2021 Vol.11(3)

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Letter
A geometry-based framework for modeling the complexity of origami folding
Samuel Schulman, Xin Ning
Theoretical and Applied Mechanics Letters  11 (2021) 100241. doi: 10.1016/j.taml.2021.100241
[Abstract](537) [FullText HTML] (285) [PDF 2737KB](9)
Abstract:
This paper presents a quantitative framework to analyze the complexity of folding origami structures from flat membranes. Extensive efforts have realized intricate origami patterns with desired functions such as mechanical properties, packaging efficiency, and deployment behavior. However, the complexity associated with the manufacturing or folding of origami patterns has not been explored. Understanding how difficult origami structures are to make, and how much time they require to form is crucial information to determining the practical feasibility of origami designs and future applications such as robotic origami assembly in space. In this work, we develop this origami complexity metric by modeling the geometric properties and crease formation of the origami structure, from which it outputs crease and pattern complexity values and a prediction of the time to complete the pattern assembly, based on the characteristics of the operator. The framework is experimentally validated by fabricating various Miura-ori origami paper models.
Why neural networks apply to scientific computing?
Shaoqiang Tang, Yang Yang
Theoretical and Applied Mechanics Letters  11 (2021) 100242. doi: 10.1016/j.taml.2021.100242
[Abstract](477) [FullText HTML] (270) [PDF 3294KB](18)
Abstract:
In recent years, neural networks have become an increasingly powerful tool in scientific computing. The universal approximation theorem asserts that a neural network may be constructed to approximate any given continuous function at desired accuracy. The backpropagation algorithm further allows efficient optimization of the parameters in training a neural network. Powered by GPU's, effective computations for scientific and engineering problems are thereby enabled. In addition, we show that finite element shape functions may also be approximated by neural networks.
Analytical solutions for inflation of pre-stretched elastomeric circular membranes under uniform pressure
Jianghong Yuan, Xianlin Liu, Haibin Xia, Yin Huang
Theoretical and Applied Mechanics Letters  11 (2021) 100243. doi: 10.1016/j.taml.2021.100243
[Abstract](592) [FullText HTML] (254) [PDF 2851KB](37)
Abstract:
Elastomeric membranes are frequently used in several emerging fields such as soft robotics and flexible electronics. For convenience of the structural design, it is very attractive to find simple analytical solutions to well describe their elastic deformations in response to external loadings. However, both the material/geometrical nonlinearity and the deformation inhomogeneity due to boundary constraints make it much challenging to get an exact analytical solution. In this paper, we focus on the inflation of a pre-stretched elastomeric circular membrane under uniform pressure, and derive an approximate analytical solution of the pressure-volume curve based upon a reasonable assumption on the shape of the inflated membrane. Such an explicit expression enables us to quantitatively design the material and geometrical parameters of the pre-stretched membrane to generate a target pressure-volume curve with prescribed peak point and initial slope. This work would be of help in the simplified mechanical design of structures involving elastomeric membranes.
