力学学报

REVIEW OF INTERFACIAL DEBONDING BEHAVIOR OF ADHESIVE STRUCTURES WITH SOFT MATERIALS

Zhu Zhongmeng, Yang Zhuoran, Jiang Han

Soft material has been widely used in soft robots, biomedicine, flexible electronics and other fields. In practical applications, soft material generally needs to be adhered to different types of substrate forming adhesive structures to accomplish specific functions. The interfacial performance of the adhesive system plays a key role in structural integrity and functional reliability. In this paper, the research efforts on the interfacial debonding behavior of adhesive structures with soft materials are systematically reviewed and summarized. The adhesive structures with soft materials can be classified into two types: (1) adhesive structures with “soft interface” in which stiff adherends are bonded by soft adhesives owning strong energy dissipative, typically viscoelastic, properties; (2) adhesive structures with “soft adherends” in which one or both of the adherends are significantly energy dissipative. In this paper, firstly, the specific mechanical characteristics and physical nature of the interfacial debonding behavior of the adhesive structures with soft materials are analyzed by comparing with those of the traditional “hard” adhesive structures. Secondly, the experimental characterization of the interfacial debonding behaviors of the adhesive structures with “soft interface” and “soft adherend” are summarized respectively. The effects of viscoelastic dissipative property of the adhesive interface and bulk adherends on the interfacial debonding mechanisms are analyzed respectively. Thirdly, the theoretical analysis methods for the interfacial debonding behavior of the adhesive structures with soft materials are reviewed and the relative theoretical models are summarized. Fourthly, the research progress of the numerical simulation, mainly based on the cohesive zone model (CZM) method, of the interfacial debonding behavior of the adhesive structures with soft materials is reviewed. Finally, based on the existing research progress, the challenges of the current research are put forward and the prospect of possible future research opportunities on the interfacial debonding behavior of adhesive structures with soft materials is discussed.

2021, 53(7): 1807-1828. doi: 10.6052/0459-1879-21-131

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STATISTICAL CHARACTERISTICS OF PRESSURE FLUCTUATION IN SHOCK WAVE AND TURBULENT BOUNDARY LAYER INTERACTION

Tong Fulin, Duan Junyi, Zhou Guiyu, Li Xinliang

Shock wave and turbulent boundary layer interaction widely exists in the internal and external flow of high-speed aircraft. The aerodynamic performance and flight safety of aircraft are seriously affected by the strong pressure fluctuation in the interaction region. To investigate statistical characteristics of fluctuating pressure, the interaction between an incident shock of 33.2° and a spatially developed Mach 2.25 turbulent boundary layer is analyzed by means of direct numerical simulation (DNS). The numerical results have been carefully validated against with previous experiment and DNS at similar flow conditions in terms of mean velocity profile, turbulence intensity and wall pressure distribution. Statistics at the wall and in the outer layer, including fluctuation intensity, power spectral density, two-point correlation and space-time correlation, are quantitatively compared. The differences between them are analyzed in detail. It is found that the effect of the shock interaction on the wall-pressure fluctuation and the fluctuating pressure in the outer layer are utterly different. Based on the analysis of the power spectra density, the fluctuations in the separated region are both characterized by the low-frequency content, but in the reattachment region, the peak frequency of outer pressure fluctuations quickly shifts to higher frequency, with the low-frequency energy of wall-pressure fluctuation still being predominant. It is identified that the two-point correlations of pressure fluctuation at the wall and in the outer layer are both more elongated in the spanwise direction than that in the streamwise direction. The integral scale at the wall is generally increased, while the one in the outer layer increases sharply after passing the shock and then gradually decreases. The analysis of space-time correlation indicates that the iso-correlation contours are similar to the elliptical distribution and the convection velocity deduced by the correlation is dramatically decreased. Downstream of the interaction, the convection velocity in the outer layer is higher than that of wall-pressure fluctuation.

2021, 53(7): 1829-1841. doi: 10.6052/0459-1879-21-094

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COMPARISON OF SUB-GRID-SCALE MODELS BASED ON PREDICTION OF COHERENT STRUCTURES IN PLANE TURBULENT JETS

Liu Qilin, Lai Huanxin

A compressible plane jet at Mach 0.9 is numerically studied by large-eddy simulation. The governing equations are discretized by fourth-order spatial and third-order temporal schemes. Five sub-grid-scale (SGS) models, namely, the standard Smagorinsky model (SM), the coherent structure kinetic model (CKM) and the selective mixed-scale model (SMSM), the localized dynamic Smagorinsky model (LDSM), and the coherent-structure Smagorinsky model (CSM), are employed for closure of the sub-grid scale (SGS) terms, respectively, and compared. Proper orthogonal decomposition (POD) method is applied to extract the leading modes of the fluctuating velocity components, i.e., $u'$ in the streamwise, $v'$ in the lateral and $w'$ in the spanwise. The averaged flow fields, dissipation, the instantaneous vortical structures and the coherent structures represented by the leading POD modes, are compared. The leading POD modes of $u'$ are two longitudinal stripes with fracted contours in the turbulent region, representing the multi-scaled flow and the decay of fluctuation strength. The leading modes of $v'$ are a row of ribs with the lateral size growing along the streamwise, while the modes of $\left( {u', v'} \right)$ are in a circular flow pattern around the ends of the ribs. The circular pattern penetrates both the jet flow and the peripheral flow, representing the flow entrainment. The leading modes of $w'$ are a train of ridges along streamwise. Their positive and negative values represent the spanwise stretching pattern of the coherent structures. In comparison of these five SGS models, the instantaneous multi-scale vortical flow is not effectively predicted by the SM and the CKM, as the small vortical scale is smeared. The POD modes are found to be sensitive to the sub-grid dissipation, since the valley regions of the mode of $u'$ coincide with the peak dissipation regions predicted by the CKM. The circular flow pattern is also not clearly predicted by the CKM. Neither the ridge pattern of the mode of $w'$ is predicted by the SM. On the other hand, the multi-scales turbulent flow and the flow patterns of POD modes are well predicted by the CSM, the SMSM, and the LDSM, in which the CSM is computationally more efficient.

