Abstract

The purpose of this paper is to present a proposal for the design of steel structures sensitive to buckling to fill the gaps in the current Standard EN 1993-1-1, providing guidelines to obtain the magnitude of the imperfection generalizing the procedure given in clause 5.3.2(11) of EN 1993-1-1 for steel structures sensitive to flexural buckling under compression. According to the standard there are still uncertainties about how to obtain the imperfection when the structures are sensitive to torsional or flexural-torsional buckling due to either compression or bending. In this paper a general procedure to obtain the imperfection is provided and it can be proved that the recommendation given in EN 1993-1-1 is a particular case.

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Abstract

A general methodology to develop hyper-elastic membrane models applicable to crystalline films one-atom thick is presented. In this method, an extension of the Born rule based on the exponential map is proposed. The exponential map accounts for the fact that the lattice vectors of the crystal lie along the chords of the curved membrane, and consequently a tangent map like the standard Born rule is inadequate. In order to obtain practical methods, the exponential map is locally approximated. The effectiveness of our approach is demonstrated by numerical studies of carbon nanotubes. Deformed configurations as well as equilibrium energies of atomistic simulations are compared with those provided by the continuum membrane resulting from this method discretized by finite elements.

Abstract

We propose to model thick multiwalled carbon nanotubes as beams with non-convex curvature energy. Such models develop stressed phase mixtures composed of smoothly bent sections and rippled sections. This model is motivated by experimental observations and large-scale atomistic-based simulations. The model is analyzed, validated against large-scale simulations, and exercised in examples of interest. It is shown that modelling MWCNTs as linear elastic beams can result in poor approximations that overestimate the elastic restoring force considerably, particularly for thick tubes. In contrast, the proposed model produces very accurate predictions both of the restoring force and of the phase pattern. The size effect in the bending response of MWCNTs is also discussed.

Abstract

We present a three-dimensional continuum model for layered crystalline materials made out of weakly interacting two-dimensional crystalline sheets. We specialize the model to multilayer graphene materials, including multi-walled carbon nanotubes (MWCNTs). We view the material as a foliation, partitioning of space into a continuous stack of leaves, thus loosing track of the location of the individual graphene layers. The constitutive model for the bulk is derived from the atomistic interactions by appropriate kinematic assumptions, adapted to the foliation structure and mechanics. In particular, the elastic energy along the leaves of the foliation results from the bonded interactions, while the interaction energy between the walls, resulting from van der Waals forces, is parametrized with a stretch transversal to the foliation. The resulting theory is distinct from conventional anisotropic models, and can be readily discretized with finite elements. The discretization is not tied to the individual walls and allows us to coarse-grain the system in all directions. Furthermore, the evaluation of the non-bonded interactions becomes local. We test the accuracy of the foliation model against a previously proposed atomistic-based continuum model that explicitly describes each and every wall. We find that the new model is very efficient and accurate. Furthermore, it allows us to rationalize the rippling deformation modes characteristic of thick MWCNTs, highlighting the role of the van der Waals forces and the sliding between the walls. By exercising the model with very large systems of hollow MWCNTs and suspended multilayer graphene, containing up to 109 atoms, we find new complex post-buckling deformation patterns.

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Abstract

The use of an anti-buckling device is proposed to avoid the appearance of undesired instabilities during biaxial testing with cruciform specimens in which the compressive loads are applied directly on the arms of the sample by means of compression plates. The device consists on a cross-shaped accessory that restricts out-of-plane displacements and a L-shaped support that forces the alignment of the fixture, the specimen and the testing machine. In addition, recommendations about the test methodology and the conditioning of the cruciform sample are given. For this purpose, analytical and numerical studies are developed to design the experiments and to describe both the global buckling of the cruciform specimen and the local instability of the central region subjected to biaxial loading. The risk of instability in the arms of the sample is reduced under tension-compression and compression-compression loading cases whenever the device is used, ensuring that the results are not affected by premature buckling of the specimen and favoring the appearance of appropriate failure modes.

Abstract