Computing mean fields with known Reynolds stresses at steady state
Xianwen Guo, Zhenhua Xia, Shiyi Chen
Theoretical and Applied Mechanics Letters  11 (2021) 100244. doi: 10.1016/j.taml.2021.100244
[Abstract](506) [FullText HTML] (240) [PDF 3354KB](20)
Abstract:
With the rising of modern data science, data-driven turbulence modeling with the aid of machine learning algorithms is becoming a new promising field. Many approaches are able to achieve better Reynolds stress prediction, with much lower modeling error (\begin{document}$\epsilon_{\rm{M}}$\end{document}), than traditional RANS models, but they still suffer from numerical error and stability issues when the mean velocity fields are estimated by solving Reynolds-averaged Navier-Stokes (RANS) equations with the predicted Reynolds stresses. This fact illustrates that the error of solving the RANS equations (\begin{document}$\epsilon_{\rm{P}}$\end{document}) is also very important for a RANS simulation. In the present work, the error \begin{document}$\epsilon_{\rm{P}}$\end{document} is studied separately by using the Reynolds stresses obtained from direct numerical simulation (DNS)/highly resolved large-eddy simulation to minimize the modeling error \begin{document}$\epsilon_{\rm{M}}$\end{document}, and the sources of \begin{document}$\epsilon_{\rm{P}}$\end{document} are derived mathematically. For the implementations with known Reynolds stresses solely, we suggest to run an auxiliary RANS simulation to make a first guess on \begin{document}$\nu_{\rm{t}}^*$\end{document} and \begin{document}$S_{ij}^0$\end{document}. With around 10 iterations, the error of the streamwise velocity component could be reduced by about one-order of magnitude in flow over periodic hills. The present work is not to develop a new RANS model, but to clarify the facts that obtaining mean field with known Reynolds stresses is nontrivial and that the nonlinear part of the Reynolds stresses is very important in flow problems with separations. The proposed approach to reduce \begin{document}$\epsilon_{\rm{P}}$\end{document} may be very useful for the a posteriori applications of the data-driven turbulence models.
Fundamental kinematics laws of interstitial fluid flows on vascular walls
Yajun Yin, Hongyi Li, Gang Peng, Xiaobin Yu, Yiya Kong
Theoretical and Applied Mechanics Letters  11 (2021) 100245. doi: 10.1016/j.taml.2021.100245
[Abstract](447) [FullText HTML] (270) [PDF 2521KB](16)
Abstract:
In the previous studies, the phenomenon that the interstitial fluid (ISF) can flow along tunica adventitia of the arteries and veins in both human and animal bodies was reported. On the basis of these studies, this paper aims to: (i) summarize the basic properties of the ISF flows in the walls of arteries and veins, (ii) combine the basic properties with axiomaticism and abstract the axiom for ISF flows, and (iii) propose three fundamental laws of the ISF flow, (i.e., the existence law, the homotropic law and the reverse law). The three laws provide solid theoretical basement for exploring the kinematic patterns of interstitial fluid flow in the cardiovascular system.
Analytical and numerical studies for seiches in a closed basin with various geometric shape of longitudinal section
I. Magdalena, Nadhira Karima, H. Q. Rif'atin
Theoretical and Applied Mechanics Letters  11 (2021) 100246. doi: 10.1016/j.taml.2021.100246
[Abstract](518) [FullText HTML] (392) [PDF 3043KB](4)
Abstract:
Seiches are long-period standing waves with a unique period called a natural resonant period, during which the phenomenon of resonance occurs. The occurrence of resonance in coastal areas can cause destruction to surrounding natural and man-made structures. By determining the resonant period of a given basin, we can pinpoint the conditions that allow waves to achieve resonance. In this study, a mathematical model is developed from the shallow water equations to examine seiches and resonances in various types of closed basin. The developed model is solved analytically using the separation of variables method to determine the seiches' fundamental resonant periods. Comparisons between the analytical solutions and experimental measurements for resonant periods are also provided. It is shown that the analytical resonant period confirms the experimental data for closed basin of various geometric profiles. Using a finite volume method on a staggered grid, the model is solved numerically to simulate the wave profile when resonance phenomenon occurs. Through those numerical simulations, we also obtain the fundamental resonant period for each basin which agrees with the derived analytical period.