2021, 53(7): 1842-1855. doi: 10.6052/0459-1879-21-145

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INVESTIGATIONS ON THE CONTROL OF WAKES DOWNSTREAM OF A ROTARY OSCILLATING PLATE

Chen Guoxiao, Liu Zhe, Shao Chuanping

The vortex wake of a flutter bridge deck can be simulated by the flow across a forced rotary oscillating plate. Two narrow strips of width ratio b/H = 0.33 are set symmetrically on the upper and lower sides of an oscillating plate of chord to thickness ratio B/H = 5, to suppress synchronized vortex shedding in the wake. The method of numerical simulation and experimental validation is used, and the ranges of amplitude and frequency of oscillation investigated are β = 0° ~ 10° and f_eH/V_∞ = 0 ~ 0.0857 respectively, and the Reynolds number Re = V_∞H/ V_∞ = 2800, where V_∞ is velocity of on-coming flow. Three kinds of stream-wise strip positions, i.e. the front edge, mid-chord and trailing edge of the plate are studied respectively, with transverse location y/H of the strip as varying parameter. The results of experiment demonstrate that, in a certain range of strip location y/H, and β = 0° ~ 7.5°, f_eH/V_∞ = 0 ~ 0.08, the peak to peak ratio of power spectra of fluctuating velocities in the wakes with and without control can be much lower than 1, and the minimum is about 0.3. The results of simulation show that, in β = 0° ~ 7.5° and a certain range of f_eH/V_∞, the root mean square values of fluctuating torque and lift of the plate can be considerably reduced, and the top reductions are 43% and 80% respectively, if the mid-chord strip position is in the vicinity of y/H = ±1. The 1st and 2nd eddy viscosity coefficients are introduced to link the normal and shear turbulent stresses in the wake with the gradients of amplitudes of the perturbation velocities, and a linear stability equation is derived. Stability analysis indicates that, the maximum amplification factor of perturbation ω_{i max} can be drastically reduced, and the frequency range of perturbation with maximum growth rate is substantially narrowed by the control. The application of the strips alters the velocity profiles and promotes the eddy viscosity, therefore weakens the instability of the wake.

2021, 53(7): 1856-1875. doi: 10.6052/0459-1879-20-423

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CROSS-FLOW VORTEX-INDUCED VIBRATION OF A FLEXIBLE RISER WITH INTERNAL FLOW IN SHEAR CURRENT

Duan Jinlong, Zhou Jifu, Wang Xu, Chen Ke

As an important component transporting resources such as oil and mineral ores mixture from the seabed to the surface in ocean engineering, vortex-induced vibration (VIV) of flexible risers can be encountered when the risers are subjected to the external environmental conditions. As VIV can lead to structural fatigue for the riser system, which threatens to the facility safety during deepsea resource exploitation, it is of great significance to investigate VIV mechanism and dynamics. Therefore, VIV dynamics of a flexible fluid-conveying riser undergoing external shear current is studied based on the combination of the Euler-Bernoulli beam theory and the semi-empirical hydrodynamic model. The finite element method and Newmark-β method are adopted to discretize and solve the governing equation. The model is firstly validated by comparing with the experimental data in order to examine the accuracy of the present model. Subsequently, cross-flow (CF) VIV response of the fluid-conveying riser is mainly examined and analyzed while various internal flow velocity and fluid density are considered and changed. The results show that when the flexible riser is subjected to both internal flow and shear current, there appears multi-frequency response for CF VIV. And the CF vibrating frequency and the CF root mean square (RMS) displacement are evidently influenced by the internal flow velocity and fluid density. With the increase of the internal flow velocity and fluid density, the CF vibrating frequency decreases while the RMS displacement shows an increasing trend in CF direction. Furthermore, in addition to the variation of the CF vibrating frequency and RMS displacement, the change of internal flow densities can cause notable mode and frequency transitions.

2021, 53(7): 1876-1884. doi: 10.6052/0459-1879-21-171

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MECHANISM ANALYSIS ON THE EFFECT OF CIRCULARIZATION ON THE WINDING CHARACTERISTICS OF A FORCED VIBRATING SQUARE COLUMN

Cheng Youliang, Jiao Shenli, Xu Qiang, Liu Xin

In order to analyze the effect mechanism of circularization on the winding characteristics of the forced vibrating square column at low Reynolds number, the secondary development of Ansys Fluent software was carried out to program the periodic forced vibration of the column, that is, the DEFINE_ CG_MOTION macro in the user-defined function (UDF) was used, and the computational domain of the flow field was divided into some regions in order to realize the forced vibration of the column by using the dynamic layer method in the dynamic grid technique, so as to realize the simulation of the fluid-solid coupling of the column-wound flow field. At Reynolds number Re = 200, considering the influence of different rounding angles of the square column cross-section, numerical simulation was made for the flow around five forced vibration square columns with rounded corners r/D = 1/2, 1/4, 1/5, 1/8 and 0 under uniform flow, and the variation laws of the drag coefficient, eddy volume and locking interval of the forced vibrating square column under these five parameters were analyzed to clarify the effect mechanism of circularization on the stability of the forced vibrating square column. It is shown that the lift and resistance coefficients of the rounded square column are significantly reduced with increasing rounded angle compared with the sharp-angled square column; the vortex shedding mode of the rounded square column under low amplitude ratio is 2S mode, and the vortex trails become narrower; the locking interval range is basically symmetric about F = 1, and the trend of the locking interval is similar to that of the cylinder.

