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Stability analysis of the projectile based on random center manifold reduction
Yong Huang, Chunyan Yang
Accepted Manuscript , doi: 10.1016/j.taml.2022.100385
[Abstract] (35) [PDF 955KB] (2)
The center manifold method has been widely used in the field of stochastic dynamics as a dimensionality reduction method. This paper studied the angular motion stability of a projectile system under random disturbances. The random bifurcation of the projectile is studied using the idea of the Routh-Hurwitz stability criterion, the center manifold reduction, and the polar coordinates transformation. Then, an approximate analytical presentation for the stationary probability density function is found from the related Fokker–Planck equation. From the results, the random dynamical system of projectile generates three different dynamical behaviors with the changes of the bifurcation parameter and the noise strength, which can be a reference for projectile design.
Constitutive modeling of particle reinforced rubber-like materials
Sankalp Gour, Deepak Kumar
Accepted Manuscript , doi: 10.1016/j.taml.2022.100383
[Abstract] (33) [PDF 1005KB] (1)
The present study is focused on the constitutive modeling for the mechanical behavior of rubber reinforced with filler particles. A filler-dependent energy density function is proposed with all the continuum mechanics-based necessities of an effective hyperelastic material model. The proposed invariant-based energy function comprises a single set of material parameters for a material subjected to several modes of loading conditions. The model solution agrees well with existing experimental results. Later, the effect of varying concentrations of filler particles in the rubber matrix is also studied.
A structure-preserving algorithm for time-scale non-shifted Hamiltonian systems
Xue Tian, Yi Zhang
Accepted Manuscript , doi: 10.1016/j.taml.2022.100368
[Abstract] (29) [PDF 2402KB] (0)
The variational calculus of time-scale non-shifted systems includes both the traditional continuous and traditional significant discrete variational calculus. Not only can the combination of Δ and ∇ derivatives be beneficial to obtaining higher convergence order in numerical analysis, but also it prompts the timescale numerical computational scheme to have good properties, for instance, structure-preserving. In this letter, a structure-preserving algorithm for time-scale non-shifted Hamiltonian systems is proposed. By using the time-scale discrete variational method and calculus theory, and taking a discrete time scale in the variational principle of non-shifted Hamiltonian systems, the corresponding discrete Hamiltonian principle can be obtained. Furthermore, the time-scale discrete Hamilton difference equations, Noether theorem, and the symplectic scheme of discrete Hamiltonian systems are obtained. Finally, taking the Kepler problem and damped oscillator for time-scale non-shifted Hamiltonian systems as examples, they show that the time-scale discrete variational method is a structure-preserving algorithm. The new algorithm not only provides a numerical method for solving time-scale non-shifted dynamic equations but can be calculated with variable step sizes to improve the computational speed.
Shapes of the fastest fish and optimal underwater and floating hulls
Igor Nesteruk
Accepted Manuscript , doi: 10.1016/j.taml.2022.100378
[Abstract] (29) [PDF 816KB] (0)
A streamlined shape of the best swimmers removes the boundary-layer separation and ensures a laminar flow pattern. The fastest fish have a very sharp convex nose (rostrum), the purpose of which remains unclear. The bodies of revolution similar to their shapes are analyzed in steady underwater and floating motion. The sources and sinks were located on the axis of symmetry and above the water surface to estimate the pressure on the body and the vertical velocities on the water surface. It was shown that the flow patterns on a special shaped body with concave nose has no stagnation points and ensure small values of the water surface elevation. These fact allow diminishing the maximum pressure on the surface and wave drag. Special shapes with the sharp concave nose and negative pressure gradients on their surface could be parts of the low drag underwater and floating hulls.
Influence of physical parameters on the collapse of a spherical bubble
Bo-Hua Sun
Accepted Manuscript , doi: 10.1016/j.taml.2022.100369
[Abstract] (35) [PDF 4010KB] (2)
This paper examines the influence of physical parameters on the collapse dynamics of a spherical bubble filled with diatomic gas (κ = 7/5). The problem is formulated by the Rayleigh-Plesset dynamical equation, whose numerical solutions are carried out by Maple. Our studies show that each physical parameter affects the bubble collapse dynamics in different degree, which reveals that bubble collapse dynamics must considers all the parameters including liquid viscosity, surface tension, etc, else the outcome cannot be trusted.
