Modeling stress wave propagation in rocks by distinct lattice spring model

In this paper, the ability of the distinct lattice spring model （DLSM） for modeling stress wave propagation in rocks was fully investigated. The influence of particle size on simulation of different types of stress waves （e.g. one-dimensional （1D） P-wave, 1D S-wave and two-dimensional （2D） cylindrical wave） was studied through comparing results predicted by the DLSM with different mesh ratios （It） and those obtained from the corresponding analytical solutions. Suggested values of lr were obtained for modeling these stress waves accurately. Moreover, the weak material layer method and virtual joint plane method were used to model P-wave and S-wave propagating through a single discontinuity. The results were compared with the classical analytical solutions, indicating that the virtual joint plane method can give better results and is recommended. Finally, some remarks of the DLSM on modeling of stress wave propagation in rocks were provided.

On the four-dimensional lattice spring model for geomechanics

Recently, a four-dimensional lattice spring model(4D-LSM) was developed to overcome the Poisson’s ratio limitation of the classical LSM by introducing the fourth-dimensional spatial interaction. In this work, some aspects of the 4D-LSM on solving problems in geomechanics are investigated, such as the ability to reproduce elastic properties of geomaterials, the capability of solving heterogeneous problems,the accuracy on modelling stress wave propagation, the ability to solve dynamic fracturing and the parallel computational efficiency. Our results indicate that the 4D-LSM is promising to deal with problems in geomechanics.

Simulation of Morphologies and Mechanical Properties of A/B Polymer Blend Film

The effects of blend composition and micro-phase structure on the mechanical behavior of A/B polymer blend film are studied by coupling the Monte Carlo(MC) simulation of morphology with the lattice spring model(LSM) of micro mechanics of materials.The MC method with bond length fluctuation and cavity diffusion algorithm on cubic lattice is adopted to simulate the micro-phase structure of A/B polymer blend.The information of morphology and structure is then inputted to the LSM composed of a three-dimensional network of springs to obtain the mechanical properties of polymer blend film.Simulated results show that the mechanical response is mainly affected by the density and the composition of polymer blend film through the morphology transition.When a force is applied on the outer boundary of polymer blend film,the vicinity of the inner cavities experiences higher stresses and strains responsible for the onset of crack propagation and the premature failure of the entire system.

A Virtual Puncture Surgery System Based on Multi-Layer Soft Tissue and Force Mesh

Puncture is a common operation in surgery,which involves all kinds of tissue materials with different geometry and mechanical properties.As a new cross-disciplinary research area,Virtual Surgery(VS)makes simulation of soft tissue in puncture operation possible in virtual environment.In this paper,we introduce a VS-based puncture system composed by three-layer soft tissue,simulated with spherical harmonic function(SHF),which is covered with a force mesh,constructed by mass spring model(MSM).The two models are combined together with a parameter of SHF named surface radius,which provides MSM with real-time deformation data needed in force calculation.Meanwhile,force calculation,divided into the surface spring force and the puncture damping force,makes the force presentation better accord to the corresponding tissue characteristics.Moreover,a deformation resumption algorithm is leveraged to simulate the resumption phenomenon of the broken tissue surface.In evaluation experiment,several residents are invited to grades our model along with other four mainstream soft tissue models in terms of 7 different indicators.After the evaluation,the scores are analyzed by a comprehensive weighted grading method.Experiment results show that the proposed model has better performance during puncture operation than other models,and can well simulate surface resumption phenomenon when tissue surface is broken.

The torsion model of soft tissue in virtual surgery

In order to solve the problem of real-time soft tissue torsion simulation in virtual surgeries,a torsion model based on coil spring is proposed to actualize real-time interactions and applications in virtual surgeries. The proposed model is composed of several connected coil springs in series. The sum of torsion deformation on every coil is equivalent to the soft tissue surface deformation. The calculation of the model is simple because the method for calculating the torsion deformation for each coil spring is the same. The virtual surgery simulation system is established on PHANTOM OMNI haptic device based on the Open GL 3 D graphic interface and VC + + software,and it is used to simulate the torsion deformation of virtual legs and arms. Experimental results show that the proposed model can effectively simulate the torsion deformation of soft tissue while being of real-time performance and simplicity,which can well meet requirements of virtual operation simulations.

ANALYSIS OF MICROBUCKLING FOR MONOMOLECULAR LAYERS ADHERING TO A SUBSTRATE

A two-dimensional linear spring model is established to study the microbuckling of a plane monomolecular layer adhering to a substrate. The model is for the layer subjected to a compressive load having an arbitrary angle with the chemical bond of the layer. The effects of the load angle, the strength of adhesion and the bending stiffness and shearing stiffness (the capability of resisting transverse bending and in-plane shearing) of the layer on the minimal buckling force and the critical buckling mode are discussed. It is found that the minimal buckling force increases with increasing load angle and, for a given bending stiffness, increases with increasing strength of adhesion and decreasing shearing stiffness. Furthermore, a critical condition under which the buckling of the layer can just occur is obtained, which is helpful to avoid buckling in an engineering application.