2021, 53(7): 1885-1899. doi: 10.6052/0459-1879-21-066

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ANALYSIS OF FLOW CHARACTERISTICS AROUND A ROTATING CYLINDER

Xu Yihang, Chen Shaosong

The flow field behind a rotating cylinder with Reynolds number Re = 20000 ~ 90000 and relative speed ɑ = 0 ~ 0.72 was measured experimentally, and the velocity distribution and turbulence distribution at different sections behind the rotating cylinder were analyzed. The flow around a rotating cylinder is numerically simulated by LES method, and the characteristics of the flow field around a rotating cylinder are analyzed. Finally, the theoretical model is used to analyze the flow field variation and came to the following conclusions: When the cylinder rotates counterclockwise, with the increase of the relative speed at the same Reynolds number, the position of the velocity mutation below the wake region of the rotating cylinder moves up with the increase of the relative speed, while the position of the velocity mutation above remains unchanged. With the increase of Reynolds number, the position of velocity mutation below the wake region of the rotating cylinder moves down to a small extent. Through numerical simulation, it is found that the position of the lower vortex behind the cylinder moves up obviously after the cylinder rotates, and the amplitude is large. The lower free shear layer has obvious upward movement, while the upper free shear layer has little change in position. Finally, through theoretical analysis, it is found that the upward movement of the lower vortex on the rear side of the rotating cylinder has a significant effect on the lift force of the rotating cylinder. Under the condition of high Reynolds number and low relative speed, the change of the lower vortex position on the rear side of the rotating cylinder has an important effect on the lift force of the rotating cylinder and the change of the free shear layer in the wake region.

2021, 53(7): 1900-1911. doi: 10.6052/0459-1879-21-153

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A FAST SOLVER BASED ON DEEP NEURAL NETWORK FOR DIFFERENCE EQUATION

Jiang Zichao, Jiang Junyang, Yao Qinghe, Yang Gengchao

In recent years, artificial neural networks (ANNs), especially deep neural networks (DNNs), have become a promising new approach in the field of numerical computation due to their high computational efficiency on heterogeneous platforms and their ability to fit high-dimensional complex systems. In the process of numerically solving the partial differential equations, the large-scale linear equations are usually the most time-consuming problems; therefore, utilizing the neural network methods to solve linear equations has become a promising new idea. However, the direct prediction of deep neural networks still has obvious shortcomings in numerical accuracy, which becomes one of the bottlenecks for its application in the field of numerical computation. To break this limitation, a solving algorithm combining Residual network architecture and correction iteration method is proposed in this paper. In this paper, a deep neural network-based method for solving linear equations is proposed to accelerate the solving process of partial differential equations on heterogeneous platforms. Specifically, Residual network resolves the problems of network degradation and gradient vanishing of deep network models, reducing the loss of the network to 1/5000 of the classical network model; the correction iteration method iteratively reduce the error of the prediction solution based on the same network model, and the residual of the prediction solution has been decreased to 10⁻⁵ times of that before the iteration. To verify the effectiveness and universality of the proposed method, we combined the method with the finite difference method to solve the heat conduction equation and the Burger’s equation. Numerical results demonstrate that the algorithm has more than 10 times the acceleration effect for equations of size larger than 1000, and the numerical error is lower than the discrete error of the second-order difference scheme.

2021, 53(7): 1912-1921. doi: 10.6052/0459-1879-21-040

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THE EFFECTIVE VISCOSITY OF A SUSPENSION OF POROUS PARTICLES BASED ON THE DARCY-STOKES COUPLING MODEL

Hu Yang, Peng Wei, Li Decai

Particle suspensions exist widely in nature and engineering applications, and their viscous characteristics have an important influence on their flow behavior. Based on the Darcy-Stokes coupling model, the analytical formulas of effective viscosity of dilute suspensions containing porous particles are derived in this paper. Firstly, an auxiliary problem is solved, that is, the disturbance caused by porous media spheres in the flow field with linear distribution under the condition of low Reynolds number. The fluid flows in the free-flow domain and porous medium are governed by the Stokes equation and Darcy’ law, respectively. The mass conservation law, the balance of normal forces, and the Beavers-Joseph (-Saffman) interface condition are used at the fluid–porous interface. An analytical solution for the present coupled free-flow and porous-medium system is derived by using the undetermined coefficient method. Then the additional heat dissipation rate caused by the porous media particle is calculated. Intrinsic viscosity of the porous media suspension under the condition of low concentration is determined as a function of the Darcy number and the Beavers-Joseph coefficient, which is based on the additional heat dissipation rate under the condition of low concentration. It is found that the intrinsic viscosity increases with increasing the Beavers-Joseph coefficient, and the larger the Beavers-Joseph coefficient is, the slower the increase of the intrinsic viscosity. When Darcy number is in the range of ${10^{ - 6}}$ to ${10^{ - 4}}$, the intrinsic viscosity is close to 2.5, which was consistent with the classical Einstein viscosity formula. When Darcy number is in the range of ${10^{ - 4}}$ to ${10^{ - 1}}$, the intrinsic viscosity decreases rapidly, so the effective viscosity coefficient of porous media suspension is closer to the viscosity of the based fluid. At last, the present effective viscosity formula is compared with that obtained by the Darcy-Brinkman equation coupling with the shear stress jump condition. It can be found that the effective viscosities obtained two different models agree well with each other in the low Darcy number regime when the sum of the Beavers-Joseph coefficient and the shear stress jump coefficient is unity.

