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Modeling of deformation processes in rock massif in the vicinity of underground goafs considering the formation of discontinuity zones

Michael Zhuravkov, Shunying Ji, Aleg Kanavalau

Corrected proof , doi: 10.1016/j.taml.2020.01.012

[Abstract] (33) [FullText HTML] (27) [PDF 2775KB] (0)

Abstract:
The construction of mechanical-mathematical model and numerical method for the deformation processes of rock massifs with goafs and underground structures is very complex and also important task in modern rock mechanics. In this study, the mechanical-mathematical model is developed for rock massif in vicinity of underground goafs considering the internal block-layered structure of the rock massif. A new constitutive model is introduced in this study to describe the negative Poisson's ratio for the lock-layered structure. Two types of defining equations systems for studying the state of a rock massif taking into account the block-layered structure are described. Finally, several examples are given using the present mechanical-mathematical model.

Modified virtual internal bond model based on deformable Voronoi particles

Oleg Konovalov, Shunying Ji, Michael Zhuravkov

Corrected proof , doi: 10.1016/j.taml.2020.01.008

[Abstract] (35) [FullText HTML] (22) [PDF 2924KB] (0)

Abstract:
In last time, the series of virtual internal bond model was proposed for solving rock mechanics problems. In these models, the rock continuum is considered as a structure of discrete particles connected by normal and shear springs (bonds). It is well announced that the normal springs structure corresponds to a linear elastic solid with a fixed Poisson ratio, namely, 0.25 for three-dimensional cases. So the shear springs used to represent the diversity of the Poisson ratio. However, the shearing force calculation is not rotationally invariant and it produce difficulties in application of these models for rock mechanics problems with sufficient displacements. In this letter, we proposed the approach to support the diversity of the Poisson ratio that based on usage of deformable Voronoi cells as set of particles. The edges of dual Delaunay tetrahedralization are considered as structure of normal springs (bonds). The movements of particle’s centers lead to deformation of tetrahedrals and as result to deformation of Voronoi cells. For each bond, there are the corresponded dual face of some Voronoi cell. We can consider the normal bond as some beam and in this case, the appropriate face of Voronoi cell will be a cross section of this beam. If during deformation the Voronoi face was expand, then, according Poisson effect, the length of bond should be decrees. The above mechanism was numerically investigated and we shown that it is acceptable for simulation of elastic behavior in 0.1-0.3 interval of Poisson ratio. Unexpected surprise is that proposed approach give possibility to simulate auxetic materials with negative Poisson's ratio in interval from –0.5 to –0.1.

On the mechanism by which nose bluntness suppresses second-mode instability

Armani Batista, Arham Amin Khan, Joseph Kuehl

Corrected proof , doi: 10.1016/j.taml.2020.01.024

[Abstract] (0) [FullText HTML] (0) [PDF 3194KB] (0)

Abstract:
A physical mechanism by which nose bluntness suppresses second-mode instability is proposed. Considered are 7 degree half-angle straight cones with nose bluntness radii of 0.15 mm, 3.556 mm, 5 mm, 9.525 mm, 12.7 mm and 25.4 mm at tunnel conditions relevant to the AFOSR-Notre Dame Large Mach 6 Quiet Tunnel. It is shown that second-mode suppression is achieved via entropy layer modulation of the basic state density gradient. A weakening of the density gradient disrupts the acoustic resonance necessary to sustain second-mode growth. These results are consistent with the thermoacoustic interpretation which posits that second-mode instability can be modeled as thermoacoustic resonance of acoustic energy trapped within an acoustic impedance well. Furthermore, the generalized inflection point criterion of Lees and Lin is applied to develop a criterion for the existence of second-mode instability based on the strength of the basic state density gradient.

A block particle coupled model and its application to landslides

Chun Feng, Shihai Li, Qindong Lin

Corrected proof , doi: 10.1016/j.taml.2020.01.022

[Abstract] (28) [FullText HTML] (23) [PDF 2959KB] (0)

Abstract:
To simulate the progressive failure of slope, a block particle coupled model is introduced. Particle oriented cell mapping (POCM) algorithm is used to enhance the search efficiency, and particle-point, particle-edge, particle-face contact detecting method is adopted to establish contact pair between particles and blocks precisely. Strain softening Mohr Coulomb model with tensile cutoff is adopted for blocks, and brittle Mohr Coulomb model is used for particles. The particle-block replacement approach is used to describe the fracture and fragmentation process of continuum media. Once the cohesion or tensile strength of one block reaches zero, the block will be deleted, and particles are generated at the same place with all information inherited from the deleted block. Some numerical cases related to landslides demonstrate the precision and rationality of the coupled model.

