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Bedding plane-embedded augmented virtual internal bonds for fracture propagation simulation in shale

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.

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.

We analyze the error of large-eddy simulation (LES) in wall pressure fluctuation of a turbulent channel flow. To separate different sources of the error, we conduct both direct numerical simulations (DNS) and LES, and apply an explicit filter on DNS data to obtain filtered DNS (FDNS) data. The error of LES is consequently decomposed into two parts: The first part is the error of FDNS with respect to DNS, which quantifies the influence of the filter operation. The second part is the difference between LES and FDNS induced by the error of LES in velocity field. By comparing the root-mean-square value and the wavenumber-frequency spectrum of the wall pressure fluctuation, it is found that the inaccuracy of the velocity fluctuations is the dominant source that induces the error of LES in the wall pressure fluctuation. The present study provides a basis on future LES studies of the wall pressure fluctuation.

In this paper, we provide exact fast Fourier transform (FFT)-based numerical bounds for the elastic properties of composites having arbitrary microstructures. Two bounds, an upper and a lower, are derived by considering usual variational principles based on the strain and the stress potentials. The bounds are computed by solving the Lippmann-Schwinger equation together with the shape coefficients which allow an exact description of the microstructure of the composite. These coefficients are the exact Fourier transform of the characteristic functions of the phases. In this study, the geometry of the microstructure is approximated by polygonals (two-dimensional, 2D objects) and by polyhedrons (three-dimensional, 3D objects) for which exact expressions of the shape coefficients are available. Various applications are presented in the paper showing the relevance of the approach. In the first benchmark example, we consider the case of a composite with fibers. The effective elastic coefficients ares derived and compared, considering the exact shape coefficient of the circular inclusion and its approximation with a polygonal. Next, the homogenized elastic coefficients are derived for a composite reinforced by 2D flower-shaped inclusions and with 3D toroidal-shaped inclusions. Finally, the method is applied to polycristals considering Voronoi tessellations for which the description with polygonals and polyhedrons becomes exact. The comparison with the original FFT method of Moulinec and Suquet is provided in order to show the relevance of these numerical bounds.

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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.

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 (

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.

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 (

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.

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.

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.

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.

The complexity of the Portevin-Le Chatelier (PLC) effect in an Al alloy at different temperatures was analyzed by modified multiscale entropy. The results show that three evolutions of entropy with scale factor, i.e., near zero, monotonically increasing and peak-shape, were observed corresponding to the smooth curves, type-A serrations and type-B/-C serrations, respectively. The scale factor at the peak was one-third of the average serration period. The sample entropy increased initially and then decreased with temperature, which was opposite to the critical strain. It is also suggested that the type-A serrations corresponded to self-organized criticality and the type-B/-C serrations corresponded to chaos through the evolutions of entropy with scale factor.

Two kinds of analytical solutions are derived through Laplace transform for the equation that governs wave-induced suspended sediment concentration with linear sediment diffusivity under two kinds of bottom boundary conditions, namely the reference concentration (Dirichlet) and pickup function (Numann), based on a variable transformation that is worked out to transform the governing equation into a modified Bessel equation. The ability of the two analytical solutions to describe the profiles of suspended sediment concentration is discussed by comparing with different experimental data. And it is demonstrated that the two analytical solutions can well describe the process of wave-induced suspended sediment concentration, including the amplitude and phase and vertical profile of sediment concentration. Furthermore, the solution with boundary condition of pickup function provides better results than that of reference concentration in terms of the phase-dependent variation of concentration.

We propose a theoretical model for spatial variations of the temperature variance

The laser-induced porous graphene (LIG) prepared in a straightforward fabrication method is presented, and its applications in stretchable strain sensors to detect the applied strain are also explored. The LIG formed on the polyimide/polydimethylsiloxane (PI/PDMS) composite exhibits a naturally high stretchability (over 30%), bypassing the transfer printing process compared to the one prepared by laser scribing on PI films. The PI/PDMS composite with LIG shows tunable mechanical and electronic performances with different PI particle concentrations in PDMS. The good cyclic stability and almost linear response of the prepared LIG's resistance with respect to tensile strain provide its access to wearable electronics. To improve the PDMS/PI composite stretchability, we designed and optimized a kirigami-inspired strain sensor with LIG on the top surface, dramatically increasing the maximum strain value that in linear response to applied strain from 3% to 79%.

We investigate the evolution of interfacial gravity-capillary waves propagating along the interface between two dielectric fluids under the action of a horizontal electric field. There is a uniform background flow in each layer, and the relative motion tends to induce Kelvin-Helmholtz (KH) instability. The combined effects of gravity, surface tension and electrically induced forces are all taken into account. Under the short-wave assumption, the expansion and truncation method of Dirichlet-Neumann (DN) operators is applied to derive a reduced dynamical model. When KH instability is suppressed linearly by a considerably large electric field, our numerical results reveal that in certain regions of parameter space, nonlinear symmetric traveling wave solutions can be found near the minimum phase speed. Additionally, the detailed bifurcation structures are presented together with typical wave profiles.