An iterative data-driven turbulence modeling framework based on Reynolds stress representation
Yuhui Yin, Zhi Shen, Yufei Zhang, Haixin Chen, Song Fu
Accepted Manuscript , doi: 10.1016/j.taml.2022.100381
[Abstract] (27) [PDF 2962KB] (0)
Data-driven turbulence modeling studies have reached such a stage that the basic framework is settled, but several essential issues remain that strongly affect the performance. Two problems are studied in the current research: (1) the processing of the Reynolds stress tensor and (2) the coupling method between the machine learning model and flow solver. For the Reynolds stress processing issue, we perform the theoretical derivation to extend the relevant tensor arguments of Reynolds stress. Then, the tensor representation theorem is employed to give the complete irreducible invariants and integrity basis. An adaptive regularization term is employed to enhance the representation performance. For the coupling issue, an iterative coupling framework with consistent convergence is proposed and then applied to a canonical separated flow. The results have high consistency with the direct numerical simulation true values, which proves the validity of the current approach.
Determination of the full-field stress and displacement using photoelasticity and sampling moiré method in a 3D-printed model
Zhangyu Ren, Qi Zhang, Yang Ju, Huimin Xie
Accepted Manuscript , doi: 10.1016/j.taml.2022.100380
[Abstract] (27) [PDF 1771KB] (0)
The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials. Various optical measurement techniques such as photoelasticity, moiré and digital image correlation methods have been developed to achieve this goal. However, these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement; however, these elements will disturb the light passing through the tested models using photoelasticity. In this study, by combining photoelasticity and the sampling moiré method, we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional (3D)-printed photoelastic model with orthogonal grating. Then, the full-field stress was determined by analyzing 10 photoelastic patterns, and the displacement fields were calculated using the sampling moiré method. The results indicate that the developed method can simultaneously determine the stress and displacement fields.
Predicting solutions of the Lotka-Volterra equation using hybrid deep network
Zi-Fei Lin, Yan-Ming Liang, Jia-Li Zhao, Jiao-Rui Li
Accepted Manuscript , doi: 10.1016/j.taml.2022.100384
[Abstract] (32) [PDF 1404KB] (0)
Prediction of Lotka-Volterra equations has always been a complex problem due to their dynamic properties. In this paper, we present an algorithm for predicting the Lotka-Volterra equation and investigate the prediction for both the original system and the system driven by noise. This demonstrates that deep learning can be applied in dynamics of population. This is the first study that uses deep learning algorithms to predict Lotka-Volterra equations. Several numerical examples are presented to illustrate the performances of the proposed algorithm, including Predator nonlinear breeding and prey competition systems, one prey and two predator competition systems, and their respective systems. All the results suggest that the proposed algorithm is feasible and effective for predicting Lotka-Volterra equations. Furthermore, the influence of the optimizer on the algorithm is discussed in detail. These results indicate that the performance of the machine learning technique can be improved by constructing the neural networks appropriately.
Mechanical characteristics of composite honeycomb sandwich structures under oblique impact
Yuechen Duan, Zhen Cui, Xin Xie, Ying Tie, Ting Zou, Tingting Wang
Accepted Manuscript , doi: 10.1016/j.taml.2022.100379
[Abstract] (38) [PDF 1244KB] (2)
Carbon fiber reinforced polymer (CFRP) and CFRP-based composite honeycomb sandwich structures are particularly sensitive to impact. The mechanical characteristics of composite honeycomb sandwich structures under oblique impact are studied by numerical simulation and experiment. The oblique impact model is established, and the reliability of the model is verified by the oblique impact test. To further analyze the influence of structural parameters on energy absorption under oblique impact, the influence of impact angle, face sheet thickness, wall thickness, and height of the honeycomb is numerically studied. The results show that the impact angle has an important effect on energy distribution. The structural parameters also have an effect on the peak contact force, contact time, and energy absorption, and the effect is different from normal impact due to the presence of frictional dissipation energy. Compared with normal impact, the debonding of oblique impact will be reduced, but the buckling range of the honeycomb core will be expanded.