The axisymmetric Rayleigh waves in a semi-infinite elastic solid

Ji Wang, Shaoyun Wang, Longtao Xie, Yangyang Zhang, Lili Yuan, Jianke Du, Han Zhang

Corrected proof , doi: 10.1016/j.taml.2020.01.018

[Abstract] (28) [FullText HTML] (21) [PDF 2812KB] (0)

Abstract:
It is well-known that Rayleigh wave, also known as surface acoustic wave (SAW), solutions in semi-infinite solids are plane waves with signatory properties like the distinct velocity and exponentially decaying deformation in the depth. Applications of Rayleigh waves are focused on the deformation and energy in the vicinity of surface of solids and less loss in the propagation. A generalized model of Rayleigh waves in axisymmetric mode is established and solutions are obtained with cylindrical coordinates. It is found that the Rayleigh waves also propagate in the axisymmetric mode with slow decay in radius, confirming the existence of surface acoustic waves is irrelevant to coordinate system. On the other hand, the solutions can be treated as plane waves in regions far away from the source. Furthermore, the particle trajectory of axisymmetric SAW is a line with constant slope rather than the signatory ellipse in Cartesian coordinate case.

Construction of irregular particles with superquadric equation in DEM

Siqiang Wang, Dzianis Marmysh, Shunying Ji

Corrected proof , doi: 10.1016/j.taml.2020.01.021

[Abstract] (27) [FullText HTML] (18) [PDF 2940KB] (2)

Abstract:
Non-spherical particles are widely present in industrial production, and significantly affect the macro and micro characteristics of granular materials. Although the superquadric equation can be used to construct non-spherical particles, its disadvantage is that the particle shape is geometrically symmetric and strictly convex. In this study, two composed approaches are used to describe geometrically asymmetric and concave particle shapes, including a multi-superquadric model and a poly-superquadric model. The multi-superquadric model is a combination of several superquadric elements, and can construct concave and geometrically asymmetric particle shapes. The poly-superquadric model is a combination of eight one-eighth superquadric elements, and can construct convex and geometrically asymmetric particle shapes. Both composed models are based on superquadric equations, and Newton's iterative method is used to calculate the contact force between the elements. Furthermore, superquadric elements, multi-superquadric elements, and poly-superquadric elements are applied for the formation of complex granular beds, and the influences of particle shape on the packing fraction can be successfully captured by the proposed models.

Particle trajectories under interactions between solitary waves and a linear shear current

Xin Guan

Corrected proof , doi: 10.1016/j.taml.2020.01.011

[Abstract] (33) [FullText HTML] (22) [PDF 2795KB] (1)

Abstract:
This paper is concerned with particle trajectories beneath solitary waves when a linear shear current exists. The fluid is assumed to be incompressible and inviscid, lying on a flat bed. Classical asymptotic expansion is used to obtain a Korteweg-de Vries (KdV) equation, then a forth-order Runge-Kutta method is applied to get the approximate particle trajectories. On the other hand, our particular attention is paid to the direct numerical simulation (DNS) to the original Euler equations. A conformal map is used to solve the nonlinear boundary value problem. High-accuracy numerical solutions are then obtained through the fast Fourier transform (FFT) and compared with the asymptotic solutions, which shows a good agreement when wave amplitude is small. Further, it also yields that there are different types of particle trajectories. Most surprisingly, periodic motion of particles could exist under solitary waves, which is due to the wave-current interaction.

Classifying wakes produced by self-propelled fish-like swimmers using neural networks

Binglin Li, Xiang Zhang, Xing Zhang

Corrected proof , doi: 10.1016/j.taml.2020.01.010

[Abstract] (29) [FullText HTML] (19) [PDF 2704KB] (0)

Abstract:
We consider the classification of wake structures produced by self-propelled fish-like swimmers based on local measurements of flow variables. This problem is inspired by the extraordinary capability of animal swimmers in perceiving their hydrodynamic environments under dark condition. We train different neural networks to classify wake structures by using the streamwise velocity component, the crosswise velocity component, the vorticity and the combination of three flow variables, respectively. It is found that the neural networks trained using the two velocity components perform well in identifying the wake types, whereas the neural network trained using the vorticity suffers from a high rate of misclassification. When the neural network is trained using the combination of all three flow variables, a remarkably high accuracy in wake classification can be achieved. The results of this study can be helpful to the design of flow sensory systems in robotic underwater vehicles.