2021, 53(7): 1922-1929. doi: 10.6052/0459-1879-21-144

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MULTI-FIELD COUPLING EFFECT AND SIMILARITY LAW OF FLOATING ICE BREAK BY VEHICLE LAUNCHED UNDERWATER

Yue Junzheng, Wu Xianqian, Huang Chenguang

Fluid structure coupling effect and dynamic load characteristics are the important basis of the safety evaluation of the vehicle in the process of underwater launching and floating ice break. In this paper, the main control parameters which influence the dynamic load and the stress at the head of the vehicle, as well as the similarity law, are obtained by dimensional analysis. Based on the LS-DYNA fluid structure coupling method, the numerical simulations for underwater launched vehicle impacting with floating ice have been conducted, and the load characteristics of the vehicle under the conditions of different impact velocities, different ice thicknesses and different ice sizes are obtained. The simulated results show that, the higher the initial velocity of the vehicle is, the greater the distinction of the influence of different ice targets on the overload and the stress at the head of the vehicle is, which is mainly due to the different destruction of different ice targets under the strong water impact generated by the underwater motion of the vehicle in the early stage. For the infinite ice sheet, when its thickness is more than 3 times the vehicle diameter, the penetration into the ice appears stable at the later stage, the rigid body acceleration and the stress at the head of the vehicle are only related to the penetration velocity and the dynamic mechanical properties of the ice; for the thinner ice target, the higher the velocity of the vehicle is, the smaller the stress at its head is. This is because the early damage of the ice under the water impact generated by the higher speed motion of the vehicle is more serious, the ice layer is easy to crack and bulge, resulting in the smaller stress at the vehicle head. For the broken ice whose radial dimension is 6 times the vehicle diameter, when its thickness is also greater than 5 times the vehicle diameter, the influence on the vehicle motion is almost the same as that of the infinite ice sheet; when its thickness is less than 3 times the diameter of the vehicle, the ice size effect can be ignored only when the vehicle velocity is low. In addition, by comparing the influence of broken ice and infinite ice on the vehicle motion, it can be observed that, the thicker ice got less damage by the water impact at the early stage, thus the influence of broken ice and infinite ice are basically the same; while the thinner ice is seriously damaged by the water impact, resulting in little influence of broken ice and infinite ice on the vehicle motion; only for the ice targets with medium thickness, their damage degrees are related to the radial size under the condition of the higher vehicle velocity, for instance, when the initial vehicle velocity is 40 m/s, there is a great damage difference between the two kinds of ice targets with dimensionless thickness 3 at the early stage, which leads to a significant difference in the influence on the vehicle motion at the later stage.

2021, 53(7): 1930-1939. doi: 10.6052/0459-1879-21-082

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MECHANICAL PROPERTIES ANALYSIS OF A NEW ENERGY ABSORBING STRUCTURE WITH NEGATIVE STIFFNESS

Hou Xiuhui, Lü You, Zhou Shiqi, Zhu Zhiwei, Zhang Kai, Deng Zichen

As a kind of mechanical metamaterial with wide application prospect, negative stiffness structures show significant advantages in energy absorption, vibration attentuation, and noise reduction . However, their engineering applications are severely limited attributed to the low specific energy absorption efficiency and non-autonomous spring-back of negative stiffness structures with the speciality of multi-stability. In order to solve this problem, by means of cell configuration design, a new kind of three-dimensional negative stiffness structure with the characteristic of autonomous spring-back is proposed in this paper. For this negative stiffness cells in series, the self rebound of curved beams during the loading and unloading process is used to realize the cyclic loading and multiple reuse of the structure.The multi-stability is restrained by adding a groove of certain depth. The buckling mode is selected via the adjustment of side wall thickness. The difference between critical loads of negative stiffness is thus enlarged, accordingly, the energy absorption efficiency is significantly improved. Then in order to achieve high energy absorption under complex load environments, the gradient design of structure size is carried out, and a gradient negative stiffness structure is proposed. The energy absorption efficiency of gradient negative stiffness structure and uniform negative stiffness structure under different load cinditons is compared by finite element simulations. Analytical and numerical results reveal that for the newly developed negative stiffness structure, not only the feature of autonomous spring-back is achieved, but also the energy absorption ability is improved. Moreover, different critical load maximums for negative stiffness are obtained for the gradient structure due to different microstructure sizes, which makes it to exhibit better energy absorption efficiency on the basis of realizing autonomous spring-back under various impact load environments. The new energy-absorption structure proposed in this paper provides technical support for engineering applications such as vibration attenuation and structure reorganization.

2021, 53(7): 1940-1950. doi: 10.6052/0459-1879-21-083

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AN UNCONDITIONALLY STABLE METHOD FOR TRANSIENT HEAT CONDUCTION

Ji Yi, Xing Yufeng

Time-dependent transient heat conduction problems are widely encountered in aerospace, civil engineering, metallurgical engineering, etc., and for such problems, accurate and fast numerical approaches have always attracted attention in the past decades. To achieve this goal, this paper proposes an unconditionally stable single-step time integration method for general transient heat conduction systems. In the proposed method, the temperature vector and its time derivative are formulated independently by the Langrage interpolation function, and then the relation between the temperature vector and its time derivative is defined with the weighted residual method. Theoretical analysis, including convergence rate and amplification factor, illustrates that the proposed method is strictly second-order accurate for the temperature vector and its time derivative, and it has the strong algorithmic dissipation (L-dissipation), meaning that it can quickly filter out the unwanted numerical oscillations in the high-frequency range. At present, most existing time integration methods, such as the Crank-Nicolson method and the Galerkin method, are unconditionally stable for linear transient heat conduction systems, but they are conditionally stable for nonlinear ones. To this end, this work improved the stability analysis theory for nonlinear transient heat conduction systems proposed by Hughes and used the improved stability analysis theory to design the free parameters of the proposed method. Because of this reason, the proposed method is unconditionally stable for both linear and nonlinear transient heat conduction problems. Due to the desirable algorithmic stability, the proposed method can still provide accurate and stable predictions for nonlinear transient heat conduction problems where the excellent Crank-Nicolson method fails. Some linear and nonlinear transient heat conduction problems are solved in this paper, and the results of these problems show that compared to the currently popular time integration methods, such as the Crank-Nicolson method and the backward difference formula, the proposed method enjoys noticeable advantages in accuracy, dissipation and stability.