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The impact attenuator is an essential system in both race cars and urban vehicles. The structure of an impact attenuator serves as a safety barrier between the impacted surface and the driver in an accident. Attenuator materials tend to have a high price; thus, alternative materials were explored in the current work, i.e., used cans from food and beverage containers. The study deployed a nonlinear finite element algorithm to calculate a series of impacts on the attenuator structures. The thickness of the cans and velocity of the impact were considered as the main parameters. Analysis results concluded that the attenuator's average energy was 16,000 J for a can thickness of 1 mm. This value is more than two times the 0.5 mm thick used cans. The attenuator's new design was then matched with an attenuator regulation, and the results surpassed the standard value of 7350 J.

Impact of viscous sublayer scale roughness elements on large scale flows have not been fully understood and require high resolution 3D flow measurements to unravel. However, existing approaches fail to provide sufficient resolution for such measurements to fully resolve the sublayer. In this study, we use digital Fresnel reflection holography to capture 3D flows within the viscous sublayer at sub-viscous resolutions. The measurement highlights the presence of novel flow structures at the scale of the sublayer, with strong spanwise meandering motions, of 2-3 viscous wall units, indicating a highly unsteady and accelerating flow within. The probability distribution of accelerations shows a stretched exponential shapes characteristic of highly intermittent turbulence seen under isotropic flows. The presence of flow structures even at the scale of the sublayer, i.e., below

The placement of pressure taps on the surface of the wind tunnel test model is an important means to obtain the surface pressure distribution. However, limited by space location and experimental cost, it is difficult to arrange enough pressure measuring taps on the surface of complex models to obtain complete pressure distribution information, thus it is impossible to obtain accurate lift and moment characteristics through integration. The paper proposes a refined reconstruction method of airfoil surface pressure based on compressed sensing, which can reconstruct the pressure distribution with high precision with less pressure measurement data. Tests on typical airfoil subsonic flow around flow show that the accuracy of lift and moment after the pressure integration reconstructed by 4-8 measuring points can meet the requirements of the national military standard. The algorithm is robust to noise, and provides a new idea for obtaining accurate force data from sparse surface pressure tests in engineering.

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2021, 11(1): 1 -1.
doi: 10.1016/j.taml.2021.100238

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2021, 11(1): 2 -15.
doi: 10.1016/j.taml.2021.100222

The amplitude and frequency modulation of near-wall flow structures by the large-scale motions in outer regions is studied in turbulent channel flows. The proper orthogonal decomposition (POD) method is applied to investigate the interactions between the near-wall motions and the large-scale flow modes of the outer regions based on two datasets from direct numerical simulation of turbulent channel flows at Reynolds numbers of 550 and 1000. The fluctuations in the fields

2021, 11(1): 16 -21.
doi: 10.1016/j.taml.2021.100225

Nowadays, studies on the mechanism of macro-scopic nonlinear behavior of materials by accumulation of micro-scopic degradation are attracting more attention from researchers. Among numerous approaches, multiscale methods have been proved as powerful and practical approaches in predicting macro-scopic material status by averaging and homogenizing physical information from associated micro-scopic material behavior. Usually in mechanical problem, the stress, consistent material modulus, and possible material state variables are quantities in interest through the upscaling process. However, the energy-related quantities are not studied much. Some initiative work has been done in the early year including but not limited to the Hill–Mandel condition in multiscale framework, which gives that the macro-scopic elastic strain energy density can be computed by volumetric averaging of that in the micro-scale. However, in the nonlinear analysis, the energy dissipation is an important quantity to measure the degradation status. In this manuscript, two typical multiscale methods, the first-order computational homogenization (FOCH) and reduced-order homogenization (ROH), are adopted to numerically analyze a fiber-reinforced composite material with capability in material nonlinearity. With numerical experiments, it can be shown that energy dissipation is the same for both approaches.

2021, 11(1): 22 -27.
doi: 10.1016/j.taml.2021.100226

In this paper, we propose a stable heat jet approach for accurate temperature control of the nonlinear Fermi-Pasta-Ulam beta (FPU-

2021, 11(1): 28 -34.
doi: 10.1016/j.taml.2021.100227

We successfully perform the three-dimensional tracking in a turbulent fluid flow of small axisymmetrical particles that are neutrally-buoyant and bottom-heavy, i.e., they have a non-homogeneous mass distribution along their symmetry axis. We experimentally show how a tiny mass inhomogeneity can affect the particle orientation along the preferred vertical direction and modify its tumbling rate. The experiment is complemented by a series of simulations based on realistic Navier–Stokes turbulence and on a point-like particle model that is capable to explore the full range of parameter space characterized by the gravitational torque stability number and by the particle aspect ratio. We propose a theoretical perturbative prediction valid in the high bottom-heaviness regime that agrees well with the observed preferential orientation and tumbling rate of the particles. We also show that the heavy-tail shape of the probability distribution function of the tumbling rate is weakly affected by the bottom-heaviness of the particles.

