2017 Vol.7(5)

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Solid Mechanics
Influences of nanotwin volume fraction on the ballistic performance of coarse-grained metals
Q.D. Ouyang, G.J. Weng, A.K. Soh, X. Guo
Theoretical and Applied Mechanics Letters  2017, 7(5): 265-268. doi: 10.1016/j.taml.2017.09.012
[Abstract](472) [PDF 1189KB](7)
Coarse-grained (CG) metals strengthened by nanotwinned (NT) regions possess high strength and good ductility. As such, they are very suitable for applications in bullet-proof targets. Here, a numerical model based on the conventional theory of strain gradient plasticity and the Johnson-Cook failure criterion is employed to study the influences of volume fraction of NT regions on their ballistic performance. The results show that in general a relatively small twin spacing (4-10 nm) and a moderate volume fraction (7%-20%) will lead to excellent limit velocity and that the influences of volume fraction on limit displacement change with the category of impact processes.
Fluid Mechanics
Analysis of the pressure at a vertical barrier due to extreme wave run-up over variable bathymetry
J. Brennan, C. Clancy, J. Harrington, R. Cox, F. Dias
Theoretical and Applied Mechanics Letters  2017, 7(5): 269-275. doi: 10.1016/j.taml.2017.11.001
[Abstract](473) [PDF 1769KB](4)
The pressure load at a vertical barrier caused by extreme wave run-up is analysed numerically, using the conformal mapping method to solve the two-dimensional free surface Euler equations in a pseudospectral model. Previously this problem has been examined in the case of a flat-bottomed geometry. Here, the model is extended to consider a varying bathymetry. Numerical experiments show that an increasing step-like bottom profile may enhance the extreme run-up of long waves but result in a reduced pressure load.
Passive forces aiding coordinated groupings of swimming animals
Daniel Weihs, Elad Farhi
Theoretical and Applied Mechanics Letters  2017, 7(5): 276-279. doi: 10.1016/j.taml.2017.09.009
[Abstract](469) [PDF 676KB](6)
The "Lighthill conjecture" regarding passive forces created in a group of self-propelled objects moving in an inviscid fluid is examined. We show that pressure gradients are produced in the wakes of anterior members of the group, which both indicate and assist rear members to stay in advantageous positions, for saving energy.
Numerical simulation of vortex-induced drag of elastic swimmer models
Thomas Engels, Dmitry Kolomenskiy, Kai Schneider, Jörn Sesterhenn
Theoretical and Applied Mechanics Letters  2017, 7(5): 280-285. doi: 10.1016/j.taml.2017.10.001
[Abstract](605) [PDF 946KB](13)
We present numerical simulations of simplified models for swimming organisms or robots, using chordwise flexible elastic plates. We focus on the tip vortices originating from three-dimensional effects due to the finite span of the plate. These effects play an important role when predicting the swimmer's cruising velocity, since they contribute significantly to the drag force. First we simulate swimmers with rectangular plates of different aspect ratios and compare the results with a recent experimental study. Then we consider plates with expanding and contracting shapes. We find the cruising velocity of the contracting swimmer to be higher than the rectangular one, which in turn is higher than the expanding one. We provide some evidence that this result is due to the tip vortices interacting differently with the swimmer.
Stability of Couette flow past a gel film
Andrew Hess, Shengqiang Cai, Tong Gao
Theoretical and Applied Mechanics Letters  2017, 7(5): 286-291. doi: 10.1016/j.taml.2017.09.006
[Abstract](492) [PDF 471KB](6)
We study instability of a Newtonian Couette flow past a gel-like film in the limit of vanishing Reynolds number. Three models are explored including one hyperelastic (neo-Hookean) solid, and two viscoelastic (Kelvin-Voigt and Zener) solids. Instead of using the conventional Lagrangian description in the solid phase for solving the displacement field, we construct equivalent "differential" models in an Eulerian reference frame, and solve for the velocity, pressure, and stress in both fluid and solid phases simultaneously. We find the interfacial instability is driven by the first-normal stress difference in the basestate solution in both hyperelastic and viscoelastic models. For the neo-Hookean solid, when subjected to a shear flow, the interface exhibits a short-wave (finite-wavelength) instability when the film is thin (thick). In the Kelvin-Voigt and Zener solids where viscous effects are incorporated, instability growth is enhanced at small wavenumber but suppressed at large wavenumber, leading to a dominant finitewavelength instability. In addition, adding surface tension effectively stabilizes the interface to sustain fluid shear.