2021, 53(7): 1951-1961. doi: 10.6052/0459-1879-21-140

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REAL TIME MEASUREMENT AND ANALYSIS OF FULL SURFACE CRACKING CHARACTERISTICS OF CONCRETE BASED ON PRINCIPAL STRAIN FIELD

Gu Liuning, Gong Wenran, Shao Xinxing, Chen Jie, Dong Zhiqiang, Wu Gang, He Xiaoyuan

The measurement of the crack propagation process is significant to reveal the failure mechanism and evaluate the mechanical properties of concrete structure. This paper presents a method of crack location and width measurement based on the deformation field of concrete surface. The high-resolution deformation field of the concrete specimens is obtained by using multi-camera digital image correlation method at first. It is found that the virtual principal strain field around the crack obviously differs from that in uncracked zone because of the gradient of displacement field caused by crack, and the principal strain field can be regarded as approximately Gaussian distributed in the normal direction of the crack. A new method of crack location based on the principle strain field is proposed based on the Steger algorithm which is widely applied in laser stripe center extracting, and the difference of in-plane displacement vectors on the normal direction between two sides of the crack is obtained. The projection along the normal direction is taken as the width of mode I crack, while the projection along the normal vertical direction is taken as the width of mode II crack. The experiment of simulating crack propagation is performed by using a high precision translation table to verify the measurement accuracy of crack width measurent. The results of the experiments show that the measurement error of crack width is between 0.010 pixel and 0.017 pixel, which is consistent with the theoretical prediction. The standard deviation is between 0.006 pixel and 0.008 pixel, which illustrates that the measurement accuracy of the proposed method is high. The accuracy of the proposed method is better than that of image-based crack measurement method at the same image resolution. The method proposed can automatically measure crack propagation in real time, which provides a reliable and accurate method for the concrete experiment.

2021, 53(7): 1962-1970. doi: 10.6052/0459-1879-21-107

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INTERNAL SPECKLE PATTERN QUALITY ASSESSMENT AND OPTIMAL SELECTION OF VOXEL POINTS FOR DIGITAL VOLUME CORRELATION

Zou Xiang, Zhang Xuanhao, Wang Yanjun, Pan Bing

Digital volume correlation (DVC) is a powerful experimental tool for quantitative 3D internal deformation measurement throughout the interior of materials or biological tissues. By comparing the volumetric images acquired at the reference and deformed states by a volumetric imaging facility (e.g., X-ray CT), DVC provides full-field displacements with subvoxel accuracy and full-field strain maps. When using DVC method for internal deformation measurement, the quality of internal speckle pattern of a test sample has an important impact on the accuracy and precision of the measured displacements. In this work, theoretical analysis and numerical simulation experiments are firstly performed to assess the quality of internal speckle patterns. The results show that the displacement measurement error of DVC is negative correlation with the sum of square of subvolume intensity gradient (SSSIG) of a subvolume. Thus, the SSSIG value of a subvolume can be used as a simple and effective metric for quality assessment of its internal speckle pattern. In practical DVC analyses, increasing the SSSIG parameter of a subvolume helps to improve the measurement accuracy and precision of DVC. Despite the SSSIG in a subvolume can be increased by enlarging its subvolume size, this simple approach, however, would lead to increased calculation burden. With a purpose to increase SSSIG without significantly increase the amount of calculation, this paper further proposes a method for optimal selection of calculation voxel points in subvolumes. Specifically, the voxel points with small gray gradients in a subvolume are excluded from DVC calculation to decrease the amount of calculation when increasing the size of the subvolume. The efficacy of the presented voxel point optimal selection method is validated by analyzing computer simulated and experimentally obtained volume images. Experimental results reveal that the proposed voxel point selection method is capable of reducing the calculation burden when increasing the subvolume size to increase the SSSIG parameters.

2021, 53(7): 1971-1980. doi: 10.6052/0459-1879-21-158

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SUCTION FORCE ANALYSIS FOR DIGITAL LIGHT PROCESSING-BASED PROJECTION STEREOLITHOGRAPHY

Fan Xuyu, Liang Haiyi

Digital light processing (DLP)-based projection stereolithography is one of the most important photo-polymerization based additive manufacturing technologies that has distinctive advantages such as high-resolution and fast printing speed. But the excessive suction force in the liquid resin film limits the further improvement of printing speed. The existing researches mainly focus on the improvement of the transparent window of the resin tank and the technological process while the mechanism of suction force is poorly understood. In this work, a multi-physical model coupled with resin flow, free radical polymerization and phase transition is established. The evolution process of the resin liquid film is studied under the combined action of mass transfer, photopolymerization, curing deposition and oxygen polymerization inhibition by numerical simulation. It is found that the solid-liquid interface presents a stable non-uniform wave attenuation morphology and the liquid film thickness is small and fluctuates sharply at the boundary which is completely different from the assumption of flat interface in previous research. The effects of elevating velocity, oxygen concentration distribution and UV intensity on the interface morphology and suction force are discussed. The results indicate that increasing the equilibrium concentration of oxygen and decreasing the UV intensity can effectively reduce the suction force while significantly affect the printing precision. We propose that adjusting the distribution of UV intensity can improve the inhomogeneity of the interface morphology and is an effective measure to reduce the suction force and increase the printing speed. This research has important reference significance for the study of different types of photo-polymerization based additive manufacturing technologies.

