General Deformation Research Articles

Exact solutions of the nonlocal Gerdjikov-Ivanov equation

The nonlocal nonlinear Gerdjikov-Ivanov (GI) equation is one of the most important integrable equations, which can be reduced from the third generic deformation of the derivative nonlinear Schrödinger equation. The Darboux transformation is a successful method in solving many nonlocal equations with the help of symbolic computation. As applications, we obtain the bright-dark soliton, breather, rogue wave, kink, W-shaped soliton and periodic solutions of the nonlocal GI equation by constructing its 2n-fold Darboux transformation. These solutions show rich wave structures for selections of different parameters. In all these instances we practically show that these solutions have different properties than the ones for local case.

Mechanically induced electric and magnetic fields in the bending and symmetric-shear deformations of a microstructure-dependent FG-MEE composite beam

A new FG-MEE composite microbeam model is developed using a general higher-order deformation theory (GHDT) to account for the symmetric thickness-shear and thickness-stretch deformations of a beam and a modified couple stress theory (MCST) to describe the microstructure-dependent size effect. Based on the basic assumption of field variables and Hamilton’s principle, the one-dimensional second-order coupled equations of motion and complete boundary conditions are obtained simultaneously. The present coupled equations include the microstructure dependence and higher-order extensions, which can reduce to the size-dependent Bernoulli-Euler, Timoshenko and Mindlin-Medick theories. Static problems of a simply supported beam loaded by uniform loading and a concentrated second-order moment are analytically solved by directly applying the newly developed equations. For the bending case, the numerical results show that the magnitudes of displacement, electric, magnetic, stress, electric displacement and magnetic flux fields are smaller than those predicted by classical theory. In addition, it is found that FG parameter can be used to control the electric and magnetic fields. For the concentrated second-order moment case, a new phenomenon of local electric and magnetic fields are demonstrated in the present FG-MEE composite microbeam structure. These results are useful for theoretically/numerically estimating or designing the MEMS of FG-MEE composites.

Testing the equivalence principle on cosmological scales using the odd multipoles of galaxy cross-power spectrum and bispectrum

One of the cornerstones of general relativity is the equivalence principle. However, the validity of the equivalence principle has only been established on solar system scales for standard matter fields; this result cannot be assumed to hold for the non-standard matter fields that dominate the gravitational dynamics on cosmological scales. Here we show how the equivalence principle may be tested on cosmological scales for non-standard matter fields using the odd multipoles of the galaxy cross-power spectrum and bispectrum. This test makes use of the imprint on the galaxy cross-power spectrum and bispectrum by the parity-violating general relativistic deformations of the past-light cone, and assumes that galaxies can be treated as test particles that are made of baryons and cold dark matter. This assumption leads to a non-zero galaxy-baryon relative velocity if the equivalence principle does not hold between baryons and dark matter. We show that the relative velocity can be constrained to be less than 28% of the galaxy velocity using the cross-power spectrum of the HI intensity mapping/Hα galaxy survey and the bispectrum of the Hα galaxy survey.

Non-contact measurements of composite aircraft wing prototype under load

AnnotationMeasurements of general deformation of the wing box prototype of a medium-range passenger aircraft under load were carried out using non-contact videogrammetry (monogrammetry) method. The wing box was 9.8 m long and was made of polymer composite material. The tests were carried out on a special stand, where the variable loading of aircraft wing was simulated at ground and flight modes of a typical flight. The loading was carried out according to the program of tests up to destruction. As a result, the fields of distributed deflection strain were obtained for each loading step. It was shown that the maximum deflection in the end section immediately before failure reached 290 mm. The error in measuring the normal deviations of surface points did not exceed 0.8 mm.

Characters of irrelevant deformations

We analyse the Toverline{T} deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the 1/c contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve Toverline{T} , Joverline{T} and Toverline{J} simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

Geodetic monitoring of deformations of engineering structures

Unfortunately, all kinds of anthropogenic and natural factors contribute to the deformation of man-made structures. Geodetic control of buildings and structures, timely detection and elimination of deformations is a guarantee of long-term operation of the building. Monitoring is one of the most important tools to ensure the reliability and safety of multi-storey and large-scale buildings and structures during construction and operation. A significant amount of instrumental control during construction and operation is carried out by geodetic methods. Geodetic methods are used to determine both local and general deformations of buildings and structures, deviations of load-bearing, fencing structures from vertical and design drawings, foundations and soil settlements, through which the technical condition of the building or structure is specially assessed. Today, the analysis of deformations is an important task for every region of our country, especially for areas with changes in the earth's surface. The field of deformation research in the Republic of Kazakhstan is quite developed and there are many necessary materials to identify such changes. In our country, special services are organized to control any benchmarks and analyze the results of high-precision measurements in several cycles to detect any changes on the earth's surface. Therefore, this article provides an overview of both the classical methods of geodetic control and the tools and technologies used to determine the quantitative characteristics of the deformation of engineering objects.

