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As indicated in the review by Cardou & Jolicoeur (1997), and depending on the application, a helically stranded system may be modelled using a semi-continuous approach whereby each layer is replaced by a continuous helical orthotropic material. For those able to read Russian, this approach is presented in a paper by Danilin & Al. specifically oriented towards Overhead Electrical Conductor mechanics: “Modelling of Deformation of Wire Spiral Structures” published in the PNRPU Mechanics Bulletin (2015, No 4, pp.

Antonino Favata's picture

Graphene is softer to bend when stretched and bent and harder to stretch when bent and moderately stretched


In the attached paper, we have shown that concomitant bending and stretching, whatever their value, concur to make bending stiffness decrease; moreover, concomitant bending and stretching make the stretching stiffness (or the Young modulus) increase until the applied forces reach a threshold value, then they make it decrease. Said differently, graphene is softer to bend when stretched and bent and harder to stretch when bent and moderately stretched.


Douglas P Holmes's picture

Rising Beyond Elastocapillarity

Douglas P. Holmes, P.-T. Brun, Anupam Pandey, and Suzie Protière, Soft Matter, 12, 4886-4890, (2016).

Overhead Electrical Conductor in bending: Papailiou's model revisited

 In a paper to appear and available online,( An analytical approach to model the hysteretic bending behavior of spiral strands, Applied Mathematical Modeling 2016, )

Cable bending stiffness: new test data

A new paper by Chen et al.: Experimental research on bending performance of structural cable. In: Construction and Building Materials, 15 October 2015, Vol. 96, pp. 279-288. Equivalent bending stiffness has been obtained applying a force at midspan of simply supported, about one meter long, specimens. A number of tensile force levels have been applied (including zero). Non-linear force-deflection curves are shown.

Overhead Electrical Conductor fatigue testing: a new standard

The International Electrotechnical Commission (IEC) just released a new international standard titled: "Overhead lines - Method for fatigue testing of conductors". IEC 62568. Edition 1.0 2015-07. . It closely follows previous CIGRE and EPRI publications on this topic:

CIGRE SC B2 WG11 TF7 "Fatigue Endurance Capability of Conductor/Clamp Systems - Update of Present Knowledge" CIGRE TB 332, 2007, Paris.

A cable bending stick-slip analytical model

Single strand cable bending, stick-slip, analytical models require that a choice be made between two contact modes between adjacent wires: either radial (between layers) or lateral (between same layer wires). In most recent models (e.g. Papailiou’s) radial contact is selected. A “lateral contact” model has been presented by Panetti in 1944 and can be found in the proceedings of the Turin Royal Academy of Science. A translated version from Italian is proposed in the attached file.

Carl T. Herakovich's picture

New Ebook on Elastic Solids at Amazon

This treatise provides a broad overview of the definitions of
fundamental quantities and methods of analysis for the use of solid materials
in structural components. The presentation is limited to the linear elastic
range of material behavior where there is a one to one relationship between
load and displacement.  Fundamental
methods of analysis and typical results for structures made of elastic solid materials
subjected to axial, bending, torsion, thermal, and internal pressure loading;

Abaqus results

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i try to simulate a 3 points bending of a glass plate with abaqus.

force 1kN !

young modulus = 7e10 Pa

Poisson's ratio = 0.22

- the plate is square (30 cm) , thickness 8.72 mm

- i use 3D extruded solid

- for the load i can't create a line load so i replace this load by pressure in a thin surface (2mm*30cm) applied in the center of the plate

- C3D8R element type

 but the results are strange:

the maximum displacement is 0.672 mm !

is that realistic ? 1kN and just 0.672 mm of central displacement  ?

dabiao liu's picture

Stress gradient plasticity

 Liu, D., He, Y., Zhang, B., 2013. Towards a further understanding of dislocation pileups in the presence of stress gradients.  Doi: 10.1080/14786435.2013.774096

Arash_Yavari's picture

On superelastic bending of shape memory alloy beams

In this paper, a closed-form solution is presented for bending analysis of shape memory alloy (SMA) beams.

Wenbin Yu's picture

Three-ways to derive the Euler-Bernoulli-Saint Venant Beam Theory

After having taught graduate structural mechanics for several years, I am finally
able to write down my lecture notes (attached) for teaching the beam theory. In
the notes, we formulated the complete classical beam model
(extension/torsion/bending in two directions), which is also called
Euler-Bernoulli-Saint beam theory, in three ways: Newtonian method, variational
method, and variational asymptotic method, using 3D elasticity theory as the
starting point. Many self-contradictions of the various assumptions used in both
Newtonian method and variational method are clearly pointed out. The

Bending and wrinkling as competing relaxation pathways for strained free-hanging films

A thin film subject to compressive strain can either bend (for large strain gradient) or wrinkle (for small strain gradient). The bending is traditionally used in thermostats (bimetal stripes), but couple of years ago, it was extended to the nanoscale thin films which can bend and roll-up to tubes with defined number of rotations. The wrinkles are also rather common in macro- and microscale thin films.
Here, we developed an equilibrium phase diagram for the shape of
compressively strained free-hanging films by total strain energy

Bending and 2D Elasticity: Going Back in Time

The following is a (relatively minor) question which had occurred to me more than two decades ago. By now I have forgotten precisely when it was... It could have been when I was in my TE (third year engineering) at COEP. ... Or, perhaps, it was later on, when I as at IIT Madras (studying stress analysis on my own). ... I don't remember precisely when it occurred to me, only *how* it did---it was when I was poring over the first part of Dieter's book.

Nonlinear mechanics of single-atomic-layer graphene sheets

Qiang Lu and Rui Huang

Department of Aerospace Engineering and Engineering mechanics, University of Texas, Austin,
TX 78712, USA

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