An analysis on a rigid-flexible coupling system of an oscillating mass and a rotating disk
Accepted Manuscript
[Abstract] (41) [PDF 0KB] (0)
A mass-rod-disk system consisting of an oscillating mass attached to a rigid rotating disk by an elastic rod is designed to study rigid-flexible coupling mechanism.Suppose the rod is lightweight and has enough stiffness,the theorems of linear momentum and angular momentum are applied to the mass-rod-disk system based on the kinematic description of the system.With respect to two deflections of the mass and one angular velocity of the system,a group of nonlinear differential equations are established where the tangential inertial force,centrifugal force,Coriolis force as well as the moments of additional inertial forces take important effects on the dynamic response.For the sake of description,these three types of inertial forces mentioned before are referred to as additional inertial forces in this paper.The horizontal deflections of the mass and the angular velocity of the disk rotating about a fixed-axis are numerically solved for the prescribed external torque.The oscillating trajectory of the mass is deeply influenced by the additional inertial forces,meanwhile the dynamic fluctuations of the angular velocity and rotary inertia of the system are strongly affected by the mass oscillation.
Optimization for vibro-impact nonlinear energy sink under random excitation
Jiamin Qian, Lincong Chen
Accepted Manuscript
[Abstract] (46) [PDF 0KB] (0)
Excessive vibrations,such as those stimulated by strong wind and severe earthquake,tend to reduce the comfort of user,shorten structure lifespan,and in extreme cases lead to structural failure or even large number of casualties[1].The attachment of nonlinear energy sink (NES) induces targeted energy transfer (TET) in an irreversible manner,thus effectively attenuating undesirable vibration[2,3].Among various forms of NES,employing the nonsmooth nonlinear element in NES which is termed as vibro-impact NES (VI-NES)[4,5].The competence of VI-NES in reducing structural response has been confirmed numerically,theoretically and experimentally[6-8].However,due to the nonlinear properties of the VI-NES and external stimuli including strong winds or severe earthquakes are random in nature,obtaining a clear analytical solution of VI-NES damper system (VI-NES-DS) under random loads still poses a challenge.In addition,general and cost-effectively optimization procedures have not been available for the design of VI-NES.This work constructs an analytical optimization procedure of VI-NES-DS subjected to random excitation.By resorting to nonsmooth transformation and stochastic averaging method (SAM)[9,10],the approximate probability density function (PDF) of the VINES-DS can be determined in a closed form.On this base,a procedure to optimize the parameters of the system is established minimizing the displacement variance of the VI-NES-DS.Finally,numerical demonstrations are performed and related results are compared with pertinent data obtained by Monte Carlo simulations (MCS).
Performance improvement of the stochastic-resonance-based tri-stable energy harvester under random rotational vibration
Tingting Zhang, Yanfei Jin, Yanxia Zhang
Accepted Manuscript
[Abstract] (50) [PDF 0KB] (0)
The vibration energy harvesting has been widely concerned by many scholars as a possible solution for continuous power supply of low-power electronics[1-5].For instance,Liu et al.[1]proposed a new quasi-conservative stochastic averaging for nonlinear vibration energy harvesters (VEHs) driven by Gaussian colored noise.They[3]further investigated the stochastic dynamics of a bi-stable VEH under filtered Gaussian white noise by combining an improved coordinate transformation.In recent years,the development of wireless sensor nodes for rotational equipment has attracted an increasing attention on energy harvesting from rotational motion[6-10].For example,Hsu et al.[6]presented a comprehensive design of a passively self-tuning composite cantilever beam for energy harvesting under rotational motion to improve power output performance.Green et al.[8]established the model of rotational energy harvester in a probabilistic manner by exploiting experimental data combined with Bayesian approach.Unfortunately,the previous investigations of tri-stable energy harvesters (TEHs) under rotational vibrations tend to ignore the effect of random excitation on system dynamics,which will result in a mismatch with the actual situation.Furthermore,the neglect of the nonlinear harvesting circuit makes the harvested alternating current incapable of powering electronics.Therefore,motivated by the above reasons,the TEH interfaced with a standard rectifier circuit under random rotational environment is considered in this paper.