Fracture analysis of mode-II crack perpendicular to imperfect bimaterial interface

The problem of a mode-II crack interface of two bonded dissimilar materials close to and perpendicular to an imperfect is investigated. The imperfect interface is modelled by a linear spring with the vanishing thickness. The Fourier transform is used to solve the boundary-value problem and to derive a singular integral equation with the Cauchy kernel. The stress intensity factors near the left and right crack tips are evaluated by numerically solving the resulting equation. SeverM special cases of the mode-II crack problem with an imperfect interface are studied in detail. The effects of the interfacial imperfection on the stress intensity factors for a bimaterial system of aluminum and steel are shown graphically. The obtained observation reveals that the stress intensity factors are dependent on the interface parameters and vary between those with a fully debonded interface and those with a perfect interface.

Estimation of interfacial damage in composites with reinforced particles based on ultrasonic data

The scattering of elastic waves by a spherical particle with imperfect interface and the nondestructive detection of interfacial damage were studied. First, the scattering of elastic waves by a spherical particle with imperfect interface, i.e. spring interface model, was studied. Then, multiple scattering by random distributed particles was investigated and the equations to evaluate the velocity and attenuation of effective waves defined by statistic averaging were given. Furthermore, on the basis of the established relation between the velocity and interfacial constants, a method to evaluate the interfacial damage nondestructively from the ultrasonic data was pro- posed. Numerical simulation was performed for the SiC-Al composites. The velocities of the effective waves were computed to show the influence of the interface constants. Using the genetic algorithm, the interfacial damage was evaluated from the synthetic experi- mental data with various noise levels. The numerical results showed the feasibility of the method proposed.

A NEW METHOD OF ANALYZING SURFACE CRACKS

The authors have developed a new line-spring boundary element method in the present paper, which combines the advantage of the line-spring model with that of the boundary element method. This method reduces the three-dimension problem of the surface cracks into a quasi-one-dimension problem and can be used to analyze the surface cracked plate under various loading conditions. In this paper theoretical analyses and numerical verifications are carried out. The calculated results are reported, which indicate that the present method is efficient and can be used to analyze the surface crack problem on a personal computer.

High-performance computing of 3D blasting wave propagation in underground rock cavern by using 4D-LSM on TianHe-3 prototype E class supercomputer

Parallel computing assigns the computing model to different processors on different devices and implements it simultaneously.Accordingly,it has broad applications in the numerical simulation of geotechnical engineering and underground engineering,of which models are always large-scale.With parallel computing,the computing time or the memory requirements will be reduced by splitting the original domain of the numerical model into many subdomains,which is thus named as the domain decomposition method.In this study,a cubic and equal volume domain decomposition strategy was utilized to realize the parallel computing on the distributed memory system of four-dimensional lattice spring model(4D-LSM)based on the message passing interface.With a more efficient communication strategy introduced,this study aimed at operating an one-billion-particle model on a supercomputer platform.The preprocessing procedure of the parallelized 4D-LSM was restructured and the particle generation strategy suitable for the supercomputer platform was employed to minimize the time consumption in preprocessing and calculation.On this basis,numerical calculations were performed on TianHe-3 prototype E class supercomputer at the National Supercomputer Center in Tianjin.Two fieldscale three-dimensional blasting wave propagation models were carried out,of which the numerical results verify the computing power and the advantage of the parallelized 4D-LSM in the simulation of large-scale three-dimension models.Subsequently,the time complexity and spatial complexity of 4D-LSM and other particle discrete element methods were analyzed.

MULTI-AXLE VEHICLE STABILITY BASED ON WHOLE VEHICLE MODEL

From the analysis of experiment data of the multi-axle vehicle chassis searching process, it is less accurate to predict multi-axle vehicle dynamic characteristic with simplified two-axle vehicle model. So it is important to find out a more effective modeling method in the study of multi-vehicle stability. In the development of heat transfer fluid（HTF） six-axle vehicle, a whole vehicle multi-body dynamic model is built through collaborate flowchart using Teamcenter Engineering, UG NX3 and MSC.Adams. The modeling method of connected hydragas spring suspension is validated by running test results. Based on this whole vehicle model, a kinematical analysis of suspension is implemented to achieve optimized suspension geometry parameters according to the stable requirement. Then, different handling simulations are carried out with regard to various tire characteristics, driving con- figurations, and equipments. According to the evaluation of whole vehicle handling characteristic, some design rules are summarized to improve the stability of multi-axle vehicle.