Physics-constrained indirect supervised learning

Yuntian Chen, Dongxiao Zhang

Corrected proof , doi: 10.1016/j.taml.2020.01.019

[Abstract] (22) [FullText HTML] (18) [PDF 2622KB] (2)

Abstract:
This study proposes a supervised learning method that does not rely on labels. We use variables associated with the label as indirect labels, and construct an indirect physics-constrained loss based on the physical mechanism to train the model. In the training process, the model prediction is mapped to the space of value that conforms to the physical mechanism through the projection matrix, and then the model is trained based on the indirect labels. The final prediction result of the model conforms to the physical mechanism between indirect label and label, and also meets the constraints of the indirect label. The present study also develops projection matrix normalization and prediction covariance analysis to ensure that the model can be fully trained. Finally, the effect of the physics-constrained indirect supervised learning is verified based on a well log generation problem.

Prediction on dispersion in elastoplastic unsaturated granular media

Chenxi Xiu, Xihua Chu, Jiao Wang

Corrected proof , doi: 10.1016/j.taml.2020.01.007

[Abstract] (42) [FullText HTML] (25) [PDF 2638KB] (4)

Abstract:
This study focuses on the propagation of the plane wave in the elastoplastic unsaturated granular media, and the wave equations and dispersion equations are derived for the media under the framework of Cosserat theory. Due to symmetry, five different wave modes are considered and predicted for the elastoplastic unsaturated granular media based on the Cosserat theory, including two longitudinal waves, one rotational longitudinal wave and two coupled transverse - rotational transverse waves. The correspondence is discussed between these Cosserat wave modes and the classical wave modes. Based on the dispersion equations, the dispersion behaviors are obtained for the five Cosserat wave modes. The results indicated that the different stress-strain stages, including the elastic, hardening and softening stages, have obvious effect on the dispersion behaviors of the Cosserat wave modes.

Exact solution of free vibration of adjacent buildings interconnected by visco-elastic dampers

Yong Chen, Zuguang Ying, Guohui Shen

Corrected proof

[Abstract] (29) [FullText HTML] (24) [PDF 2973KB] (2)

Abstract:
With consideration of a high-rise coupled building system, a flexible beams-based analytical model is setup to characterize the dynamic behavior of the system. The general motion equation for the two beams interconnected by multiple viscous/visco-elastic dampers is rewritten into a non-dimensional form to identify the minimal set of parameters governing the dynamic characteristics. The corresponding exact solution suitable for arbitrary boundary conditions is presented. Furthermore, the methodology for computing the coefficients of the modal shape function is proposed. As an example, the explicit expression of the modal shape function is derived, provided only one damper is adopted to connect the adjacent buildings. Finally, to validate the proposed methodologies, three case studies are performed, in which the existence of the overdamping and the optimal damping coefficient are revealed. In the case of using one damper in connecting two similar buildings, the estimating equations for the first modal damping ratio are formulated.

Frame-indifference of cross products, rotations, and the permutation tensor

Maolin Du

Corrected proof , doi: 10.1016/j.taml.2020.01.015

[Abstract] (100) [FullText HTML] (31) [PDF 2484KB] (40)

Abstract:
Under improper transformations, the traditional transformation laws for cross products, the permutation tensor, and rotations are incorrect. For a cross product, using a counter-example the left-hand rule is proved wrong. The unique rule for a cross product is the right-hand rule. Coordinate systems have handedness, while a cross product is frame-indifference. Since the permutation tensor is defined as a triple product including a cross product, the law for the permutation tensor is false. For a rotation, its pseudovector representation is incorrect, because the mirror is an auxiliary device to produce the virtual image rather than a new coordinate system or reference frame.