Hydrothermal analysis of Hybrid nanofluid flow on a vertical plate by considering slip condition
M. R. Zangooee, Kh. Hosseinzadeh, D. D. Ganj
Accepted Manuscript
[Abstract] (44) [PDF 0KB] (0)
Hybrid nanofluids have attracted burgeoning attention owing to their outstanding capacity to improve heat transfer.The influence of velocity and temperature slip parameter and Nanoparticls'(NPs') volume fraction on a vertical plate in the existence of suction has been explored in this work.The investigation's controlling partial differentiation equations were transformed into a conventional differential equation mechanism using resemblance modifications.Equations were then solved employing the fifth-order Runge-Kutta method.The skin coefficient of friction,temperature,and temperature gradient all rise when the volume percentage of NPs increases from 0 to 2%.Furthermore,a rise in the temperature slip variable was linked to a drop in the Nusselt number (heat transfer).The Nusselt number increased 0.15% and 5.63% respectively when the velocity slip parameter enhanced from 0 to 5 and the NPs volume percentage were increased from 0 to 1.5%.Furthermore,an increase in the temperature slip from 0 to 3 inflated the x-direction skin friction coefficient 8.2%,while inflation in the velocity slip from 0 to 5 was associated with a decline in the x-direction skin friction coefficient 95%.
A machine learning based solver for pressure Poisson equations
Ruilin Chen, Xiaowei Jin, Hui Li
Accepted Manuscript
[Abstract] (44) [PDF 0KB] (0)
The Navier-Stokes equations are nonlinear partial differential equations (PDEs) describing viscous fluid flow,which are applicable to various scientific and engineering flow problems,such as river flow,air flow around wings,ocean currents,blood flow in the human cardiovascular system,etc.The solution of the NavierStokes equations is of great significance in the field of fluid mechanics.The convection term leads to the high nonlinearity of Navier-Stokes equations,and the solutions contain multi-scale flow structures.Nowadays,the numerical method is still a workhorse tool for solving complex flow phenomena.Thanks to the rapid growth of computer computing power and speed,the computational fluid dynamics (CFD) has made great progress[1-4].For incompressible Navier-Stokes equations,the main difficulty of numerical solution lies in the treatment of pressure,that is,how to deal with the coupling between velocity and pressure under incompressible constraints.To overcome this difficulty,Chorin[5]proposed the projection method (or fractional step method),which is widely used for its skillfully decoupling of the velocity and pressure fields.In the projection method,an incomplete form of momentum equations is first solved to obtain an intermediate velocity field,which is usually not divergence-free,then the velocity field is projected into the divergence-free field without changing the vorticity.This projection step is achieved by solving the pressure Poisson equation (PPE) and is usually more timeconsuming and computationally expensive than other steps in the overall solution process.
Elastoplastic constitutive modeling under the complex loading driven by GRU and small-amount data
Zefeng Yu, Chenghang Han, Hang Yang, Yu Wang, Shan Tang, Xu Guo
Accepted Manuscript
[Abstract] (44) [PDF 0KB] (0)
Engineering structures often are subjected to a variety of load types.Some parts of them may experience a complex deformation history,for example,plastic deformation under cyclic loading.The materials of such structures often include nonlinearity and path (history) dependence.Appropriate nonlinear constitutive models considering loading path (history) can assist in structural design,help monitor structural health and assess the redundancy life of the engineering structures.Many constitutive models have been proposed to describe the behavior of elastoplastic materials[1-4]based on an explicit-functions-based paradigm with basic elements such as the plastic flow,loading and unloading judgment etc..However,the formulation of function-based constitutive model along with the traditional approach is a challenging and time-consuming job.It requires complex mathematical derivation and intuition into the plastic deformation mechanisms of the materials.In recent years,with the development of the data-driven approach and the machine learning by the deep neural networks[5,6],building the constitutive models through the combination of data science and solid mechanics attracted the research attention of the researchers around the world.