Magnetic-field-assisted triboelectric nanogenerator for harvesting multi-directional wave energy

Ocean wave energy is a significant and promising source of renewable energy.However,the energy harvesting is challenging due to the multi-directional nature of waves.This paper proposes a magnetic-field-assisted triboelectric nanogenerator(MFATENG)for harvesting multi-directional wave energy.By incorporating a magnetic field,the planar motion of the pendulum is converted into spatial motion,increasing the triggering of multilayered TENG(M-TENG)and enhancing the output energy of the MFA-TENG.Experimental results demonstrate that the output energy of the MFA-TENG is increased by 73%by utilizing the magnetic field.Moreover,a spring model based on the origami-structured M-TENG is established to analyze the effect of different equivalent stiffnesses on the performance of the M-TENG,aiming to obtain optimal output performance.The results showcase the impressive output performance of the M-TENG,generating outputs of 250 V,18μA,and 255 nC.Furthermore,the proposed MFA-TENG effectively harvests multi-directional wave energy under water-wave driven conditions.This study significantly enhances the ability of the MFA-TENG to harvest multi-directional wave energy and presents a promising approach for self-powered marine monitoring in the future.

Stability analysis on tunnels with karst caves using the distinct lattice spring model

The effects of karst caves on tunnel stability were numerically investigated using the distinct lattice spring model(DLSM).The DLSM was validated by investigating the mechanical behavior of Brazilian discs with various sizes of central circular holes.Then,the effects of karst cave on U-shaped tunnel were investigated under various karst caves positions(top,bottom,and right side of the tunnel),tunnelcave distances(0.5-4 times the radius of the tunnel arc),and cave shapes(circular,rectangular flat,and rectangular vertical caves).The failure processes of the tunnel under those various conditions were analyzed and both the failure process and the final failure patterns of the tunnel were discussed.Numerical simulation demonstrated that karst caves around the tunnel could weaken the stability of the tunnel,indicating tunnel-cave distance effects.The closer the cave to the tunnel,the weaker the tunnel under loading.This effect was not significant when the tunnel-cave distance(d)was larger than three times the tunnel arc radius(R).In addition,the final failure pattern of the tunnel and its surrounding rock mass were dependent on both the position and the size of the cave.The larger the cave,the weaker the tunnel and its surrounding rock mass.Furthermore,compared with those cases with top and bottom caves,the tunnel with a right side cave had more impacts on tunnel stability.The main research finding could help engineers carry out stability analysis on tunnels in karst areas and take effective measures to enhance tunnel stability.

On the “spring predictability barrier” for strong El Nio events as derived from an intermediate coupled model ensemble prediction system

Using predictions for the sea surface temperature anomaly(SSTA) generated by an intermediate coupled model(ICM)ensemble prediction system(EPS), we first explore the "spring predictability barrier"(SPB) problem for the 2015/16 strong El Nio event from the perspective of error growth. By analyzing the growth tendency of the prediction errors for ensemble forecast members, we conclude that the prediction errors for the 2015/16 El Nio event tended to show a distinct season-dependent evolution, with prominent growth in spring and/or the beginning of the summer. This finding indicates that the predictions for the 2015/16 El Nio occurred a significant SPB phenomenon. We show that the SPB occurred in the 2015/16 El Nio predictions did not arise because of the uncertainties in the initial conditions but because of model errors. As such, the mean of ensemble forecast members filtered the effect of model errors and weakened the effect of the SPB, ultimately reducing the prediction errors for the 2015/16 El Nio event. By investigating the model errors represented by the tendency errors for the SSTA component,we demonstrate the prominent features of the tendency errors that often cause an SPB for the 2015/16 El Nio event and explain why the 2015/16 El Nio was under-predicted by the ICM EPS. Moreover, we reveal the typical feature of the tendency errors that cause not only a significant SPB but also an aggressively large prediction error. The feature is that the tendency errors present a zonal dipolar pattern with the west poles of positive anomalies in the equatorial western Pacific and the east poles of negative anomalies in the equatorial eastern Pacific. This tendency error bears great similarities with that of the most sensitive nonlinear forcing singular vector(NFSV)-tendency errors reported by Duan et al. and demonstrates the existence of an NFSV tendency error in realistic predictions. For other strong El Nio events, such as those that occurred in 1982/83 and 1997/98, we obtain the tendency errors of the NFSV structure, which cause a significant SPB and yield a much larger prediction error. These results suggest that the forecast skill of the ICM EPS for strong El Nio events could be greatly enhanced by using the NFSV-like tendency error to correct the model.