2021, 53(7): 1981-1991. doi: 10.6052/0459-1879-21-099

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INVERSE DESIGN OF PHONONIC CRYSTALS BY ARTIFICIAL NEURAL NETWORKS

Cao Leilei, Zhu Wang, Wu Jianhua, Zhang Chuanzeng

Phononic crystals represent a special kind of artificial periodic composite materials. The peculiar band-gap characteristics provide potential applications in the vibration reduction, wave filtering, sound insulation and acoustic functional devices. However, how to accurately manipulate acoustic and elastic waves is a major challenge for designing phononic crystals. The conventional design method is based on matching the specific application requirements by analyzing and adjusting the geometrical and material parameters of the phononic crystal structures. This method has a low efficiency and can hardly achieve the optimal performance. An artificial neural networks inverse design method for muti-layered phononic crystals based on the Softmax logistic regression and the multi-task learing is proposed in this study. In the proposed method, the Softmax logistic regression is used to choose the material type and the multi-task learing is used to determine the material distribution for each area of the multi-layered structure, so the phononic crystal reverse design problem is transformed into the classification problem of multi-component materials for the unit cell by the proposed method. First, a large number of the samples for the topological structures are randomly generated. Second, the band-gap structures of the samples are obtained by parallel finite element calculation. After that, the relationship between the topological structures and the band-gaps are established by the neural networks. Finally, the trained neural network is ultimately employed to design a phononic crystal structure with the targeted band-gaps, that is, the targeted band gap is used as the input of the neural network, and the trained neural network will output the corresponding cell topology of the phononic crystal unit cell directly. The example shows that the proposed method can obtain one-dimensional (1D) phononic crystals with the targeted band-gaps for the specified application requirements quickly and efficiently. This method provides a new way for the inverse design of phononic crystals.

2021, 53(7): 1992-1998. doi: 10.6052/0459-1879-21-142

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EXPLICITLY MODELING PERMANENT SET AND ANISOTROPY PROPERTY INDUCED BY STRESS SOFTENING FOR RUBBER-LIKE MATERIALS

Wang Xiaoming, Wu Rongxing, Jiang Yi, Xiao Heng

Stress softening, known as the Mullins effect, is observed in rubber-like materials after initial loading cycles. Experimental observations have shown that the Mullins effect leads to a permanent set and induces anisotropic properties. A multi-axial, compressible strain energy function based on the Hencky strain is proposed to account for the stress softening and simulate the permanent set and anisotropic properties by introducing two variables, separately characterizing the permanent set and anisotropic properties, which are dependent on dissipation. A comprehensive, explicit shape function is proposed by using the spherical coordinate system to make the model effective in arbitrary direction. The new model exhibits isotropic properties when it not yet induced stress softening, and becomes anisotropy when the Mullins effect occurs. The residual strain increases and reach a fixed value as the loading-unloading cycles proceeds, and the anisotropy becomes more obvious. The simulation results are shown good accord with the classical experimental data and successfully forecast the permanent set and anisotropic properties induced by stress softening.

2021, 53(7): 1999-2009. doi: 10.6052/0459-1879-21-060

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CAPUTO Δ-TYPE FRACTIONAL TIME-SCALES NOETHER THEOREM

Tian Xue, Zhang Yi

The time-scales theory combines differential equations theory with difference equations theory, and fractional calculus can provide more realistic models in practical problems. The fractional time-scales calculus has attracted much attention because it can unify continuous fractional systems and discrete fractional systems. Combining the time-scales calculus and the fractional calculus, we focus on the fractional time-scales Noether theorem with Caputo Δ-derivatives, which provides a new perspective for studying the dynamic behaviors of complex systems. This paper begins with a review of the definitions of fractional time-scales integrals and derivatives. Then, according to the proposed Caputo Δ-type fractional time-scales Hamilton principle, the fractional time-scales Lagrange equation is derived. Under certain conditions, the fractional time-scales Lagrange equation can be reduced to the time-scales Lagrange equation, the Caputo-type fractional Lagrange equation and the classical Lagrange equation. Furthermore, in the two cases of special infinitesimal transformations and general infinitesimal transformations, the definitions and criteria of Caputo Δ-type fractional time-scales Noether symmetries are given. In addition, the fractional time-scales Noether theorem under special infinitesimal transformations (Theorem 1) and the fractional time-scales Noether theorem under general infinitesimal transformations (Theorem 2) are proposed and proved. When $\alpha=1$, Theorem 1 can be reduced to the classical time-scales Noether theorem under special infinitesimal transformations, and Theorem 2 becomes the time-scales Noether theorem obtained by the generalized Jost method. Not only that, but Theorem 2 can be reduced to the Caputo-type fractional Noether theorem if $T=\mathbb{R}$. At the end of this paper, the fractional time-scales Kepler problem in the plane and the fractional time-scales single freedom linear vibration system are taken as examples to verify the correctness of theorems.

2021, 53(7): 2010-2022. doi: 10.6052/0459-1879-21-108

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DESIGN AND DYNAMIC ANALYSIS OF A NOVEL BIO-INSPIRED ERECTING STRUCTURE

Qian Jiawei, Sun Xiuting, Xu Jian, Fang Hongbin

Since organisms can accomplish specific tasks through various motion forms, bionic design methods have been received extensive attention from scholars. Inspired by the fact that earthworms have excellent mobility and adaptability in a variety of environments, earthworm-like robots have been proposed and applied in search and rescue, medical treatment and other fields. However, existing earthworm-like robots generally realize rectilinear motion through axial deformation of its body segments, which cannot be applied to realize the erecting function of snake organisms. In order to solve the problem that existing earthworm-like robot cannot erect, a bio-inspired flexible joint with nonlinear multi-stable property is proposed. Based on the proposed bio-inspired flexible joint, a multi-segment bio-inspired erecting structure is built to realize the erecting function of inchworms, snakes and other organisms. First, the model of the bio-inspired erecting joint is proposed. The potential energy of multi-segment bio-inspired erecting structure is obtained, and the dynamic model of the multi-segment bio-inspired erecting structure is established. Then, based on the potential energy and extremum principle, the structural design criteria is proposed to realize required erecting configuration. The effectiveness of structural design criteria is verified and the condition to trigger required configuration is studied by using the dynamic model. Finally, according to different design requirement for the number of erecting segments, corresponding bio-inspired erecting structure is designed. The results show that the design criteria of structural parameters can make the multi-segment bio-inspired erecting structure reach the required erecting configuration and maintain stable at the required erecting configuration. Besides, based on the basin of attraction of different stable configurations, the configuration triggering criteria of the bio-inspired erecting structure is studied, and the configuration triggering criteria composed of the excitation variables and configuration variables is revealed, which provide a theoretical basis for configuration switching of the bio-inspired erecting structure. The bio-inspired erecting structure proposed in this paper provide guidelines for function expansion of the earthworm-like robot. It is also a further improvement of the bionic design theory.