Multiple solutions and stability of the steady transonic small-disturbance equation
Ya Liu, Shijun Luo, Feng Liu
Theoretical and Applied Mechanics Letters  2017, 7(5): 292-300. doi: 10.1016/j.taml.2017.09.011
[Abstract](516) [PDF 413KB](8)
Numerical solutions of the steady transonic small-disturbance (TSD) potential equation are computed using the conservative Murman-Cole scheme. Multiple solutions are discovered and mapped out for the Mach number range at zero angle of attack and the angle of attack range at Mach number 0.85 for the NACA 0012 airfoil. We present a linear stability analysis method by directly assembling and evaluating the Jacobian matrix of the nonlinear finite-difference equation of the TSD equation. The stability of all the discovered multiple solutions are then determined by the proposed eigen analysis. The relation of stability to convergence of the iterative method for solving the TSD equation is discussed. Computations and the stability analysis demonstrate the possibility of eliminating the multiple solutions and stabilizing the remaining unique solution by adding a sufficiently long splitter plate downstream the airfoil trailing edge. Finally, instability of the solution of the TSD equation is shown to be closely connected to the onset of transonic buffet by comparing with experimental data.
"Equilibrium" and "non-equilibrium" turbulence
Robert Rubinstein, Timothy T. Clark
Theoretical and Applied Mechanics Letters  2017, 7(5): 301-305. doi: 10.1016/j.taml.2017.09.010
[Abstract](513) [PDF 313KB](7)
We review the concept of "equilibrium" in turbulence. It generally means a property of the energy spectrum, it can also be understood in terms of a scalar property, the Taylor-Kolmogorov formula relating the dissipation rate to the total energy and integral length scale. The implications of equilibrium and strong departure from equilibrium for turbulence modeling are stressed.
A minimum-domain impulse theory for unsteady aerodynamic force with discrete wake
Linlin Kang, Luoqin Liu, Weidong Su, Jiezhi Wu
Theoretical and Applied Mechanics Letters  2017, 7(5): 306-310. doi: 10.1016/j.taml.2017.11.003
[Abstract](511) [PDF 829KB](6)
We extend the impulse theory for unsteady aerodynamics, from its classic global form to finite-domain formulation, then to a minimum-domain version for discrete wake. Each extension has been confirmed numerically. The minimum-domain theory indicates that the numerical finding of Li and Lu (2012) is of general significance:The entire force is completely determined by only the time rate of impulse of those vortical structures still connecting to the body, along with the Lamb-vector integral thereof that captures the contribution of all the rest disconnected vortical structures.
Causal mechanism behind the stall delay by airfoil's pitching-up motion
Shufan Zou, Ankang Gao, Yipeng Shi, Jiezhi Wu
Theoretical and Applied Mechanics Letters  2017, 7(5): 311-315. doi: 10.1016/j.taml.2017.11.004
[Abstract](562) [PDF 1103KB](8)
Why the stall of an airfoil can be significantly delayed by its pitching-up motion? Various attempts have been proposed to answer this question over the past half century, but none is satisfactory. In this letter we prove that a chain of vorticity-dynamics processes at accelerating boundary is fully responsible for the causal mechanism underlying this peculiar phenomenon. The local flow behavior is explained by a simple potential-flow model.