Clamping force of a multilayered cylindrical clamper with internal friction
Bo-Hua Sun, Xiao-Lin Guo
Accepted Manuscript
[Abstract] (47) [PDF 0KB] (0)
Holding an object by clamping force is a fundamental process for functional structures in natural and manmade systems.Examples encompass different applications as shown in Fig.1,such as,medical clips,glass frame,hairband,headphone as well as robots[1-3]
Simulation and experimental analysis of melt pool evolution in laser engineered net shaping
Zhuangzhuang Mao, Wei Feng, Ce Hao, Zhanwei Liu
Accepted Manuscript
[Abstract] (42) [PDF 0KB] (0)
In this work,the evolution of melt pool under single-point and single-line printing in the Laser Engineered Net Shaping (LENS) process is analyzed.Firstly,the basic structure of the melt pool model of the LENS process is established and the necessary assumptions are made.Then,the establishment process of the multi-physical field model of the melt pool is introduced in detail.It is concluded that the simulation model results are highly consistent with the online measurement experiment results in terms of melt pool profile,space temperature gradient,and time temperature gradient.Meanwhile,some parameters,such as the 3D morphology and surface fluid field of the melt pool,which are not obtained in the online measurement experiment,are analyzed.Finally,the influence of changing the scanning speed on the profile,peak temperature,and temperature gradient of the single-line melt pool is also analyzed,and the following conclusions are obtained:With the increase in scanning speed,the profile of the melt pool gradually becomes slender;The relationship between peak temperature and scanning speed is approximately linear in a certain speed range;The space temperature gradient at the tail of the melt pool under different scanning speeds hardly changes with the scanning speed,and the time temperature gradient at the tail of the melt pool is in direct proportion to the scanning speed.

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Design of elliptical underwater acoustic cloak with truss-latticed pentamode materials
Yuanyuan Ge, Xiaoning. Liu, Gengkai Hu
Theoretical and Applied Mechanics Letters  12 (2022) 100346.  
[Abstract] (165) [PDF 2572KB] (33)
Pentamode acoustic cloak is promising for underwater sound control due to its solid nature and broadband efficiency, however its realization is only limited to simple cylindrical shape. In this work, we established a set of techniques for the microstructure design of elliptical pentamode acoustic cloak based on truss lattice model, including the inverse design of unit cell and algorithms for latticed cloak assembly. The designed cloak was numerically validated by the well wave concealing performance. The work proves that more general pentamode acoustic wave devices beyond simple cylindrical geometry are theoretically feasible, and sheds light on more practical design for waterborne sound manipulation.
On the Number of Fractured Segments of Spaghetti Breaking Dynamics
Yi Zhang, Xiang Li, Yuanfan Dai, and Bo-Hua Sun
Theoretical and Applied Mechanics Letters  12 (2022) 100347.  
[Abstract] (219) [PDF 1436KB] (6)
Why are pieces of spaghetti generally broken into three to ten segments instead of two as one thinks? How can one obtain the desired number of fracture segments? To answer those questions, the fracture dynamics of a strand of spaghetti is modelled by elastic rod and numerically investigated by using finite-element software ABAQUS. By data fitting, two relations are obtained: the number of fracture segments in terms of rod diameter-length ratio and fracture limit curvature with the rod diameter. Results reveal that when the length is constant, the larger the diameter and/or the smaller the diameter-length ratio D/L, the smaller the limit curvature; and the larger the diameter-length ratio D/L, the fewer the number of fractured segments. The relevant formulations can be used to obtain the desired number of broken segments of spaghetti by changing the diameter-to-length ratio.
Independent component analysis of streamwise velocity fluctuations in turbulent channel flows
Ting Wu, Guowei He
Theoretical and Applied Mechanics Letters  12 (2022) 100349.  