2021, 53(7): 2023-2036. doi: 10.6052/0459-1879-21-176

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COMBINED CONTROL OF VEHICLE SUSPENSION WITH FRACTIONAL-ORDER MAGNETORHEOLOGICAL FLUID DAMPER MODEL

Zhang Wenjing, Niu Jiangchuan, Shen Yongjun, Wen Shaofang

The fractional-order Bingham model of magnetorheological fluid damper has simple structure and can better describe the hysteretic characteristics of the system. The vibration control of a nonlinear vehicle suspension system with magnetorheological fluid damper under harmonic excitation is studied, where the single-degree-of-freedom 1/4 vehicle suspension system with fractional-order Bingham model of magnetorheological fluid damper is considered. The primary resonance response of suspension system with fractional-order Bingham model under sky-hook damping semi-active control is analyzed, and the approximate analytical solution is obtained by means of averaging method. The amplitude-frequency response equation of the steady-state solution of the suspension system is obtained, and the stability condition of the suspension system is also obtained according to Lyapunov’s stability theory. By comparing the amplitude-frequency response curves of the numerical solution and approximate analytical solution, the accuracy of the approximate analytical solution has been verified. The influence of semi-active control on the ride comfort of the vehicle is illustrated by the root mean square values of acceleration of the sprung mass in the vertical direction, it is found that the semi-active control strategy of sky-hook damping can not improve the ride comfort of vehicle in low frequency excitation region of road. Therefore, a combined control strategy of passive control and semi-active control is proposed, and the influence of semi-active control parameter on the vibration control effect is analyzed. The results show that the combined control strategy can not only improve the ride comfort of the vehicle, but also effectively suppress the primary resonance vibration amplitude of suspension system.

2021, 53(7): 2037-2046. doi: 10.6052/0459-1879-21-137

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RESEARCH OF LSTM MODEL-BASED INTELLIGENT GUIDANCE OF FLIGHT AIRCRAFT

Wang Ren, Hui Junpeng, Yu Qidong, Li Tianren, Yang Ben

The breakthrough of artificial intelligence provides a new technical approach for the research of aircraft reentry guidance. Aiming at the disadvantage in predictor-corrector guidance, where a large amount of integrations need to be calculated in the prediction step and the bank angle amplitude is iteratively solved based on secant method in the correction step. All the above calculation are difficult to meet real-time demand. Moreover, the dynamic equations need to be integrated both in the longitudinal and lateral guidance, which exist an obvious redundant calculation. In this paper, we propose LSTM (long short term memory)-based intelligent guidance technology. On the one hand, the integration of the dynamic equations in longitudinal guidance is no longer required to predict the range, that is, the prediction step is eliminated, which will greatly reduce the amount of integral calculation and increase the calculation speed. On the other hand, the amplitude of the bank angle will be no longer iteratively solved based on the secant method, that is, the correction step is eliminated. Based on the natural advantages of deep learning both in neural network mapping capabilities and real-time performance, bank angle command is generated by the output of a trained LSTM model based on the real-time state information of the gliding vehicle. At the same time, the longitudinal and lateral guidance periods in the traditional predictor-corrector guidance will be merged into one period, which has the advantage to ensure that the guidance system meets real-time requirements for online using. Monte Carlo simulation analysis show that the proposed method has the advantages both in accuracy and calculation speed under the condition of initial state error and aerodynamic parameter perturbation. The interdisciplinary fusion of guidance technology and artificial intelligence is a hot research direction, which will greatly promote the development of guidance and control of aircraft.

2021, 53(7): 2047-2057. doi: 10.6052/0459-1879-20-388

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EFFECT OF FLUID-STRUCTURE INTERACTION OF L4/L5 INTERVERTEBRAL DISC UNDER TRANSIENT LOADS

Li Huazhong, Wang Bo, Wang Dandan, Liu Sijin, Chen Xiaodong, Shi Bin

The spine manipulation of traditional Chinese medicine treats the degeneration of the lumbar intervertebral disc by applying transient distraction and rotation forces on the lumbar spine. In this paper, numerical simulation considering fluid-structure interaction is used to study the underlying biomechanical mechanisms. Through experimental measurement and literature research, reasonable parameters of distraction and rotation loads have been determined. A method is developed to build a detailed geometric model of lumbar spine, which uses data from computed tomography scans of human body and anatomical knowledge. Cancellous bones, endplates, and intervertebral discs are considered as poroelastic materials, while others are considered as linear elastic materials, in order to consider the effect of fluid-structure interaction in biological tissues considered here. Through numerical simulations, the stress, strain and fluid flow in the intervertebral disc under transient loads and their combination are obtained. It is found that the transient load generates fluid flow in the nucleus pulposus by changing the stress of the solid matrix of the L4/L5 intervertebral disc and producing pressure gradient across the nucleus pulposus. Distraction causes the fluid to flow out of the nucleus pulposus first and then flow into the nucleus pulposus to produce a change of water content. Under clockwise rotation, opposite flow processes occur on left and right sides of the nucleus pulposus. Water content on the right side of the nucleus pulposus changes greater than the left side. The method used in this research provides a new method for the study of the pathophysiological mechanism of human intervertebral disc degeneration related to the flow process. This method also provides a pathway to make the spine manipulation of traditional Chinese medicine scientific. An entry point is provided additionally for the related study of mechanical and biological coupling study, as well as the basic research of nucleus pulposus regeneration.

