Institute of Mechanics,

Chinese Academy of Sciences

## 2022 Vol.12(4)

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*Theoretical and Applied Mechanics Letters*12 (2022) 100346.

**Abstract:**

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.

*Theoretical and Applied Mechanics Letters*12 (2022) 100347.

**Abstract:**

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.

*Theoretical and Applied Mechanics Letters*12 (2022) 100349.

**Abstract:**

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.

*Theoretical and Applied Mechanics Letters*12 (2022) 100350.

**Abstract:**

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.

*Theoretical and Applied Mechanics Letters*12 (2022) 100352.

**Abstract:**

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.

*Theoretical and Applied Mechanics Letters*12 (2022) 100356.

**Abstract:**

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

*N*rises from 0.1 to 0.2.For all

_{b}*N*values,at least 55.44%,18.69%,for

_{t}*F*(

*η*),and Ω(

*η*),and 20.23% rise for ψ(

*η*) function is observed.Furthermore,enlarging the

*N*parameter from 0.25 to 0.1 leads

^{r}*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.

*Theoretical and Applied Mechanics Letters*12 (2022) 100359.

**Abstract:**

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.

*Theoretical and Applied Mechanics Letters*12 (2022) 100360.

**Abstract:**

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.

*Theoretical and Applied Mechanics Letters*12 (2022) 100358.

**Abstract:**

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.

*Theoretical and Applied Mechanics Letters*12 (2022) 100361.

**Abstract:**

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".