[Abstract] (57) [PDF 3373KB] (6)
Independent component analysis (ICA) is used to study the multiscale localised modes of streamwise velocity fluctuations in turbulent channel flows.ICA aims to decompose signals into independent modes,which may induce spatially localised objects.The height and size are defined to quantify the spatial position and extension of these ICA modes,respectively.In contrast to spatially extended proper orthogonal decomposition (POD) modes,ICA modes are typically localised in space,and the energy of some modes is distributed across the near-wall region.The sizes of ICA modes are multiscale and are approximately proportional to their heights.ICA modes can also help to reconstruct the statistics of turbulence,particularly the third-order moment of velocity fluctuations,which is related to the strongest Reynolds shear-stressproducing events.The results reported in this paper indicate that the ICA method may connect statistical descriptions and structural descriptions of turbulence.
Mathematical modeling of fractional derivatives for magnetohydrodynamic fluid flow between two parallel plates by the radial basis function method
Saman Hosseinzadeh, Seyed Mahdi Emadi, Seyed Mostafa Mousavi, Davood Domairry Ganji
Theoretical and Applied Mechanics Letters  12 (2022) 100350.  
[Abstract] (49) [PDF 2086KB] (1)
Investigations into the magnetohydrodynamics of viscous fluids have become more important in recent years,owing to their practical significance and numerous applications in astro-physical and geo-physical phenomena.In this paper,the radial base function was utilized to answer fractional equation associated with fluid flow passing through two parallel flat plates with a magnetic field.The magnetohydrodynamics coupled stress fluid flows between two parallel plates,with the bottom plate being stationary and the top plate moving at a persistent velocity.We compared the radial basis function approach to the numerical method (fourth-order Range-Kutta) in order to verify its validity.The findings demonstrated that the discrepancy between these two techniques is quite negligible,indicating that this method is very reliable.The impact of the magnetic field parameter and Reynolds number on the velocity distribution perpendicular to the fluid flow direction is illustrated.Eventually,the velocity parameter is compared for diverse conditions α,Reynolds and position (y),the maximum of which occurs at α=0.4.Also,the maximum velocity values occur in α=0.4 and Re=1000 and the concavity of the graph is less for α=0.8.
Motion of a sphere and the suspending low-Reynolds-number fluid confined in a cubic cavity
Gaofeng Chen, Xikai Jiang
Theoretical and Applied Mechanics Letters  12 (2022) 100352.  
[Abstract] (50) [PDF 2390KB] (2)
Dynamics of a spherical particle and the suspending low-Reynolds-number fluid confined by a cubic cavity were studied numerically.We calculated the particle's hydrodynamic mobilities along x-,y-,and z directions at various locations in the cavity.The mobility is largest in the cavity center and decays as the particle becomes closer to no-slip walls.It was found that mobilities in the entire cubic cavity can be determined by a minimal set in a unit tetrahedron therein.Fluid vortices in the cavity induced by the particle motion were observed and analyzed.We also found that the particle can exhibit a drift motion perpendicular to the external force.Magnitude of the drift velocity normalized by the velocity along the direction of the external force depends on particle location and particle-to-cavity sizes ratio.This work forms the basis to understand more complex dynamics in microfluidic applications such as intracellular transport and encapsulation technologies.
Investigation of nanofluid flow in a vertical channel considering polynomial boundary conditions by Akbari-Ganji's method
M. Fallah Najafabadi, H. TalebiRostami, Kh. Hosseinzadeh, D. D. Ganji
Theoretical and Applied Mechanics Letters  12 (2022) 100356.  
[Abstract] (43) [PDF 5834KB] (1)
In this research,a vertical channel containing a laminar and fully developed nanofluid flow is investigated.The channel surface's boundary conditions for temperature and volume fraction functions are considered qth-order polynomials.The equations related to this problem have been extracted and then solved by the AGM and validated through the Runge-Kutta numerical method and another similar study.In the study,the effect of parameters,including Grashof number,Brownian motion parameter,etc.,on the motion,velocity,temperature,and volume fraction of nanofluids have been analyzed.The results demonstrate that increasing the Gr number by 100% will increase the velocity profile function by 78% and decrease the temperature and fraction profiles by 20.87% and 120.75%.Moreover,rising the Brownian motion parameter in five different sizes (0.1,0.2,0.3,0.4,and 0.5) causes lesser velocity,about 24.3% at first and 4.35% at the last level,and a maximum 52.86% increase for temperature and a 24.32% rise for ψ occurs when Nb rises from 0.1 to 0.2.For all Nt values,at least 55.44%,18.69%,for F(η),and Ω(η),and 20.23% rise for ψ(η) function is observed.Furthermore,enlarging the Nr parameter from 0.25 to 0.1 leads F(η) to rise by 199.7%,fluid dimensionless temperature,and dimensional volume fraction to decrease by 18% and 92.3%.In the end,a greater value of q means a more powerful energy source,amplifying all velocity,temperature,and volume fraction functions.The main novelty of this research is the combined convection qth-order polynomials boundary condition applied to the channel walls.Moreover,The AMG semi-analytical method is used as a novel method to solve the governing equations.
