Multi-scale Simulation Method with Coupled Finite/Discrete Element Model and Its Application

The existing research on continuous structure is usually analyzed with finite element method (FEM) and granular medium with discrete element method (DEM), but there are few researches on the coupling interaction between continuous structure and discrete medium. To the issue of this coupling interaction, a multi-scale simulation method with coupled finite/discrete element model is put forward, in their respective domains of discrete and finite elements, the nodes follow force law and motion law of their own method, and on the their interaction interface, the touch type between discrete and finite elements is distinguished as two types: full touch and partial touch, the interaction force between them is calculated with linear elastic model. For full touch, the contact force is proportional to the overlap distance between discrete element and finite element patch. For partial touch, first the finite element patch is extended on all sides indefinitely to be a complete plane, the full contact force can be obtained with the touch type between discrete element and plane being viewed as full touch, then the full overlap area between them and the actual overlap area between discrete element and finite element patch are computed, the actual contact force is obtained by scaling the full contact force with a factor which is determined by the ratio of the actual overlap area to the full overlap area. The contact force is equivalent to the finite element nodes and the force and displacement on the nodes can be computed, so the ideal simulation results can be got. This method has been used to simulate the cutter disk of the earth pressure balance shield machine (EPBSM) made in North Heavy Industry (NHI) with its excavation diameter of 6.28 m cutting and digging the sandy clay layer. The simulation results show that as the gradual increase of excavating depth of the cutter head, the maximum stress occurs at the roots of cutters on the cutter head, while for the soil, the largest stress is distributed at the region which directly contacted with the cutters. The proposed research can provide good solutions for correct design and installation of cutters, and it is necessary to design mounting bracket to fix cutters on cutter head.

STRAIGHTFORWARD MULTI-SCALE BOUNDARY ELEMENT METHOD FOR GLOBAL/LOCAL MECHANICAL ANALYSIS OF ELASTIC HETEROGENEOUS MATERIAL

A straightforward multi-scale boundary element method is proposed for global and local mechanical analysis of heterogeneous material.The method is more accurate and convenient than finite element based multi-scale method.The formulations of this method are derived by combining the homogenization approach and the fundamental equations of boundary element method.The solution gives the convenient formulations to compute global elastic constants and the local stress field.Finally,two numerical examples of porous material are presented to prove the accuracy and the efficiency of the proposed method.The results show that the method does not require the iteration to obtain the solution of the displacement in micro level.

Fatigue Performance Evaluation for Welded Details in Orthotropic Steel Deck Bridges Using Multi-Scale Finite Element Method

In order to study the fatigue properties of rib-to-deck welded connection and rib-to-rib welded connection in orthotropic steel bridge decks,a multi-scale finite element model was set up to analyze the stress distribution characteristics and the load test was conducted on the Taizhou Yangtze River Bridge.Comparing the vehicle test results with the muli-scale finite element model results to verify the accuracy of the finite element simulation for the stress response of two welded details.The results indicated that The stress at the rib-to-deck welded connection and the rib-to-rib welded connection are the bending stress and the membrane stress,respectively;the stress response of the two welded connection has strong local characteristics;the lateral stress influence line of the two welded connection is relatively short and the length of the lateral stress influence line is greatly affected by the longitudinal ribs;increasing the thickness of the roof and longitudinal ribs can reduce the stress response and improve the stress performance of the heavy lanes.For the two welded details,the fatigue damage increment of the ordinary lane is greater than the heavy lane.The thickened roof and longitudinal ribs at the position of the heavy lane still cannot balance the fatigue damage caused by the heavy truck.Therefore,it is necessary to strictly control the fatigue effect of overloaded vehicles on steel box girders.

Numerical failure analysis of a continuous reinforced concrete bridge under strong earthquakes using multi-scale models

Previous failure analyses of bridges typically focus on substructure failure or superstructure failure separately. However, in an actual bridge, the seismic induced substructure failure and superstructure failure may influence each other. Moreover, previous studies typically use simplified models to analyze the bridge failure; however, there are inherent defects in the calculation accuracy compared with using a detailed three-dimensional （3D） finite element （FE） model. Conversely, a detailed 3D FE model requires more computational costs, and a proper erosion criterion of the 3D elements is necessary. In this paper, a multi-scale FE model, including a corresponding erosion criterion, is proposed and validated that can significantly reduce computational costs with high precision by modelling a pseudo-dynamic test of an reinforced concrete （RC） pier. Numerical simulations of the seismic failures of a continuous RC bridge based on the multi-scale FE modeling method using LS-DYNA are performed. The nonlinear properties of the bridge, various connection strengths and bidirectional excitations are considered. The numerical results demonstrate that the failure of the connections will induce large pounding responses of the girders. The nonlinear deformation of the piers will aggravate the pounding damages. Furthermore, bidirectional earthquakes will induce eccentric poundingsto the girders and different failure modes to the adjacent piers.