Simulation of shear layers interaction and unsteady evolution under different double backward-facing steps

Fang Deng, Guilai Han, Zonglin Jiang

Corrected proof , doi: 10.1016/j.taml.2020.01.020

[Abstract] (59) [FullText HTML] (29) [PDF 2693KB] (3)

Abstract:
High-order accurate schemes are employed to numerically simulate the interaction of a supersonic jet and a co-directional supersonic inflow. A double backward-facing step model is proposed to investigate the interaction between the jet shear layer and the supersonic inflow shear layer. It is found that due to the interaction of the shear layer, a secondary jet is injected into the recirculation zone at the intersection of the two shear layers. The secondary jet produced by the interaction of the two shear layers has a periodicity because of shear layers interaction. The distinction in the shape of double backward-facing steps will induce changes in the period of the secondary jet. The analysis and discussion of the periodicity of the secondary jet are mainly focused in this letter.

Application of Multi-dimensional Wavelet Transform to Fluid Mechanics

Akira Rinoshika, Hiroka Rinoshika

Corrected proof , doi: 10.1016/j.taml.2020.01.017

[Abstract] (40) [FullText HTML] (25) [PDF 5562KB] (0)

Abstract:
This paper first reviews the application research works of wavelet transform on the fluid mechanics. Then the theories of continuous wavelet transform and multi-dimensional orthogonal (discrete) wavelet transform, including wavelet multiresolution analysis, are introduced. At last the applications of wavelet transform on 2D and 3D turbulent wakes and turbulent boundary layer flows are described based on the hot-wire, 2D particle image velocimetry (PIV) and 3D tomographic PIV.

Universal scaling law of an origami paper spring

Bo-Hua Sun

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.002

[Abstract] (154) [FullText HTML] (102) [PDF 2469KB] (4)

Abstract:
This letter solves an open question of origami paper spring risen by Yoneda et al.(Phys. Rev. E 2019). By using both dimensional analysis and data fitting, an universal scaling law of a paper spring is formulated. The scaling law shows that origami spring force obeys power square law of spring extension, however strong nonlinear to the total twist angle. The study has also successfully generalized the scaling law from the Poisson ratio 0.3 to an arbitrary Poisson's ratio with the help of dimensional analysis.

Neurodynamics analysis of cochlear hair cell activity

Weifeng Rong, Rubin Wang, Jianhai Zhang, Wanzeng Kong

Accepted Manuscript

[Abstract] (169) [PDF 3000KB] (2)

Abstract:
There have been many studies on the effect of cochlea basal membrane movement on the resolution of different frequencies and intensities. However, these studies did not take into account the influence of power and energy consumption of the hair cells in the process of the electromotility movement, as well as the neurodynamic mechanism that produced this effect. This makes previous studies unable to fully clarify the function of outer hair cells and the mechanism of sound amplification. To this end, we introduce the gate conductance characteristics of the hair cells in the mechanical process of increasing frequency selectivity. The research finds that the low attenuation of outer hair cell (OHCs) membrane potential and the high gain in OHC power and energy consumption caused that OHC amplification is driven by electromotility. The research results show that the amplification of the outer hair cells is driven by low attenuation of membrane potential and high gain of power and energy consumption. This conclusion profoundly reveals the physiological mechanism of the electromotility movement.

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Article

Extreme mechanics

Xiaojing Zheng

2020, 10(1): 1 -7. doi: 10.1016/j.taml.2020.01.014

[Abstract] (44) [FullText HTML] (18) [PDF 2281KB] (4)

Abstract:
With the development of cutting-edge sciences and new technologies, we have to consider the size, the density, the hardness, the stiffness and other properties of engineering materials and structures beyond the conventional ranges, as well as their mechanical behavior in extreme environments, such as ultra-conventional temperature, speed, physical and chemical fields, and severe weather, and more effective theories and methods of mechanics are required. This paper first gives the fundamental definition and the scientific connotation of extreme mechanics, then reviews the studies of extreme mechanics from three aspects: the extreme properties, the extreme loads, and the discipline development, as well as major engineering and scientific challenges. The characteristics of extreme mechanics and major challenges in the aspects of mechanical theory, computational methods and experimental techniques are discussed. Prospectivei developments of extreme mechanics are suggested.