A new dynamic subgrid-scale model using artificial neural network for compressible flow
Han Qi, Xinliang Li, Ning Luo, Changping Yu
Theoretical and Applied Mechanics Letters  12 (2022) 100359.  
[Abstract] (47) [PDF 2851KB] (1)
The subgrid-scale (SGS) kinetic energy has been used to predict the SGS stress in compressible flow and it was resolved through the SGS kinetic energy transport equation in past studies.In this paper,a new subgrid-scale (SGS) eddy-viscosity model is proposed using artificial neural network to obtain the SGS kinetic energy precisely,instead of using the SGS kinetic energy equation.Using the infinite series expansion and reserving the first term of the expanded term,we obtain an approximated SGS kinetic energy,which has a high correlation with the real SGS kinetic energy.Then,the coefficient of the modelled SGS kinetic energy is resolved by the artificial neural network and the modelled SGS kinetic energy is more accurate through this method compared to the SGS kinetic energy obtained from the SGS kinetic energy equation.The coefficients of the SGS stress and SGS heat flux terms are determined by the dynamic procedure.The new model is tested in the compressible turbulent channel flow.From the a posterior tests,we know that the new model can precisely predict the mean velocity,the Reynolds stress,the mean temperature and turbulence intensities,etc.
Hydrothermal analysis of non-Newtonian fluid flow (blood) through the circular tube under prescribed non-uniform wall heat flux
Shahin Faghiri, Shahin Akbari, Mohammad Behshad Shafii, Kh. Hosseinzadeh
Theoretical and Applied Mechanics Letters  12 (2022) 100360.  
[Abstract] (50) [PDF 3834KB] (0)
Non-Newtonian fluids are described by the nonlinear relationship between shear stress and rate of deformation at a specified temperature and pressure[1].The flows of non-Newtonian fluids play important role in many industrial applications and disciplinary fields such as biomedicine,polymer and food processing,thermal oil recovery,and discharge of industrial wastes[2-8].From a mechanical engineering viewpoint,the complicated rheological behavior of shear-thinning fluid like blood cannot be modeled by a very plain,one parameter,and linearized law of viscosity as presented by Newton[9-13].The properties of this type of fluid can only be characterized by higher-order constitutive equations,such as the power-law model[14-16],which considers thefluid's nonNewtonian featuresincluding shear thinning and yield stress characteristics[17-22].In the recent few decades,the investigation of fluid dynamics and heat transfer in the non-Newtonian fluid flow has been identified as one of the most important issues for researchers.In points of the fact,comprehension of the property of non-Newtonian fluid movement and the thermal-mechanical behavior of the fluid stream can result in a better understanding of scientific phenomena occurring in real life[23-28],which has triggered many investigators in different branches of engineering to concentrate on the non-Newtonian fluid flow simulation with different methodologies.
Stirring by anisotropic squirming
Zhi Lina, Sirui Zhu, Lingyun Ding
Theoretical and Applied Mechanics Letters  12 (2022) 100358.  
[Abstract] (57) [PDF 1940KB] (1)
We consider a fluid stirred by the locomotions of squirmers through it and generalize the stochastic hydrodynamic model proposed by Thiffeault et.al.[1,2]to the case in which the swimmers move in anisotropically random directions.A non-diagonal effective diffusivity tensor is derived with which the diffusive preference of a passive particle along any given direction can be computed to provide more details of the phenomena beyond scalar statistics.We further identify a fraction from the orthogonal decomposition of the drift-induced particle displacement to distinguish the underlying nonlinear mixing mechanism for different types of swimmers.Numerical simulations verify the analytical results with explicit examples of prescribed,anisotropic stirring motions.We also connect our formulation to several measures used in clinical medical research such as diffusion tensor imaging where anisotropic diffusion has a significant consequence.