2021, 53(7): 2058-2068. doi: 10.6052/0459-1879-21-084

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NUMERICAL INVESTIGATION ON THE SPACE-TIME CORRELATION BETWEEN OBLIQUE DETONATION AND NORMAL DETONATION PROPAGATION

Zhang Wenshuo, Yang Pengfei, Jiang Zonglin, Liu Yunfeng

The propagation theory of one-dimensional detonation is complete and accurate, while prediction of two-dimensional oblique detonation propagation with large scale and high accuracy is still difficult primarily due to the treatment of wedge wall during the calculation and the modelling of viscosity. In this paper, the space-time correlation between two-dimensional steady oblique detonation induced by finite wedge and one-dimensional unsteady detonation supported by piston is investigated by numerical simulations of multi-species Euler equations with H₂-Air detailed chemical kinetics. The initiation and propagation process of detonation wave, together with its interaction with rarefaction waves are numerically analyzed from the perspective of both space and time. The results show that under the same overdriven degree, the wave structure, wall parameters and profile variation calculated from one-dimensional case fit well both qualitatively and quantitatively with two-dimensional case after a certain space-time transformation, which validates the space-time correlation between one- and two-dimensional detonation waves. The difference mainly lies in the transition process between different stages of detonation development, such as the transition from over-driven oblique detonation wave to near Chapman-Jouguet (CJ) oblique detonation wave under the effect of rarefaction waves. Since most features of oblique detonation waves over finite wedge can be obtained efficiently by one-dimensional numerical calculation of piston-driven detonation and space-time transformation, the present work provides a feasible way to understand the spatial structure of oblique detonations waves, including detonation initiation, formation of over-driven oblique detonation and cellular structure downstream. Besides, this paper also provides a novel method to distinguish the effect of wall compression and boundary layer by comparing one- and two-dimensional numerical results. Moreover, the results imply that two-dimensional flow field over wedges of different shapes can be obtained with satisfying accuracy by altering the velocity of piston, which greatly reduces the time, cost and complexity of numerical simulation during the design of combustion chamber in an oblique detonation wave engine.

2021, 53(7): 2069-2078. doi: 10.6052/0459-1879-20-411

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LAMB’S PROBLEM AND CHARACTERISTIC OF ENERGY TRANSMISSION IN UNSATURATED HALF-SPACE

Zhou Fengxi, Zhang Yasen, Cao Xiaolin, Mu Zhanlin

Because unsaturated soil is widely distributed on the earth’s surface, when the traditional saturated two-phase medium theory is used for dynamic analysis, the results are often inconsistent with the actual situation. Aiming at this problem, this paper takes unsaturated elastic half-space as the research object, firstly based on continuum mechanics and porous media theory, and then considers the basic equations of mass conservation equation, momentum conservation equation, constitutive equation and effective stress principle of each phase in unsaturated porous media, and finally, we established a dynamic control equation in which skeleton displacement, pore water pressure and pore gas pressure are basically unknown quantities. Aiming at the dynamic response and energy transmission of the unsaturated half-space surface under the action of vertical concentrated harmonic loads, an axisymmetric calculation model of the classical Lamb problem in the frequency domain is established. The Helmholtz decomposition method is used and the displacement component of the skeleton uses the potential function Φ and Ψ to represent, and combined with the constitutive equation, the analytical solutions of physical quantities such as the displacement field and energy field of the half-space surface under different boundary conditions are obtained. Finally, influencing factors such as load parameters (excitation frequency) and material parameters (saturation, permeability coefficient) are analyzed and discussed through numerical examples. The results show that: (1) An increase in saturation or a decrease in excitation frequency will increase the surface displacement amplitude of the unsaturated half-space; (2) When the permeability coefficient drops to a critical value, the surface displacement amplitude will tend to a limit value, and the influence of permeability coefficient under permeable (gas) boundary and impermeable (gas) boundary conditions shows obvious difference.

2021, 53(7): 2079-2089. doi: 10.6052/0459-1879-21-195

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THE FORCE PARAMETER AND PROFILE CHANGE OF LIQUID BRIDGE BETWEEN TWO UNEQUAL SPHERES—AN EXPERIMENT STUDY

Pu Cheng, Liu Fengyin, Wang Shaohan, Zhong Lijia

The study of liquid force, which is commonly encountered in nature, has a special meaning to crystallization, removal of heavy metals from wastewater, and particle separation in industry. The Nano UTM T150 tensile machine and CCD camera were used respectively to record the force value and the profile change of liquid bridge between two unequal particles during stretching. The influences of radius ratio and liquid volume on the liquid force-displacement curves, maximum liquid force, and rupture distance were analyzed. And the experiment results were then compared with the calculating results according to the circle hypothesis and Y-L equation. Finally, the deficiency of the circle hypothesis in calculating the liquid force was analyzed, meanwhile, combining the influence of gravity, the changes of liquid profile in the whole process of stretch were further analyzed. The results show that the maximum liquid force was greatly influenced by radius ratio while the rupture distance was influenced by liquid volume a lot. What is more, the circle hypothesis can well predict the maximum liquid force, while its prediction of liquid force during the whole stretch is not accurate, this can be attributed to the fact that the liquid profile cannot be expressed as a ring after the liquid force reaches its maximum. Last but not least, based on the influence of gravity, the changes of liquid profile during the experiment were simplified as a circular to a quadratic parabola when the influence of gravity can be neglected; An ellipse which ratio of the long axis to the minor axis gradually increased when the influence of gravity is in the transition stage or has little impact. And a “cooling tower shape” to a hyperbolic, which upper out curvature is small and lower out curvature is large, when the influence of gravity can not be neglected.

2021, 53(7): 2090-2100. doi: 10.6052/0459-1879-21-019

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