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 - Royal Society. Mathematical, Physical and engineering sciences/Philosophical transactions - Royal Society. 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'.
We present a new algorithm for near-interactive simulation of skeleton driven, high resolution elasticity models. Our methodology is used for soft tissue deformation in character animation. The ...algorithm is based on a novel discretization of corotational elasticity over a hexahedral lattice. Within this framework we enforce positive definiteness of the stiffness matrix to allow efficient quasistatics and dynamics. In addition, we present a multigrid method that converges with very high efficiency. Our design targets performance through parallelism using a fully vectorized and branch-free SVD algorithm as well as a stable one-point quadrature scheme. Since body collisions, self collisions and soft-constraints are necessary for real-world examples, we present a simple framework for enforcing them. The whole approach is demonstrated in an end-to-end production-level character skinning system.
The article is devoted to the study behavior of car structural elements during operation and in extreme conditions that occur during road traffic accidents (RTA).
At present, a promising direction of ...research in this area is the development methods based on the analysis of structural elements of a damaged car deformed as a result an accident and the restoration of the energy exchange pattern upon impact.
Research carried out both theoretically and experimentally. Theoretical studies based on the methods of theoretical and applied mechanics, strength of materials and elasticity theory.
The goal is to improve the methodology for conducting an autotechnical examination of an accident.
Method or methodology of work: solving inverse problems of continuum mechanics.
Results: a technique developed for determining the initial speed of a car before an accident based on the results measuring deformed structural elements. The accuracy determining the initial speed of the car is proportional to the accuracy measuring the deformations damaged car.
Scope results: it is advisable to apply the obtained results when conducting an autotechnical examination of an accident.
The article is devoted to the improvement of the methodology for the examination of the operation the vehicles in extreme conditions that occur during road traffic accidents (RTA). Of great interest ...in the field of road safety are the tasks of determining the causes of RTA and the conditions under which they occur. There are computer systems that allow modeling the processes of interaction automobile vehicles with obstacles and among themselves during an accident. These developments based on various mathematical models of the car collision process. The most reliable and promising are systems that based on methods for analyzing plastic deformations and destruction of car structural elements during an accident. The basis of these methods is the law of conservation energy or the model of the transition of the kinetic energy of a moving vehicle into the potential energy of a structure deformed after an accident. This process described with the help of the parameter – the energy equivalent of the speed. The analysis of the object is study – automobile body structures carried out. They classified as thin-walled shell structures that are easily plastically deformed. The available methods for solving the problems of analysis the elastic-plastic deformations in such structures do not allow providing the high accuracy of the solution necessary for the examination of the RTA.
Purpose – improvement of the methodology for conducting an autotechnical examination of an accident.
Methodology: solution of inverse problems of continuum mechanics.
Results: a variant of the finite element representation of the design and a method of the variational approach to determining the energy criteria of the process under study were developed. It provides the greatest accuracy in solving the tasks.
Practical implications: it is expedient to apply the obtained results when carrying out an autotechnical examination of an accident.
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