Deformation and Failure Onset of Random Elastic Beam Networks Generated From the Same Type of Random Graph

Mühlich, Uwe

doi:10.1007/978-3-030-50464-9_22

Cited by 3 publications

(3 citation statements)

References 32 publications

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“…Though, their significance for the understanding of the behavior of real foams is currently limited: Direct numerical simulation (DNS), i.e., simulations with discretely resolved mesostructure, have mostly been performed for periodic structures [1, 9, 11-15, 29, 32, 33, 45, 47]. The few studies on (more or less) irregular mesostructures [22,26,42] are limited to plane models (and so are very most of the aforementioned DNS). And even for a stochastically generated 3d model like in [30], the question on the transferability to real foams arises.…”

Section: Introductionmentioning

confidence: 99%

On the question of the sign of size effects in the elastic behavior of foams

Kirchhof¹,

Ams²,

Hütter³

2023

Preprint

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Due to their good ratio of stiffness and strength to weight, foam materials find use in lightweight engineering. Though, in many applications like structural bending or tension, the scale separation between macroscopic structure and the foam's mesostructure like cells size, is relatively weak and the mechanical properties of the foam appear to be size dependent. Positive as well as negative size effects have been observed for certain basic tests of foams, i.e., the material appears either to be more compliant or stiffer than would be expected from larger specimens. Performing tests with sufficiently small specimens is challenging as any disturbances from damage of cell walls during sample preparation or from loading devices must be avoided. Correspondingly, the number of respective data in literature is relatively low and the results are partly contradictory.In order to avoid the problems from sample preparation or bearings, the present study employs virtual tests with CT data of real medium-density ceramic foams. A number of samples of different size is "cut" from the resulting voxel data. Subsequently, the apparent elastic properties of each virtual sample are "measured" directly by a free vibrational analysis using finite cell method, thereby avoiding any disturbances from load application or bearings. The results exhibit a large scatter of the apparent moduli per sample size, but with a clear negative size effect in all investigated basic modes of deformation (bending, torsion, uniaxial). Finally, the results are compared qualitatively and quantitatively to available experimental data from literature, yielding common trends as well as open questions.

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Section: Introductionmentioning

confidence: 99%

On the question of the sign of size effects in the elastic behavior of foams

Kirchhof¹,

Ams²,

Hütter³

2023

Preprint

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“…It is well-known that the effective elastic moduli and the effective strength depend on mesoscopic topological properties of foams like connectivity of struts (bending/tension dominated) [5,32,40], distribution of material between struts and nodes [12,22,33,34] as well as stochastic properties [22,23,25,28,29,35].…”

Section: Introductionmentioning

confidence: 99%

“…Alternatively, direct numerical simulations (DNS) with discretely resolved mesostructures of foams have been performed, firstly in order to investigate the reasons and mechanisms of size effects and, secondly, as benchmark for generalized continuum theories. Most DNS employed beam lattices [8,14,25,28,35,40,41], but also continuum models have been used [2,18,21,23,30,38]. The quantitative comparison of DNS of tension tests and shearing tests in [18,20] exhibited differences, even in normalized data for hexagonal structures between beam models and continuum models.…”

Section: Introductionmentioning

confidence: 99%

Influence of Topology and Porosity on Size Effects in Stripes of Cellular Material with Honeycomb Structure under Shear, Tension and Bending

Pham,

Hütter

2020

Preprint

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Cellular solids are known to exhibit size effects, i. e. differences in the apparent effective elastic moduli, when the specimen size becomes comparable to the cell size. The present contribution employs direct numerical simulations (DNS) of the mesostructure to investigate the influences of porosity, shape of pores, and thus material distribution along the struts, and orientation of loading on the size effects and effective moduli of regular hexagonal foams. Beam models are compared to continuum models for simple shear, uniaxial loading and pure bending. It is found that the hexagonal structure exhibits a considerable anisotropy of the size effects and that hexagonal structures with circular pores exhibit considerably stronger size effects than those with hexagonal pores (and thus straight struts). Furthermore, the negative size effects under bending and uniaxial loading are interpreted in terms of the stress-gradient theory.

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On the Question of the Sign of Size Effects in the Elastic Behavior of Foams

Kirchhof,

Ams,

Hütter

2023

J Elast

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Due to their good ratio of stiffness and strength to weight, foam materials find use in lightweight engineering. Though, in many applications like structural bending or tension, the scale separation between macroscopic structure and the foam’s mesostructure like cells size, is relatively weak and the mechanical properties of the foam appear to be size dependent. Positive as well as negative size effects have been observed for certain basic tests of foams, i.e., the material appears either to be more compliant or stiffer than would be expected from larger specimens. Performing tests with sufficiently small specimens is challenging as any disturbances from damage of cell walls during sample preparation or from loading devices must be avoided. Correspondingly, the number of respective data in literature is relatively low and the results are partly contradictory.In order to avoid the problems from sample preparation or bearings, the present study employs virtual tests with CT data of real medium-density ceramic foams. A number of samples of different size is “cut” from the resulting voxel data. Subsequently, the apparent elastic properties of each virtual sample are “measured” directly by a free vibrational analysis using finite cell method, thereby avoiding any disturbances from load application or bearings. The results exhibit a large scatter of the apparent moduli per sample size, but with a clear negative size effect in all investigated basic modes of deformation (bending, torsion, uniaxial). Finally, the results are compared qualitatively and quantitatively to available experimental data from literature, yielding common trends as well as open questions.

show abstract

Deformation and Failure Onset of Random Elastic Beam Networks Generated From the Same Type of Random Graph

Cited by 3 publications

References 32 publications

On the question of the sign of size effects in the elastic behavior of foams

On the question of the sign of size effects in the elastic behavior of foams

Influence of Topology and Porosity on Size Effects in Stripes of Cellular Material with Honeycomb Structure under Shear, Tension and Bending

On the Question of the Sign of Size Effects in the Elastic Behavior of Foams

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