A comment on instantons and their fermion zero modes in adjoint QCD_2

The adjoint 2-dimensional QCD with the gauge group SU(N)/Z_NSU(N)/ZN admits topologically nontrivial gauge field configurations associated with nontrivial \pi_1[SU(N)/Z_N] = Z_Nπ1[SU(N)/ZN]=ZN. The topological sectors are labelled by an integer k=0,\ldots, N-1k=0,…,N−1. However, in contrast to QED_2QED2 and QCD_4QCD4, this topology is not associated with an integral invariant like the magnetic flux or Pontryagin index. These instantons may admit fermion zero modes, but there is always an equal number of left-handed and right-handed modes, so that the Atiyah-Singer theorem, which determines in other cases the number of the modes, does not apply. The mod. 2 argument [1] suggests that, for a generic gauge field configuration, there is either a single doublet of such zero modes or no modes whatsoever. However, the known solution of the Dirac problem for a wide class of gauge field configurations indicates the presence of k(N-k) zero mode doublets in the topological sector k. In this note, we demonstrate in an explicit way that these modes are not robust under a generic enough deformation of the gauge background and confirm thereby the conjecture of Ref. [1]. The implications for the physics of this theory (screening vs. confinement issue) are briefly discussed.

A nonlocal operator method for finite deformation higher-order gradient elasticity

We present a general finite deformation higher-order gradient elasticity theory. The governing equations of the higher-order gradient solid along with boundary conditions of various orders are derived from a variational principle using integration by parts on the surface. The objectivity of the energy functional is achieved by carefully selecting the invariants under rigid-body transformation. The third-order gradient solid theory includes more than 10.000 material parameters. However, under certain simplifications, the material parameters can be greatly reduced; down to 3. With this simplified formulation, we develop a nonlocal operator method and apply it to several numerical examples. The numerical analysis shows that the high gradient solid theory exhibits a stiffer response compared to a ’conventional’ hyperelastic solid. The numerical tests also demonstrate the capability of the nonlocal operator method in solving higher-order physical problems.

Microstructure and properties of Cu-Ag alloy prepared by continuously directional solidification

A Φ40 μm Cu-4 wt%Ag alloy wire with high strength and high electrical conductivity was prepared by continuously directional solidification and cold drawing. The evolution of microstructure and properties was investigated by means of optical microscope observation, electron microscopes observation, hardness test, tensile test, and electrical conductivity measurement. The continuous columnar-grain structure uniformly distributed along the solidification direction in the as-cast alloy. The drawing process was divided into three stages: general deformation stage, large deformation stage and extreme deformation stage. The main deformation mechanisms of the alloy in each stage are corresponding to the dislocation slip and twinning, the dynamic recovery, the evolution of layered interface, and partial dynamic recrystallization. After the deformation with the drawing strain of 11.28, the tensile strength, yield strength, and electrical conductivity of the alloys were 1048 MPa, 886 MPa, and 75.2%IACS, respectively. The main strengthening mechanism of the alloys was grain refinement strengthening according to the calculation results of the strengthening model.

Geometric approach to inhomogeneous Floquet systems

We present a new geometric approach to Floquet many-body systems described by inhomogeneous conformal field theory in 1+1 dimensions. It is based on an exact correspondence with dynamical systems on the circle that we establish and use to prove existence of (non)heating phases characterized by the (absence) presence of fixed or higher-periodic points of coordinate transformations encoding the time evolution: Heating corresponds to energy and excitations concentrating exponentially fast at unstable such points while nonheating to pseudoperiodic motion. We show that the heating rate (serving as the order parameter for transitions between these two) can have cusps, even within the overall heating phase, and that there is a rich structure of phase diagrams with different heating phases distinguishable through kinks in the entanglement entropy, reminiscent of Lifshitz phase transitions. Our geometric approach generalizes previous results for a subfamily of similar systems that used only the $\mathfrak{sl}(2)$ algebra to general smooth deformations that require the full infinite-dimensional Virasoro algebra, and we argue that it has wider applicability, even beyond conformal field theory.