Multi-Scale Analysis of Fretting Fatigue in Heterogeneous Materials Using Computational Homogenization

This paper deals with modeling of the phenomenon of fretting fatigue in heterogeneous materials using the multi-scale computational homogenization technique and finite element analysis(FEA).The heterogeneous material for the specimens consists of a single hole model(25% void/cell,16% void/cell and 10% void/cell)and a four-hole model(25%void/cell).Using a representative volume element(RVE),we try to produce the equivalent homogenized properties and work on a homogeneous specimen for the study of fretting fatigue.Next,the fretting fatigue contact problem is performed for 3 new cases of models that consist of a homogeneous and a heterogeneous part(single hole cell)in the contact area.The aim is to analyze the normal and shear stresses of these models and compare them with the results of the corresponding heterogeneous models based on the Direct Numerical Simulation(DNS)method.Finally,by comparing the computational time and%deviations,we draw conclusions about the reliability and effectiveness of the proposed method.

A Signal Based “W” Structural Elements for Multi-scale Mathematical Morphology Analysis and Application to Fault Diagnosis of Rolling Bearings of Wind Turbines

Working conditions of rolling bearings of wind turbine generators are complicated, and their vibration signals often show non-linear and non-stationary characteristics. In order to improve the efficiency of feature extraction of wind turbine rolling bearings and to strengthen the feature information, a new structural element and an adaptive algorithm based on the peak energy are proposed,which are combined with spectral correlation analysis to form a fault diagnosis algorithm for wind turbine rolling bearings. The proposed method firstly addresses the problem of impulsive signal omissions that are prone to occur in the process of fault feature extraction of traditional structural elements and proposes a "W" structural element to capture more characteristic information. Then, the proposed method selects the scale of multi-scale mathematical morphology, aiming at the problem of multi-scale mathematical morphology scale selection and structural element expansion law. An adaptive algorithm based on peak energy is proposed to carry out morphological scale selection and structural element expansion by improving the computing efficiency and enhancing the feature extraction effect.Finally, the proposed method performs spectral correlation analysis in the frequency domain for an unknown signal of the extracted feature and identifies the fault based on the correlation coefficient. The method is verified by numerical examples using experimental rig bearing data and actual wind field acquisition data and compared with traditional triangular and flat structural elements. The experimental results show that the new structural elements can more effectively extract the pulses in the signal and reduce noise interference,and the fault-diagnosis algorithm can accurately identify the fault category and improve the reliability of the results.

Multi-scale finite element simulation on large deformation behavior of wood under axial and transverse compression conditions

Multi-scale finite element method is adopted to simulate wood compression behavior under axial and transverse loading. Representative volume elements (RVE) of wood microfibril and cell are proposed to analyze orthotropic mechanical behavior. Lignin, hemicellulose and crystalline-amorphous cellulose core of spruce are concerned in spruce nanoscale model. The equivalent elastic modulus and yield strength of the microfibril are gained by the RVE simulation. The anisotropism of the crystalline-amorphous cellulose core brings the microfibril buckling deformation during compression loading. The failure mechanism of the cell-wall under axial compression is related to the distribution of amorphous cellulose and crystalline cellulose. According to the spruce cell observation by scanning electron microscope, numerical model of spruce cell is established using simplified circular hole and regular hexagon arrangement respectively. Axial and transverse compression loadings are taken into account in the numerical simulations. It indicates that the compression stress-strain curves of the numerical simulation are consistent with the experimental results. The wood microstructure arrangement has an important effect on the stress plateau during compression process. Cell-wall buckling in axial compression induces the stress value drops rapidly. The wide stress plateau duration means wood is with large energy dissipation under a low stress level. The numerical results show that loading velocity affects greatly wood microstructure failure modes in axial loading. For low velocity axial compression, shear sliding is the main failure mode. For high velocity axial compression, wood occur fold and collapse. In transverse compression, wood deformation is gradual and uniform, which brings stable stress plateau.