A New Prediction Model for Grain Yield in Northeast China Based on Spring North Atlantic Oscillation and Late-Winter Bering Sea Ice Cover

Accurate estimations of grain output in the agriculturally important region of Northeast China are of great strategic significance for guaranteeing food security.New prediction models for maize and rice yields are built in this paper based on the spring North Atlantic Oscillation index and the Bering Sea ice cover index.The year-to-year increment is first forecasted and then the original yield value is obtained by adding the historical yield of the previous year.The multivariate linear prediction model of maize shows good predictive ability,with a low normalized root-mean-square error（NRMSE）of 13.9%,and the simulated yield accounts for 81%of the total variance of the observation.To improve the performance of the multivariate linear model,a combined forecasting model of rice is built by considering the weight of the predictors.The NRMSE of the model is 12.9%and the predicted rice yield explains 71%of the total variance.The corresponding cross-validation test and independent samples test further demonstrate the efficiency of the models.It is inferred that the statistical models established here by applying year-to-year increment approach could make rational prediction for the maize and rice yield in Northeast China before harvest.The present study may shed new light on yield prediction in advance by use of antecedent large-scale climate signals adequately.

Elastic Characteristics of Digital Cores from Longmaxi Shale Using Lattice Spring Models

Effective medium methods for the attribution of micro-structures to macro elastic properties of shales are important for the prediction of sweet spots in the shale-gas production.With X-ray micro-computed tomography(XMCT),the micro-structures of shale core samples from Longmaxi Formation are visualized and characterized by 3D digital images.As an efficient alternative to conventional effective medium methods for estimating elastic properties,we propose a consistent workflow of lattice spring modeling(LSM)to emulate the digital cores using three types of lattices.Particular attention is paid to investigate the effective Young’s moduli,Poisson’s ratios,and preferred orientations,by uniaxial compression tests along two directions.Within elastic deformation,the impact of lattice arrangements on the anisotropy is even more than those of stress disturbances and micro-structural features.Compared with analytical approximations and theoretical predictions,the LSM numerical scheme shows general applicability for heterogeneous porous rocks.

Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

We use front tracking data structures and functions to model the dynamic evolution of fabric surface.We represent the fabric surface by a triangulated mesh with preset equilibrium side length.The stretching and wrinkling of the surface are modeled by the mass-spring system.The external driving force is added to the fabric motion through the"Impulse method"which computes the velocity of the point mass by superposition of momentum.The mass-spring system is a nonlinear ODE system.Added by the numerical and computational analysis,we show that the spring system has an upper bound of the eigen frequency.We analyzed the system by considering two spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for the eigen-frequency.This upper bound plays an important role in determining the numerical stability and accuracy of the ODE system.Based on this analysis,we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal motion.We used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system.

A DLM/FD/IB Method for Simulating Cell/Cell and Cell/Particle Interaction in Microchannels

A spring model is used to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the red blood cell (RBC) rheology in Poiseuille flow with an immersed boundary method. The lateral migration properties of many cells in Poiseuille flow have been investigated. The authors also combine the above methodology with a distributed Lagrange multiplier/fictitious domain method to simulate the interaction of cells and neutrally buoyant particles in a microchannel for studying the margination of particles.

A DLM/FD/IB Method for Simulating Compound Cell Interacting with Red Blood Cells in a Microchannel

In this article, a computational model and related methodologies have been tested for simulating the motion of a malaria infected red blood cell （iRBC for short） in Poiseuille flow at low Reynolds numbers. Besides the deformability of the red blood cell membrane, the migration of a neutrally buoyant particle （used to model the malaria parasite inside the membrane） is another factor to determine the iRBC motion. Typically an iRBC oscillates in a Poiseuille flow due to the competition between these two factors. The interaction of an iRBC and several RBCs in a narrow channel shows that, at lower flow speed, the iRBC can be easily pushed toward the wall and stay there to block the channel. But, at higher flow speed, RBCs and iRBC stay in the central region of the channel since their migrations axe dominated by the motion of the RBC membrane.

A Vibration-Based Method for the Measurement of Subgrade Soil Scaling Factor

The subgrade soil scaling factor （SSSF） shows the basic properties of soil such as stiffness, gravimetry, density, and particle distribution, which are essential for disaster prediction and geotechnical engineering activities. In this paper, methods used for soil properties analysis are firstly summarized, and then a fiber Bragg grating （FBG） sensing technology is introduced. In order to acquire the properties and mechanical characteristics of soil accurately, a vibration-based method is presented, and an experiment for judging the properties of soil is conducted. As for the experiment, an FBG sensor is adhered to the upside of the vibration rod to measure its fundamental frequency. The rod vibrates freely at different-depth level of soil, and the changed data of wavelength from the FBG sensor are carefully collected. The Winkler spring model is used to analyze the relationship between the fundamental frequency and stiffness of soil. The results of this experiment suggest that data collected from FBG sensor can reflect vibration situation clearly and quantitatively. Thus the SSSF value can be calculated from the frequency-stiffness equation. The experimental results are almost identical with the theoretical derivation results. This confirms that the method presented in the paper can determine the SSSF effectively.