Directional amorphization of covalently-bonded solids: A generalized deformation mechanism in extreme loading

Shock compression subjects materials to a unique regime of high quasi-hydrostatic pressure and coupled shear stresses for durations on the order of 1–10 nanoseconds for laser-driven loading of samples. There is, additionally, an attendant temperature increase due to the shock and the mechanisms of plastic deformation in metals whereby dislocations, twins, and phase transitions nucleate and propagate at velocities near the sound speed. Covalently bonded materials have, by virtue of the directionality of their bonds, great difficulty in responding by conventional plastic deformation to this extreme regime of shock compression. We propose that the shear from shock compression induces amorphization, as observed in Si, Ge, B4C, SiC, and olivine ((Mg, Fe)2SO4) and that this is a general deformation mechanism in a broad class of covalently bonded materials. The crystalline structure transforms to amorphous along regions of maximum shear stress, forming nanoscale bands, and thereby relaxing the shear component of the imposed shock stress. This process is usually preceded by the emission and propagation of a critical concentration of dislocations.

Biaxial ratcheting analysis based on real behaviors of subsequent yield surface

To develop a plastic constitutive equation for general plastic deformation analysis, it is useful to confirm that the constitutive equation is viable for analyzing mechanical ratcheting in which a small strain accumulates along with cyclic loading. Many constitutive models and analyses on mechanical ratcheting have been proposed. However, most models do not consider distortion and rotation of the subsequent yield surface observed in the process of ratcheting deformations. In this study, behaviors of both the subsequent yield surface and the ratcheting deformations have been experimentally evaluated for the initially isotropic metals of SUS316FR stainless steel, 6-4 brass and S25C mild steel, which were subjected to biaxial mechanical ratcheting. Simulation analysis of biaxial ratcheting was conducted based on real behaviors of the subsequent yield surfaces such as swing rotation, translation, and distortion observed in ratcheting, and the two-surface hardening rule. The reliability of the proposed plastic constitutive model was verified by comparing the numerical results with the corresponding experimental results.

Exact summation of leading logs around Toverline{T} deformation of O(N + 1)-symmetric 2D QFTs

We consider a general (beyond Toverline{T} ) deformation of the 2D O(N + 1) σ-model by the irrelevant dimension-four operators. The theory deformed in this most general way is not integrable, and the S-matrix loses its factorization properties. We perform the all-order summation of the leading infrared logs for the 2 → 2 scattering amplitude and provide the exact result for the 2 → 2 S-matrix in the leading logarithmic approximation. These results can provide us with new insights into the properties of the theories deformed by irrelevant operators more general than the Toverline{T} deformation.

The Bystrinskii Earthquake in the Southern Baikal Region (Sep. 21, 2020, M w = 5.4): General Characteristics, Basic Parameters, and Deformation Signs of the Transition of the Focus to the Meta-Unstable State

The Bystrinskii Earthquake in the Southern Baikal Region (Sep. 21, 2020, M w = 5.4): General Characteristics, Basic Parameters, and Deformation Signs of the Transition of the Focus to the Meta-Unstable State

Modeling of Personalized Anatomy Using Plastic Strains

We present a method for modeling solid objects undergoing large spatially varying and/or anisotropic strains, and use it to reconstruct human anatomy from medical images. Our novel shape deformation method uses plastic strains and the finite element method to successfully model shapes undergoing large and/or anisotropic strains, specified by sparse point constraints on the boundary of the object. We extensively compare our method to standard second-order shape deformation methods, variational methods, and surface-based methods, and demonstrate that our method avoids the spikiness, wiggliness, and other artifacts of previous methods. We demonstrate how to perform such shape deformation both for attached and un-attached (“free flying”) objects, using a novel method to solve linear systems with singular matrices with a known nullspace. Although our method is applicable to general large-strain shape deformation modeling, we use it to create personalized 3D triangle and volumetric meshes of human organs, based on magnetic resonance imaging or computed tomography scans. Given a medically accurate anatomy template of a generic individual, we optimize the geometry of the organ to match the magnetic resonance imaging or computed tomography scan of a specific individual. Our examples include human hand muscles, a liver, a hip bone, and a gluteus medius muscle (“hip abductor”).

Poisson–Hopf deformations of Lie–Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra

The formalism for Poisson–Hopf (PH) deformations of Lie–Hamilton (LH) systems, recently proposed in Ballesteros Á et al (2018 J. Phys. A: Math. Theor. 51 065202), is refined in one of its crucial points concerning applications, namely the obtention of effective and computationally feasible PH deformed superposition rules for prolonged PH deformations of LH systems. The two new notions here proposed are a generalization of the standard superposition rules and the concept of diagonal prolongations for Lie systems, which are consistently recovered under the non-deformed limit. Using a technique from superintegrability theory, we obtain a maximal number of functionally independent constants of the motion for a generic prolonged PH deformation of a LH system, from which a simplified deformed superposition rule can be derived. As an application, explicit deformed superposition rules for prolonged PH deformations of LH systems based on the oscillator Lie algebra are computed. Moreover, by making use that the main structural properties of the book subalgebra of are preserved under the PH deformation, we consider prolonged PH deformations based on as restrictions of those for -LH systems, thus allowing the study of prolonged PH deformations of the complex Bernoulli equations, for which both the constants of the motion and the deformed superposition rules are explicitly presented.