Finite element analysis for general elastic multi-structures

A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method.

Multi-scale crystal plasticity finite element simulations of the microstructural evolution and formation mechanism of adiabatic shear bands in dual-phase Ti20C alloy under complex dynamic loading

A dynamic compression test was performed on α+β dual-phase titanium alloy Ti20C using a split Hopkinson pressure bar.The formation of adiabatic shear bands generated during the compression process was studied by combining the proposed multi-scale crystal plasticity finite element method with experimental measurements.The complex local micro region load was progressively extracted from the simulation results of a macro model and applied to an established three-dimensional multi-grain microstructure model.Subsequently,the evolution histories of the grain shape,size,and orientation inside the adiabatic shear band were quantitatively simulated.The results corresponded closely to the experimental results obtained via transmission electron microscopy and precession electron diffraction.Furthermore,by calculating the grain rotation and temperature rise inside the adiabatic shear band,the microstructural softening and thermal softening effects of typical heavily-deformed α grains were successfully decoupled.The results revealed that the microstructural softening stress was triggered and then stabilized(in general)at a relatively high value.This indicated that the mechanical strength was lowered mainly by the grain orientation evolution or dynamic recrystallization occurring during early plastic deformation.Subsequently,thermal softening increased linearly and became the main softening mechanism.Noticeably,in the final stage,the thermal softening stress accounted for 78.4% of the total softening stress due to the sharp temperature increase,which inevitably leads to the stress collapse and potential failure of the alloy.

Multi-scale thermodynamic analysis method for 2D SiC/SiC composite turbine guide vanes

Ceramic Matrix Composite （CMC） turbine guide vanes possess multi-scale stress and strain with inhomogeneity at the microscopic scale. Given that the macroscopic distribution cannot reflect the microscopic stress fluctuation, the macroscopic method fails to meet the requirements of stress and strain analysis of CMC turbine guide vanes. Furthermore, the complete thermodynamic properties of 2D woven SiC/SiC-CMC cannot be obtained through experimentation, Accordingly, a method to calculate the thermodynamic properties of CMC and analyze multi-scale stress and strain of the turbine guide vanes should be established. In this study, the multi-scale thermodynamic analysis is investigated. The thermodynamic properties of Chemical Vapor Infiltration （CVI） pro- cessed SiC/SiC-CMC are predicted by a Representative Volume Element （RVE） model with porosity, leading to the result that the relative error between the calculated in-plane tensile modulus and the experimental value is 4.2%. The macroscopic response of a guide vane under given conditions is predicted. The relative error between the predicted strain on the trailing edge and the experimental value is 9.7%. The calculation of the stress distribution of micro-scale RVE shows that the maximum value of microscopic stress, which is located in the interlayer matrix, is more than 1.5 times that of macroscopic stress in the same direction and the microscopic stress distribution of the interlayer matrix is related to the pore distribution of the composite.

Whole-mine subsidence over tabular deposits and related seismicity

The challenge of estimating mine-wide subsidence and linkages to seismicity over tabular deposits is addressed by a special finite element technique(dual node–dual mesh). Subsidence and mine-induced seismicity begins near the face when caving occurs and propagates to the surface as extraction reaches a critical extent. Thus, the challenge is to obtain details at the face at the meter scale and also at the surface over the whole mine at the kilometer scale. Interactions between old and new sections of a mine are automatically taken into account with this technique. The finite element method is well established technology based on fundamentals of physical laws, kinematics and material laws. With this technique, no empirical ‘‘scaling" or fitting computer output by input data ‘‘adjustment" to mine measurements is necessary. Capability is demonstrated for doing practical whole-mine subsidence analysis from first principles. Mine-induced seismicity is shown to correlate well with face advance and element failure.

Three-dimensional modelling of shear keys in concrete gravity dams using an advanced grillage method

Contraction joint shear keys are resilient features of gravity dams that can be considered to increase the sliding safety factors or minimise seismic residual sliding displacements,allowing costly remedial actions to be avoided.This paper presents a novel,robust,and computationally efficient three-dimensional(3D)modelling and simulation strategy of gravity dams,using a series of adjacent cantilever beam elements to represent individual monoliths.These monoliths are interconnected in the longitudinal direction by 3D no-tension link elements representing the lumped shear key stiffness contributions at a particular elevation.The objective is to assess the shear key internal force demands,including the axial force,shear,and moment demands.Shear key demand-capacity ratios can then be assessed with related multi-axial failure envelopes.The 3D link element stiffness coefficients were derived from a series of 3D finite element(FE)solid models with a detailed representation of geometrical features of multiple shear keys.The results from the proposed method based on advanced grillage analysis show strong agreement with reference solutions from 3D FE solid models,demonstrating high accuracy and performance of the proposed method.The application of the proposed advanced grillage method to a dam model with two monoliths clearly shows the advantage of the proposed method,in comparison to the classical approach used in practise.

