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Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.


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Journal ArticleDOI
TL;DR: In this paper, a general purpose elastic finite element routine was designed for use on images of random porous composite materials to study the linear elastic properties of these models, and the results of Young's modulus and Poisson's ratio depend on the porosity and morphology of the pore space.
Abstract: Porous materials are formed in nature and by man by many different processes. The nature of the pore space, which is usually the space left over as the solid backbone forms, is often controlled by the morphology of the solid backbone. In particular, sometimes the backbone is made from the random deposition of elongated crystals, which makes analytical techniques particularly difficult to apply. This paper discusses simple two- and three-dimensional porous models in which the solid backbone is formed by different random arrangements of elongated solid objects (bars/crystals). We use a general purpose elastic finite element routine designed for use on images of random porous composite materials to study the linear elastic properties of these models. Both Young's modulus and Poisson's ratio depend on the porosity and the morphology of the pore space, as well as on the properties of the individual solid phases. The models are random digital image models, so that the effects of statistical fluctuation, finite size effect and digital resolution error must be carefully quantified. It is shown how to average the numerical results over random crystal orientation properly. The relations between two and three dimensions are also explored, as most microstructural information comes from two-dimensional images, while most real materials and experiments are three dimensional.

139 citations

Book ChapterDOI
TL;DR: In this article, three main methods have been used to develop one dimensional theories of rods, mostly in the context of isothermal linear elasticity, including ad hoc assumptions which are apparently independent of any general theory.
Abstract: Three main methods have been used to develop one dimensional theories of rods, mostly in the context of isothermal linear elasticity. The first consists of ad hoc assumptions which are apparently independent of any general theory. In the second approach one can start with the three-dimensional equations of elasticity and use an expansion or perturbation procedure, see for example Hay [1]. However, most of the authors who adopt the three-dimensional approach employ additional assumptions or variational methods. The third approach may be called the direct approach. This is the method employed by Green and Laws [2] whose work we discuss here. A further contribution has been given by Cohen [3) who uses a variational method to produce a theory of elastic rods, but his idea of a rod differs from that of Green and Laws.

139 citations

Journal ArticleDOI
TL;DR: In this article, the authors examined the mechanical properties of graphene samples of thicknesses ranging from 1 to 17 atomic layers placed on a microscale-corrugated elastic substrate and showed that the graphene adheres to the substrate surface and can substantially deform the substrate, with larger graphene thicknesses creating greater deformations.
Abstract: We examine the mechanical properties of graphene samples of thicknesses ranging from 1 to 17 atomic layers, placed on a microscale-corrugated elastic substrate. Using atomic force microscopy, we show that the graphene adheres to the substrate surface and can substantially deform the substrate, with larger graphene thicknesses creating greater deformations. We use linear elasticity theory to model the deformations of the composite graphene-substrate system. We compare experiment and theory, and thereby extract information about graphene’s bending rigidity, adhesion, critical stress for interlayer sliding, and sample-dependent tension.

139 citations

Journal ArticleDOI
TL;DR: In this paper, the authors introduce the notion of odd elasticity, a generalization of linear elasticity to active media with non-conservative microscopic interactions that violate mechanical reciprocity.
Abstract: Hooke's law states that the forces or stresses experienced by an elastic object are proportional to the applied deformations or strains. The number of coefficients of proportionality between stress and strain, i.e., the elastic moduli, is constrained by energy conservation. In this Letter, we lift this restriction and generalize linear elasticity to active media with non-conservative microscopic interactions that violate mechanical reciprocity. This generalized framework, which we dub odd elasticity, reveals that two additional moduli can exist in a two-dimensional isotropic solid with active bonds. Such an odd-elastic solid can be regarded as a distributed engine: work is locally extracted, or injected, during quasi-static cycles of deformation. Using continuum equations, coarse-grained microscopic models, and numerical simulations, we uncover phenomena ranging from activity-induced auxetic behavior to wave propagation powered by self-sustained active elastic cycles. Besides providing insights beyond existing hydrodynamic theories of active solids, odd elasticity suggests design principles for emergent autonomous materials.

139 citations

01 Jan 2003
TL;DR: In this article, a 2D triaxial atbraided composite (2DTBC) is modeled as a transversely isotropic linear elastic solid and a representative unit cell (RUC) of the braid-architecture is identified along with its constituent.
Abstract: Thispaperisconcernedwiththedevelopmentofananalyticalmodelforthecalculationoftheeectivelinearelasticstinessofa2Dtriaxialatbraidedcomposite(2DTBC)andtheeectofinitialunintendedmicrostructural imperfections on the calculated stinesses. A representative unit cell (RUC) of the braidarchitectureisrstidentiedalongwithitsconstituents.Towgeometryisrepresentedanalyticallytakingaccount of tow undulation. Each tow is modeled as a transversely isotropic linear elastic solid and thecontributionfromeachtowtotheRUCelasticstinessisobtainedbyvolumeaveraging,takingaccountofthevolumefractionofeachconstituent.Predictionsoftheelasticconstantsarecomparedagainstexperimentaldataandafully3DniteelementcomputationbasedontheRUC.Eectsofthebiastowangle,theangleuncertaintyand,thebiastowundulationmagnitudeontheelasticconstantsareexaminedbyconsideringcomposites with bias tows at 30 ◦ and 60 ◦ . This latter part, thus, examines the eect of microstructuralimperfections on the elastic stiness of 2DTBCs. It also serves as a tool to assess the most signicantparameterthataectscompositestiness.? 2003ElsevierLtd.Allrightsreserved.

138 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202386
2022223
2021318
2020317
2019312
2018335