Size effects in two-dimensional Voronoi foams: A comparison between generalized continua and discrete models

Tekoğlu, Cihan; Onck, Patrick

doi:10.1016/j.jmps.2008.06.007

Cited by 125 publications

(53 citation statements)

References 64 publications

(44 reference statements)

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“…Thus, uniaxial compression tests are first conducted on cubic sample with the dimension of 40mm in three mutually perpendicular principal directions (shown in Figure 2) in order to characterize directional properties of this foam, which should be taken into consideration before investigating mechanical behavior. On the other hands, it is well-known that mechanical behavior of metallic foam is strongly sensitive to the ratio of the sample size to the cell size at length scales where the two are of the same order of magnitude (Bastawros et al, 2000;Onck et al, 2001;Andrews et al, 2001;Jeon and Asahina, 2005;Joseph et al, 2005;Rakow and Waas,2005;Tekoğlu and Onck, 2008;Caner and Bazant, 2009;Jeon et al, 2009;Tekoğlu et al, 2011;Su et al, 2014). Most researchers have adopted big size samples in the mechanical tests to avoid the size effect of cellular materials (McCullough et al, 1999;Ruan et al, 2002;Saha et al, 2005;Amsterdam et al, 2008;Lu et al, 2008;Shen et al, 2010;Mangipudi and Onck, 2011;Luong et al, 2013;Jin et al, 2015).…”

Section: Sample Sizesmentioning

confidence: 99%

Impact Response of Aluminium Alloy Foams Under Complex Stress States

Zhou

Wang

et al. 2016

Lat. Am. j. solids struct.

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A series of dynamic tests were conducted on a closed-cell aluminum alloy foams in order to determine experimental failure surface under impact loading conditions. Quasi-static tests have also been performed to investigate failure mechanism under different stress paths. Three typical types of deformation modes can be observed, which corresponds to the different failure mechanism. The failure loci of the foam in principal stress plane are explored from quasistatic to dynamic loading conditions. A significant strength enhancement is identified experimentally. The expansion of the failure locus from the quasi-static to the dynamic test is almost isotropic. A modified failure criterion for the metallic foam is proposed to predict failure locus as a function of strain rate. This rate-dependence failure criterion is capable of giving a good description of the biaxial failure stresses over a wide range of the strain rates.

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Section: Sample Sizesmentioning

confidence: 99%

Impact Response of Aluminium Alloy Foams Under Complex Stress States

Zhou

Wang

et al. 2016

Lat. Am. j. solids struct.

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“…This is interesting because of their physical meaning. For straingradient elasticity, V ∇sph is the gradient of the infinitesimal volume variation δV, meanwhile V ∇dev is the strain divergence [27]. For the stress-gradient elasticity 1 3 V ∇sph represents the gradient of the isostatic pressure p, and V ∇dev is proportional to the volumic forces f. Those vectors have, both for strain and stress gradient elasticity, a clear physical meaning.…”

Section: Synthesismentioning

confidence: 99%

Geometrical Picture of Third-Order Tensors

Auffray

2013

Advanced Structured Materials

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Because of its strong physical meaning, the decomposition of a symmetric second-order tensor into a deviatoric and a spheric part is heavily used in continuum mechanics. When considering higher-order continua, third-order tensors naturally appear in the formulation of the problem. Therefore researchers had proposed numerous extensions of the decomposition to third-order tensors. But, considering the actual literature, the situation seems to be a bit messy: definitions vary according to authors, improper uses of denomination flourish, and, at the end, the understanding of the physics contained in third-order tensors remains fuzzy. The aim of this paper is to clarify the situation. Using few tools from group representation theory, we will provide an unambiguous and explicit answer to that problem.

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“…In the latter study, the intrinsic material length was naturally identified with the cell size. Furthermore, regarding cellular solids, Tekoglu and Onck (2008) compared the analytical results of various gradient type generalized continuum theories with the computational results of discrete models through a range of basic boundary value problems based on Voronoi representations of cellular microstructures. The analysis that was performed, strictly within the elastic regime, assessed the capabilities of generalized continuum theories in capturing size effects in cellular solids and connected the cell size with the microstructural length-scale.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the tilted flat punch in couple-stress elasticity

Gourgiotis

Zisis

Baxevanakis

2016

International Journal of Solids and Structures

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Abstract. In the present paper we explore the response of a half-plane indented by a tilted flat punch with sharp corners in the context of couple-stress elasticity theory. Contact conditions arise in a number of modern engineering applications ranging from structural and geotechnical engineering to micro and nanotechnology. As the contact scales reduce progressively the effects of the microstructure upon the macroscopic material response cannot be ignored. The generalized continuum theory of couple-stress elasticity introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying material microstructure. The problem under investigation is interesting for three reasons: Firstly, the indentor's geometry is simple so that benchmark results may be extracted. Secondly, important deterioration of the macroscopic results may emerge in the case that a tilting moment is applied on the indentor inadvertently or in the case that the flat punch itself is not self-aligning so that asymmetrical contact pressure distributions arise on the contact faces. Thirdly, the voluntary application of a tilting moment on the flat punch during an experiment gives rise to potential capabilities of the flat punch for the determination of the material microstructural characteristic lengths. The solution methodology is based on singular integral equations which have resulted from a treatment of the mixed boundary value problems via integral transforms and generalized functions. The results show significant departure from the predictions of classical elasticity revealing that valuable information may be deducted from the indentation of a tilted punch of a microstructured solid.

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Size effects in two-dimensional Voronoi foams: A comparison between generalized continua and discrete models

Cited by 125 publications

References 64 publications

Impact Response of Aluminium Alloy Foams Under Complex Stress States

Impact Response of Aluminium Alloy Foams Under Complex Stress States

Geometrical Picture of Third-Order Tensors

Analysis of the tilted flat punch in couple-stress elasticity

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