The elastic deformations in the conical nanowires are considered. An analytical expression was obtained for the distribution of elastic deformations along the length of the conical nanowire. It was ...found that at certain cone angles in nanowire there is an extended area of sufficiently high deformations comparable or even large than the deformation at the base of the nanowire. So, for example, when bending the conical (conical coefficient
a
= –0.7) nanowire with length
L
= 1 μm and radius
R
= 50 nm by Δ
z
= 200 nm, the maximum deformation values are ε
xx
, max
= 8%, while more than 95% of the nanowire is deformed by >3%.
Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases ...gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on ‘bar-and-hinge’ models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.
•Problems involved in determining geometrical deviations of crankshafts with limited detection possibilities due to the use of a set of rigid supports have been investigated.•An algorithm for ...supporting crankshaft measurements that allowed the accurate assessment of the geometric state under such conditions was proposed.•Practical application of proposed algorithm was presented.
This article is a continuation of previous research in which we analysed the effect of deflections and elastic deformations caused by unsupervised support conditions on the measurements of geometrical deviations of large crankshafts. Supporting the shaft using a set of rigid supports at the same height limited the ability to detect deviations in the pin axis position and pin profile. Formula for supporting crankshaft measurements was proposed using the results and metrology fundamentals, which allowed the accurate assessment of the geometric state under such conditions. The results provide solutions for measuring large crankshafts while eliminating the imperfections of current shaft measurement techniques. In result a high correlation (correlation coefficent at level 0.9935) with datum-based method was obtained. Therefore it was stated than proposed formula largely eliminates the disadvantages of shaft measurements using V-blocks with rigid supports.
Using an analytically tractable example, the pseudomorphic inclusion, this article examines the influence of elastic deformations on the form factor of polyhedral nanocrystals. A control parameter, ...the total amplitude of the variation of the complex density phase, is identified and it is shown that for low enough deformations the characteristic asymptotic behaviours as a function of the scattering vector associated with the polyhedral crystal shape are preserved, leading to a strong contrast in the dependence of the form factor on orientation. Using the sections method, it is explained why these results can be generalized to more realistic elastic situations.
Using a simple model, the modification of the contrast in the form factor dependence on q orientation by elastic deformations is studied.
If an elastic body is defined as one that does not dissipate energy into heat, the classes of elastic bodies not only include the Green elastic solid, but also some types of implicit constitutive ...relations recently presented in the literature. In this paper one of such new implicit relations is studied in detail, wherein the energy function depend on the second Piola–Kirchhoff stress tensor and the Green Saint-Venant strain tensor. It is assumed that the function is anisotropic having two directions of anisotropy, thus the case of a transversely isotropic body and an isotropic body are special cases of the above function. Spectral invariants are used and explicit expressions for some second derivatives of the energy function are found. Such second derivatives appear in the implicit constitutive relation.
Consecutive stages of synthesizing epitaxial SiC films on
n
-type Si(111) and
p
-type Si(111) surfaces in a mixture of gaseous carbon monoxide and silane are studied by X-ray diffraction and Raman ...scattering methods. In films grown on an
n
-type Si(111) surface, only weak elastic deformations are observed during synthesis; however, in films grown on
p
-type Si substrates, relatively strong elastic deformations form, which are completely relaxed by the 40th min. It is found that the film structure is sharply changed at the third minute of the growth, which is related to the formation and growth of pores in the SiC layer. The differences of the lattice parameters of SiC films grown on
n
-Si and
p
-Si substrates are determined and confirmed by analyzing the change in the curvatures of the SiC/Si plates.
Likely equilibria of the stochastic Rivlin cube Mihai, L Angela; Woolley, Thomas E; Goriely, Alain
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences,
05/2019, Volume:
377, Issue:
2144
Journal Article
Peer reviewed
Open access
The problem of the Rivlin cube is to determine the stability of all homogeneous equilibria of an isotropic incompressible hyperelastic body under equitriaxial dead loads. Here, we consider the ...stochastic version of this problem where the elastic parameters are random variables following standard probability laws. Uncertainties in these parameters may arise, for example, from inherent data variation between different batches of homogeneous samples, or from different experimental tests. As for the deterministic elastic problem, we consider the following questions: what are the likely equilibria and how does their stability depend on the material constitutive law? In addition, for the stochastic model, the problem is to derive the probability distribution of deformations, given the variability of the parameters. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.
Residual stress may have an important influence on the mechanical response of residually stressed materials. This paper is concerned with the effects of residual stress on the stability of inflated, ...axially extended, residually stressed circular cylindrical tube. To this end, the theory of small incremental deformations superimposed on a large underlying finite deformation is used. Asymmetric and axisymmetric types of bifurcation are considered. It is found that for residual stress parameter γ of the same sign the effect of the residual stress is different depending on the type of bifurcation. For example, for asymmetric bifurcations with mode number m = 1 and with positive γ inclusion of residual stress makes the tube more stable, on the other hand, for axisymmetric bifurcations inclusion of residual stress, corresponding to positive residual stress parameter γ, leads to increase of instabilities. In all cases, residual stress with positive and negative residual stress parameter γ leads to a symmetric character of bifurcation curves.
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