Neurodynamics analysis of cochlear hair cell activity

Weifeng Rong, Rubin Wang, Jianhai Zhang, Wanzeng Kong

2020, 10(1): 8 -15. doi: 10.1016/j.taml.2019.06.007

[Abstract] (149) [FullText HTML] (93) [PDF 3037KB] (6)

Abstract:
There have been many studies on the effect of cochlea basal membrane movement on the resolution of different frequencies and intensities. However, these studies did not take into account the influence of power and energy consumption of the hair cells in the process of the electromotility movement, as well as the neurodynamic mechanism that produced this effect. This makes previous studies unable to fully clarify the function of outer hair cells (OHCs) and the mechanism of sound amplification. To this end, we introduce the gate conductance characteristics of the hair cells in the mechanical process of increasing frequency selectivity. The research finds that the low attenuation of OHCs membrane potential and the high gain in OHC power and energy consumption caused that OHC amplification is driven by electromotility. The research results show that the amplification of the OHCs is driven by low attenuation of membrane potential and high gain of power and energy consumption. This conclusion profoundly reveals the physiological mechanism of the electromotility movement.

Micromechanical analysis on tensile properties prediction of discontinuous randomized zalacca fibre/high-density polyethylene composites under critical fibre length

Dody Ariawan, Eko Surojo, Joko Triyono, Ibrahim Fadli Purbayanto, Agil Fitri Pamungkas, Aditya Rio Prabowo

2020, 10(1): 57 -65. doi: 10.1016/j.taml.2020.01.009

[Abstract] (32) [FullText HTML] (16) [PDF 2934KB] (0)

Abstract:
In this research, the tensile properties' performance of compression moulded discontinuous randomized zalacca fibre/high-density polyethylene under critical fibre length was analysed by means of experimental method and micromechanical models. These investigations were used to verify the tensile properties models toward the effect of fibre length and volume fraction on the composites. The experimental results showed that the tensile properties of composites had significantly increased due to the enhancement of fibre length. On the contrary, a decline in the tensile properties was observed with the increase of volume fraction. A comparison was made between the available experimental results and the performances of Tsai-Pagano, Christensen and Cox-Krechel models in their prediction of composites elastic modulus. The results showed that the consideration of fibre's elastic anisotropy in the Cox-Krenchel model had yielded a good prediction of the composites modulus, nevertheless the models could not accurately predict the composites modulus for fibre length study.

Letter

Prolonged simulation of near-free surface underwater explosion based on Eulerian finite element method

Ming He, A-Man Zhang, Yun-Long Liu

2020, 10(1): 16 -22. doi: 10.1016/j.taml.2020.01.003

[Abstract] (107) [FullText HTML] (45) [PDF 4724KB] (4)

Abstract:
In the area of naval architecture and ocean engineering, the research about the underwater explosion problem is of great significance. To achieve prolonged simulation of near-free surface underwater explosion, the underwater explosion transient numerical model is established in this paper based on compressible Eulerian finite element method (EFEM). Compared with Geers–Hunter formula, EFEM is availably validated by simulating the free-field underwater explosion case. Then, the bubble pulsation and flow field dynamic characteristics of the cases with different underwater explosive depth are compared in this work. Lastly, the height of the water hump and the pressure of flow flied are analyzed quantitatively through the simulation results.

Minimizing electrostatic interactions from piezoresponse force microscopy via capacitive excitation

Qingfeng Zhu, Ehsan Nasr Esfahani, Shuhong Xie, Jiangyu Li

2020, 10(1): 23 -26. doi: 10.1016/j.taml.2020.01.001

[Abstract] (101) [FullText HTML] (52) [PDF 2825KB] (5)

Abstract:
Piezoresponse force microscopy (PFM) has emerged as one of the most powerful techniques to probe ferroelectric materials at the nanoscale, yet it has been increasingly recognized that piezoresponse measured by PFM is often influenced by electrostatic interactions. In this letter, we report a capacitive excitation PFM (ce-PFM) to minimize the electrostatic interactions. The effectiveness of ce-PFM in minimizing electrostatic interactions is demonstrated by comparing the piezoresponse and the effective piezoelectric coefficient measured by ce-PFM and conventional PFM. The effectiveness is further confirmed through the ferroelectric domain pattern imaged via ce-PFM and conventional PFM in vertical modes, with the corresponding domain contrast obtained by ce-PFM is sharper than conventional PFM. These results demonstrate ce-PFM as an effective tool to minimize the interference from electrostatic interactions and to image ferroelectric domain pattern, and it can be easily implemented in conventional atomic force microscope (AFM) setup to probe true piezoelectricity at the nanoscale.