Strain rate dependency of dislocation plasticity

Dislocation glide is a general deformation mode, governing the strength of metals. Via discrete dislocation dynamics and molecular dynamics simulations, we investigate the strain rate and dislocation density dependence of the strength of bulk copper and aluminum single crystals. An analytical relationship between material strength, dislocation density, strain rate and dislocation mobility is proposed, which agrees well with current simulations and published experiments. Results show that material strength displays a decreasing regime (strain rate hardening) and then increasing regime (classical forest hardening) as the dislocation density increases. Accordingly, the strength displays universally, as the strain rate increases, a strain rate-independent regime followed by a strain rate hardening regime. All results are captured by a single scaling function, which relates the scaled strength to a coupling parameter between dislocation density and strain rate. Such coupling parameter also controls the localization of plasticity, fluctuations of dislocation flow and distribution of dislocation velocity.

Coordinated grain boundary deformation governed nanograin annihilation in shear cycling

Grain growth and shrinkage are essential to the thermal and mechanical stability of nanocrystalline metals, which are assumed to be governed by the coordinated deformation between neighboring grain boundaries (GBs) in the nanosized grains. However, the dynamics of such coordination has rarely been reported, especially in experiments. In this work, we systematically investigate the atomistic mechanism of coordinated GB deformation during grain shrinkage in an Au nanocrystal film through combined state-of-the-art in situ shear testing and atomistic simulations. We demonstrate that an embedded nanograin experiences shrinkage and eventually annihilation during a typical shear loading cycle. The continuous grain shrinkage is accommodated by the coordinated evolution of the surrounding GB network via dislocation-mediated migration, while the final grain annihilation proceeds through the sequential dislocation-annihilation-induced grain rotation and merging of opposite GBs. Both experiments and simulations show that stress distribution and GB structure play important roles in the coordinated deformation of different GBs and control the grain shrinkage/annihilation under shear loading. Our findings establish a mechanistic relation between coordinated GB deformation and grain shrinkage, which reveals a general deformation phenomenon in nanocrystalline metals and enriches our understanding on the atomistic origin of structural stability in nanocrystalline metals under mechanical loading.

Free Vibration of Functionally Graded Carbon Nanotube-reinforced Doubly-curved Shells

Background:: Carbon nanotubes (CNTs) reinforced structures are the main elements of structural equipment. Hence a wide range of investigations has been performed on the response of these structures. A lot of studies covered the static and dynamic phenomenon of CNTs reinforced beams, plates and shells. However, there is no study on the free vibration analysis of a doubly-curved nano-size shell made of CNTs reinforced composite materials. Methods:: This work utilized a general third-order shear deformation theory to model the nanoshell where the general strain gradient theory is used in order to capture both nonlocality and strain gradient size-dependency. The Navier solution solving procedure is adopted to solve the partial differential equations (PDEs) and get the natural frequency of the system which is obtained through the Hamilton principle. Results:: The current study shows the importance of small-scale coefficients. The natural frequency increases with rising the strain gradient-size dependency which is because of stiffness enhancement, while the natural frequency decreases by increasing the nonlocality. In addition, the numerical examples covered the CNTs distribution patterns. Conclusion:: This work also studied the importance of shell panel’s shape. It has been observed that spherical shell panel has a higher frequency compared to the hyperbolic one. Furthermore, the frequency of the system increases with growing length-to-thickness ration.

A unified thermal vibration and transient analysis for quasi-3D shear deformation composite laminated beams with general boundary conditions

A unified procedure is proposed in this study to analyze the free and transient vibration behaviors of a composite laminated beam subjected to general boundary conditions under thermal scenario. A general theoretical quasi-3D shear deformation beam model incorporating both the shear deformation and thickness stretching effects is derived using the Hamilton's principle. The coupling of axial–shear–flexural–stretching with the thermal stress and the Poisson's ratio effect is taken into account. The natural frequencies, mode shapes and transient responses of composite laminated beams are evaluated analytically by the method of reverberation ray matrix (MRRM). The inhomogeneous term and the artificial spring boundary technique are introduced in MRRM to acclimatize itself to the general boundary conditions and the impulse loads of arbitrary distributions. The validity, reliability and efficiency of the proposed analytical solutions are verified by comparing with the results obtained from the published studies and finite element simulation. A considerable number of parametrical studies for the composite laminated beams with different elastic restraint parameters, lamination schemes, geometry parameters, material properties as well as various temperature rises are also analyzed and discussed. The present procedure is powerful in terms of its applicability for different high-order shape functions including polynomial and non-polynomial, as well as thin and thick beams subjected to arbitrary boundary conditions in practical engineering.