Effect of interfacial stiffness on the stretchability of metal/elastomer bilayers under in-plane biaxial tension
Zheng Jia, Teng Li
Theoretical and Applied Mechanics Letters  11 (2021) 100247. doi: 10.1016/j.taml.2021.100247
[Abstract](617) [FullText HTML] (232) [PDF 2733KB](5)
Abstract:
Flexible electronic devices are often subjected to large and repeated deformation, so that their functional components such as metal interconnects need to sustain strains up to tens of percent, which is far beyond the intrinsic deformability of metal materials (~1%). To meet the stringent requirements of flexible electronics, metal/elastomer bilayers, a stretchable structure that consists of a metal film adhered to a stretchable elastomer substrate, have been developed to improve the stretch capability of metal interconnects. Previous studies have predicted that the metal/elastomer bilayers are much more stretchable than freestanding metal films. However, these investigations usually assume perfect bonding between the metal and elastomer layers. In this work, the effect of the metal/elastomer interface with a finite interfacial stiffness on the stretchability of bilayer structures is analyzed. The results show that the assumption of perfect interface (with infinite interfacial stiffness) may lead to an overestimation of the stretchability of bilayer structures. It is also demonstrated that increased adhesion between the metal and elastomer layers can enhance the stretchability of the metal layer.
Neuroevolution-enabled adaptation of the Jacobi method for Poisson’s equation with density discontinuities
T.-R. Xiang, X. I. A. Yang, Y.-P. Shi
Theoretical and Applied Mechanics Letters  11 (2021) 100252. doi: 10.1016/j.taml.2021.100252
[Abstract](399) [FullText HTML] (222) [PDF 4093KB](3)
Abstract:
Lacking labeled examples of working numerical strategies, adapting an iterative solver to accommodate a numerical issue, e.g., density discontinuities in the pressure Poisson equation, is non-trivial and usually involves a lot of trial and error. Here, we resort to evolutionary neural network. A evolutionary neural network observes the outcome of an action and adapts its strategy accordingly. The process requires no labeled data but only a measure of a network’s performance at a task. Applying neuro-evolution and adapting the Jacobi iterative method for the pressure Poisson equation with density discontinuities, we show that the adapted Jacobi method is able to accommodate density discontinuities.
Bedding plane-embedded augmented virtual internal bonds for fracture propagation simulation in shale
Zihan Liu, Zhennan Zhang, Ahmad Ghassemi
Theoretical and Applied Mechanics Letters  11 (2021) 100253. doi: 10.1016/j.taml.2021.100253
[Abstract](307) [FullText HTML] (188) [PDF 3178KB](11)
Abstract:
To effectively simulate the fracture propagation in shale, the bedding plane (BP) effect is incorporated into the augmented virtual internal bond (AVIB) constitutive relation through BP tensor. Comparing the BP-embedded AVIB with the theory of transverse isotropy, it is found the approach can represent the anisotropic properties induced by parallel BPs. Through the simulation example, it is found that this method can simulate the stiffness anisotropy of shale and can represent the effect of BPs on hydraulic fracture propagation direction. Compared with the BP-embedded VIB, this method can account for the various Poisson's ratio. It provides a feasible approach to simulate the fracture propagation in shale.
Article
Experimental study of the effect of slotted blades on the Savonius wind turbine performance
Dominicus Danardono Dwi Prija Tjahjana, Zainal Arifin, Suyitno Suyitno, Wibawa Endra Juwana, Aditya Rio Prabowo, Catur Harsito
Theoretical and Applied Mechanics Letters  11 (2021) 100249. doi: 10.1016/j.taml.2021.000249
[Abstract](808) [FullText HTML] (385) [PDF 3798KB](36)
Abstract:
This study investigates the effect of Reynolds number on the performance of Savonius wind turbine with slotted blades. The turbine performance investigation was based on the torque coefficient (Ct), power coefficient (Cp), and tip speed ratio (TSR). The experiment used two number of blade configuration, blade overlap ratio of 10%, 12.5% and 20%, slotted position of 15%, 20%, 25% and 35%, and also slotted gap width of 3 mm, 5 mm, 7 mm, and 9 mm. The wind speed carried out in this experiment are 5.94 m/s, 6.46 m/s, 6.99 m/s, and 7.27 m/s, which are generated from the fan blowers as a wind source. The Savonius turbine with 10% overlap ratio shows the best performance. The highest Cp obtained is 0.138 by the variation of a 3 mm gap with Re of 1.44 × 104 and 0.526 tip speed ratio (TSR).