Spatial artificial neural network model for subgrid-scale stress and heat flux of compressible turbulence

Chenyue Xie, Jianchun Wang, Hui Li, Minping Wan, Shiyi Chen

2020, 10(1): 27 -32. doi: 10.1016/j.taml.2020.01.006

[Abstract] (99) [FullText HTML] (54) [PDF 3000KB] (6)

Abstract:
The subgrid-scale (SGS) stress and SGS heat flux are modeled by using an artificial neural network (ANN) for large eddy simulation (LES) of compressible turbulence. The input features of ANN model are based on the first-order and second-order derivatives of filtered velocity and temperature at different spatial locations. The proposed spatial artificial neural network (SANN) model gives much larger correlation coefficients and much smaller relative errors than the gradient model in an a priori analysis. In an a posteriori analysis, the SANN model performs better than the dynamic mixed model (DMM) in the prediction of spectra and statistical properties of velocity and temperature, and the instantaneous flow structures.

An analytical model to predict diffusion induced intermetallic compounds growth in Cu-Sn-Cu sandwich structures

Yuexing Wang, Yao Yao, Leon Keer

2020, 10(1): 33 -37. doi: 10.1016/j.taml.2020.01.005

[Abstract] (87) [FullText HTML] (61) [PDF 2876KB] (3)

Abstract:
A mass diffusion model is developed to describe the growth kinetics of Cu₆Sn₅ intermetallic compounds (IMC) in the Cu-Sn-Cu sandwich structure. The proposed model is based on the local interfacial mass conversation law where interfacial Cu/Sn reactions and atomic diffusion are considered. Theoretical analysis shows that the IMC thickness growth is proportional to the square root of the product of the diffusion coefficient and time. The proposed model can explain the polarity effect of electromigration on kinetics of IMC growth where all the parameters have clear physical meaning. The theoretical predictions are compared with experimental results and show reasonable accuracy.

Molecular investigation on the compatibility of epoxy resin with liquid oxygen

Mingfa Ren, Lei Wang, Tong Li, Bingqing Wei

2020, 10(1): 38 -45. doi: 10.1016/j.taml.2019.06.010

[Abstract] (304) [FullText HTML] (97) [PDF 3270KB] (5)

Abstract:
Conventional fiber reinforced plastics (FRPs) have compatibility issues with solid oxygen while used as a fuel tank, which might cause combustion and explosion. To study the compatibility of different epoxy resins with liquid oxygen, molecular dynamics was used to simulate the phase changes of cross-linked epoxy resins under the impact of solid oxygen. Three curing resin systems, which are bisphenol A epoxy resin (DGEBA), bisphenol F epoxy resin (DGEBF), and tetrahydrophthalate diglycidyl ester (epoxy resin 711), are modeled to investigate the rational material system for the application of fuel tanks in launching vehicles. The simulation results show that the order of solid oxygen compatibility of these epoxy resins is DGEBA > DGEBF > epoxy resin 711 at the same density of crosslinking. The selection of curing agent also has an impact on the compatibility, with the same epoxy, diaminodiphenyl methane (DDM) has more advanced performance comparing to diaminodiphenyl sulfone (DDS).

On the plastic buckling of curved carbon nanotubes

Mohammad Malikan

2020, 10(1): 46 -56. doi: 10.1016/j.taml.2020.01.004

[Abstract] (143) [FullText HTML] (49) [PDF 3079KB] (11)

Abstract:
This research, for the first time, predicts theoretically static stability response of a curved carbon nanotube (CCNT) under an elastoplastic behavior with several boundary conditions. The CCNT is exposed to axial compressive loads. The equilibrium equations are extracted regarding the Euler–Bernoulli displacement field by means of the principle of minimizing total potential energy. The elastoplastic stress-strain is concerned with Ramberg–Osgood law on the basis of deformation and flow theories of plasticity. To seize the nano-mechanical behavior of the CCNT, the nonlocal strain gradient elasticity theory is taken into account. The obtained differential equations are solved using the Rayleigh–Ritz method based on a new admissible shape function which is able to analyze stability problems. To authorize the solution, some comparisons are illustrated which show a very good agreement with the published works. Conclusively, the best findings confirm that a plastic analysis is crucial in predicting the mechanical strength of CCNTs.