foams. Such comparisons indicate that the used method is somewhat limited in terms of polydispersity but provides a controlled way of varying the foam morphology.

In Paper C equilibrium models are used to study the inuence of polydispersity, relative density and distribution of solid on the elastic properties of foams. It is found that the elastic moduli are very weakly coupled to the polydispersity while the inuence from the relative density and distribution of solid is considerably stronger. Existing analytical models from the literature are fitted to the results and generalizations are suggested for better agreement over the investigated range of relative density and distribution of solid.

In Paper D equilibrium foam models with prescribed polydispersity are generated, analyzed and compared to real foams. The polydispersity of real foams is measured in micro-CT images and the results are applied to the models. The elastic properties are computed and the results are compared with experimental results and previous models with significantly lower polydispersity. No clear relation is found between the elastic properties and the polydispersity of equilibrium foams.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. , xiii, 28 p.
Series
TRITA-AVE, ISSN 1651-7660 ; 2015:21
National Category
Other Materials Engineering
Identifiers
URN: urn:nbn:se:kth:diva-166197ISBN: 978-91-7595-562-9 (print)OAI: oai:DiVA.org:kth-166197DiVA: diva2:809668
Public defence
2015-05-22, D3, Lindstedtsvägen 5, KTH, Stockholm, 09:15 (English)
Opponent
Supervisors
Note

QC 20150505

Available from: 2015-05-05 Created: 2015-05-05 Last updated: 2015-05-05Bibliographically approved
List of papers
1. Generation of periodic stochastic foam models for numerical analysis
Open this publication in new window or tab >>Generation of periodic stochastic foam models for numerical analysis
2014 (English)In: Journal of cellular plastics (Print), ISSN 0021-955X, E-ISSN 1530-7999, Vol. 50, no 1, 37-54 p.Article in journal (Refereed) Published
Abstract [en]

Stochastic cellular models of rigid foam based on Voronoi spatial partitioning are generated and investigated for potential use in numerical analysis using finite element methods. Such partitions are deterministic once a distribution of cell nuclei has been defined. A drawback is that the models tend to exhibit a significant share of short edges and small faces. Such small geometrical features are not likely to occur in real foams since they are unfavorable from a surface energy point of view and they also generate problems in numerical analysis due to associated meshing challenges. Through minimization of the surface area, using the computer software Surface Evolver, the Voronoi models are brought to better resemblance with ideal dry foam and the occurrence of small geometrical features is strongly reduced. It is generally seen that different seed point distribution algorithms result in different model topologies. The presented methodology is systematic, parameterized and the results are very promising. Good grounds are provided for modeling of real rigid foam materials, that do not necessarily fully resemble ideal dry foam.

Place, publisher, year, edition, pages
Sage: , 2014
Keyword
cellular, micro structure, simulation, structural foams
National Category
Aerospace Engineering Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-136575 (URN)10.1177/0021955X13503848 (DOI)000328696900002 ()2-s2.0-84890938110 (Scopus ID)
Funder
Swedish Research Council, 50576001
Note

QC 20140124. Updated from accepted to published.

Available from: 2013-12-06 Created: 2013-12-06 Last updated: 2017-12-06Bibliographically approved
2. Influence of sphere packing fraction on polydispersity an morphology of Voronoi and equilibrium foams
Open this publication in new window or tab >>Influence of sphere packing fraction on polydispersity an morphology of Voronoi and equilibrium foams
(English)Manuscript (preprint) (Other academic)
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-166191 (URN)
Note

QS 2015. QS 2016

Available from: 2015-05-05 Created: 2015-05-05 Last updated: 2016-01-29Bibliographically approved
3. Elastic properties of equlibrium foams
Open this publication in new window or tab >>Elastic properties of equlibrium foams
2016 (English)In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 113, 11-18 p.Article in journal (Refereed) Published
Abstract [en]

Stochastic equilibrium finite element (FE) foam models are used to study the influence of relative density and distribution of solid material between cell walls and edges on the elastic properties of foam materials. It is first established that the models contain a sufficient number of cells to ascertain isotropy and numerically and statistically robust results. It is then found that the elastic moduli are very weakly coupled to cell size variation in the models, when the latter is varied systematically. The influence from relative density and distribution of solid on the elastic parameters is considerably stronger. Analytical estimates from the literature, based on idealized cell models and dimension analysis, are matched by fitting coefficients to the FE results, providing good qualitative but relatively poor quantitative correlation. An expansion of the analytical coupling functions is then suggested in order to reduce their level of idealization. The expanded formulation shows virtually perfect agreement with the numerical results for almost the whole range of relative densities and distributions of solid in the FE parameter study. The presented analytical expression is believed to be general and provide accurate estimates of the elastic properties of a wide range of foam materials, provided that their bulk material properties and micro structure can be established. (C) 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2016
Keyword
Stochastic; Cellular materials; Relative density; Distribution of solid
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-166194 (URN)10.1016/j.actamat.2016.01.025 (DOI)000378670300002 ()2-s2.0-84964608777 (Scopus ID)
Note

QC 20161215

Available from: 2015-05-05 Created: 2015-05-05 Last updated: 2017-12-04Bibliographically approved
4. Elastic properties from equilibrium models with statistically representative polydispersity
Open this publication in new window or tab >>Elastic properties from equilibrium models with statistically representative polydispersity
(English)Manuscript (preprint) (Other academic)
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-166193 (URN)
Note

QS 2015. QS 2016

Available from: 2015-05-05 Created: 2015-05-05 Last updated: 2016-01-29Bibliographically approved

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