2021, 11(1): 35 -41.
doi: 10.1016/j.taml.2021.100228

Turbulent flows over rough surfaces widely exist in nature and industry. Investigating its mechanism is of theoretical and practical significance. In this work we simulate the turbulent channel flow with rough walls using large-eddy simulation with rough elements resolved using the curvilinear immersed boundary method and compare the results obtained in this work with those in the paper by Yuan and Piomelli (J. Fluid Mech. 2014), where the volume of fluid method was employed for modeling rough elements. The mean streamwise velocity profiles predicted by the two methods agree well with each other. Differences in Reynolds stresses and dispersive stresses are observed, which are attributed to the different approaches in dealing with the complex geometry of the rough surface.

2021, 11(1): 42 -47.
doi: 10.1016/j.taml.2021.100229

In this work we extend the method of the constrained large-eddy simulation (CLES) to simulate the turbulent flow over inhomogeneous rough walls. In the original concept of CLES, the subgrid-scale (SGS) stress is constrained so that the mean part and the fluctuation part of the SGS stress can be modelled separately to improve the accuracy of the simulation result. Here in the simulation of the rough-wall flows, we propose to interpret the extra stress terms in the CLES formulation as the roughness-induced stress so that the roughness inhomogeneity can be incorporated by modifying the formulation of the constrained SGS stress. This is examined with the simulations of the channel flow with the spanwise alternating high/low roughness strips. Then the CLES method is employed to investigate the temporal response of the turbulence to the change of the wall condition from rough to smooth. We demonstrate that the temporal development of the internal boundary layer is just similar to that in a spatial rough-to-smooth transition process, and the spanwise roughness inhomogeneity has little impact on the transition process.

2021, 11(1): 48 -53.
doi: 10.1016/j.taml.2021.100230

Dislocation creep at elevated temperatures plays an important role for plastic deformation in crystalline metals. When using traditional discrete dislocation dynamics (DDD) to capture this process, we often need to update the forces on

2021, 11(1): 54 -59.
doi: 10.1016/j.taml.2021.100234

The behaviors of a neutrally buoyant ellipsoidal particle in vortical flow confined by a microcavity are numerically studied using the Lattice-Boltzmann method. For specific initial position, an isolated ellipsoid may develop a stable limit cycle orbit inside microcavity due to the interaction between particle and the carrier flow. It is observed that ellipsoidal particles of different shapes exhibit two different stable rotational modes depending on the initial orientation and lateral position. A prolate spheroid tends to enter a tumbling mode whereas an oblate spheroid is apt to achieve a rolling mode. The evolution of rotational velocities along the stable orbit is also analyzed for particles of defferent shapes.

2021, 11(1): 60 -66.
doi: 10.1016/j.taml.2021.100220

In this work, a physics-informed neural network (PINN) designed specifically for analyzing digital materials is introduced. This proposed machine learning (ML) model can be trained free of ground truth data by adopting the minimum energy criteria as its loss function. Results show that our energy-based PINN reaches similar accuracy as supervised ML models. Adding a hinge loss on the Jacobian can constrain the model to avoid erroneous deformation gradient caused by the nonlinear logarithmic strain. Lastly, we discuss how the strain energy of each material element at each numerical integration point can be calculated parallelly on a GPU. The algorithm is tested on different mesh densities to evaluate its computational efficiency which scales linearly with respect to the number of nodes in the system. This work provides a foundation for encoding physical behaviors of digital materials directly into neural networks, enabling label-free learning for the design of next-generation composites.

2021, 11(1): 67 -72.
doi: 10.1016/j.taml.2021.100221

A composite absorber made of a polyurethane sponge and multi-layer micro-perforated plates is presented in this study. Results from an acoustic impedance tube test show that the polyurethane sponge can exhibits higher low-frequency sound absorption in front of the micro-perforated plate, while sound absorption at medium and high-frequencies remains low. The physical mechanism behind this is that the micro-perforated plate increases the denpth cavity. If the polyurethane sponge is placed behind the micro-perforated plate, the amplitude of the original absorption peak will remain constant, but the absorption peaks will shift to lower frequencies. The reason for this phenomenon is that porous materials with low flow resistance can be approximately equivalent to fluid, which not only does not affect the resonance absorption coefficient of micro-perforated plate, but also makes the peaks move to low frequency. This study has the potential applications in the sound absorption design of composite structure.

2019, 9(6): 339-352
doi: 10.1016/j.taml.2019.06.001

2019, 9(4): 236-245
doi: 10.1016/j.taml.2019.03.004

2020, 10(3): 141-142
doi: 10.1016/j.taml.2020.01.041

2020, 10(2): 116-119
doi: 10.1016/j.taml.2020.01.015

2018, 8(4): 252-256
doi: 10.1016/j.taml.2018.04.006

2020, 10(6): 377-381
doi: 10.1016/j.taml.2020.01.055

2020, 10(5): 327-332
doi: 10.1016/j.taml.2020.01.051

2018, 8(5): 299-303
doi: 10.1016/j.taml.2018.05.007

2019, 9(6): 403-408
doi: 10.1016/j.taml.2019.06.005