An alternative form of energy density demonstrating the severe strain-stiffening in thin spherical and cylindrical shells
Md. Moonim Lateefi, Deepak Kumar, Somnath Sarangi
Theoretical and Applied Mechanics Letters  12 (2022) 100361.  
[Abstract] (59) [PDF 3021KB] (3)
In the current scenario,rubbers and rubber-like materials have attracted many researchers for modern soft engineering and medical field applications[1-3].Since the 1940s,enormous progress has been achieved in developing hyperelastic material modeling to characterize the stress-strain response at large deformations.The significant results have been obtained in incompressible hyperelastic material modeling and have also been experimentally confirmed[4,5].This remarkable success projected a considerable light on the physical behavior of rubber-like materials.However,the theory of elasticity for hyperelastic materials subjected to large deformations is highly nonlinear.Therefore,so many mathematical difficulties are still encountered at the current time.In general,rubber-like materials are assumed to be an incompressible isotropic hyperelastic materials.A preliminary step toward complete modeling is analyzing their elastic properties and nonlinear stress-strain characteristics[6,7].In line with that,the uniaxial and biaxial loading tests on such materials reveal a nonlinear stress-strain response with higher extensibility in the lowstress range and progressively lower extensibility at large strain.This phenomenon is well-known as "strain-hardening" or "strainstiffening".
Crack propagation simulation in brittle elastic materials by a phase field method
Xingxue Lu, Cheng Li, Ying Tie, Yuliang Hou, Chuanzeng Zhang
2019, 9(6): 339-352   doi: 10.1016/j.taml.2019.06.001
[Abstract](1468) [FullText HTML](849) [PDF 3845KB](96)
Investigation on Savonius turbine technology as harvesting instrument of non-fossil energy: Technical development and potential implementation
Aditya Rio Prabowo, Dandun Mahesa Prabowoputra
2020, 10(4): 262-269   doi: 10.1016/j.taml.2020.01.034
[Abstract](1240) [FullText HTML](594) [PDF 3192KB](87)
Mechanistic Machine Learning: Theory, Methods, and Applications
2020, 10(3): 141-142   doi: 10.1016/j.taml.2020.01.041
[Abstract](9013) [FullText HTML](753) [PDF 3081KB](86)
On the Weissenberg effect of turbulence
Yu-Ning Huang, Wei-Dong Su, Cun-Biao Lee
2019, 9(4): 236-245   doi: 10.1016/j.taml.2019.03.004
[Abstract](1001) [FullText HTML](567) [PDF 2579KB](79)
Physics-informed deep learning for incompressible laminar flows
Chengping Rao, Hao Sun, Yang Liu
2020, 10(3): 207-212   doi: 10.1016/j.taml.2020.01.039
[Abstract](1284) [FullText HTML](584) [PDF 4183KB](72)
Dynamic mode decomposition and reconstruction of transient cavitating flows around a Clark-Y hydrofoil
Rundi Qiu, Renfang Huang, Yiwei Wang, Chenguang Huang
2020, 10(5): 327-332   doi: 10.1016/j.taml.2020.01.051
[Abstract](1094) [FullText HTML](686) [PDF 2862KB](65)
Frame-indifference of cross products, rotations, and the permutation tensor
Maolin Du
2020, 10(2): 116-119   doi: 10.1016/j.taml.2020.01.015
[Abstract](1130) [FullText HTML](606) [PDF 2494KB](63)
Multiscale mechanics
G.W. He, G.D. Jin
11 (2021) 100238   doi: 10.1016/j.taml.2021.100238
[Abstract](567) [FullText HTML](481) [PDF 2196KB](62)
On the interaction between bubbles and the free surface with high density ratio 3D lattice Boltzmann method
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[Abstract](1488) [FullText HTML](950) [PDF 2725KB](62)
A modified Lin equation for the energy balance in isotropic turbulence
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