MULTI-SCALE METHODS FOR INVERSE MODELING IN 1-D MOS CAPACITOR

In this paper, we investigate multi-scale methods for the inverse modeling in 1-D Metal-Oxide-Silicon (MOS) capacitor. First, the mathematical model of the device is given and the numerical simulation for the forward problem of the model is implemented using finite element method with adaptive moving mesh. Then numerical analysis of these parameters in the model for the inverse problem is presented. Some matrix analysis tools are applied to explore the parameters' sensitivities. And third, the parameters are extracted using Levenberg-Marquardt optimization method. The essential difficulty arises from the effect of multi-scale physical difference of the parameters. We explore the relationship between the parameters' sensitivities and the sequence for optimization, which can seriously affect the final inverse modeling results. An optimal sequence can efficiently overcome the multi-scale problem of these parameters. Numerical experiments show the efficiency of the proposed methods.

Multi-scale analysis of void evolution in large-section plastic mold steel during multi-directional forging

The void evolution of large-section plastic mold steel during multi-directional forging(MDF)was investigated using multiscale analysis.To simulate the forging process of the plastic mold steel(SDP1 steel)and realize micro-void reconstruction in a representative volume element(RVE),MDF experiment and void-characteristic evaluation of the SDP1 steel were carried out.Traditional upsetting and stretching forging(TUSF)and MDF were simulated to comparatively analyze the evolution of temperature,effective stress,and effective strain.By embedding RVE with a micro-void and using boundary condition by point tracking into the forging process,the single-void evolution in TUSF and MDF was studied.The effect of void orientation on single-void evolution was also investigated.The multi-scale analysis revealed the following results.(1)Compared with TUSF,MDF achieved a higher efficiency in void closure.(2)The closing efficiency of the void increased with the increase in angle h(the angle between the Z and long axes of the void).(3)The closing efficiency increased with the increase in the orientation angle during the forging process.On the basis of the important role of the main stress in each forging step on the void closure,an integral formula of the main stress was proposed.When main compressive-stress integration reached-0.4,the closed state of the void could be accurately determined.

Elastic Predictions of 3D Orthogonal Woven Composites Using Micro/meso-scale Repeated Unit Cell Models

This presentation predicts the elastic properties of three-dimensional(3D)orthogonal woven composite(3DOWC)by finite element analysis based on micro/meso repeated unit cell(RUC)models.First,the properties of fiber yarn are obtained by analysis on a micro-scale RUC model assuming fibers in a hexagonal distribution pattern in the polymer matrix.Then a full thickness meso-scale RUC model including weft yarns,warp yarns,Z-yarns and pure resin zones is established and full stiffness matrix of the 3DOWC including the in-plane and flexural constants are predicted.For thick 3DOWC with large number of weft,warp layers,an alternative analysis method is proposed in which an inner meso-RUC and a surface meso-RUC are established,respectively.Then the properties of 3DOWC are deduced based on laminate theory and properties of the inner and surface layers.The predicted results by the above two alternative methods are in good experimental agreement.

MULTISCALE FINITE ELEMENT METHOD FOR SUBDIVIDED PERIODIC ELASTIC STRUCTURES OF COMPOSITE MATERIALS

Deals with a study which discussed the mechanical behaviour for subdivided periodic elastic structures of composite materials, from the viewpoint of macro- and meso-scale coupling. Multiscale asymptotic expansion and truncation error estimates; Discussion on multiscale finite element method; Details of higher order difference quotients and total error estimates; Numerical experiments.

Finite Element Prediction of the Thermal Conductivity of GNP/Al Composites

A 3 D multi-scale finite element model was developed to predict the effective thermal conductivity of graphene nanoplatelet(GNP)/Al composites.The factors influencing the effective thermal conductivity of the GNP/Al composites were investigated,including the orientation,shape,aspect ratio,configuration and volume fraction of GNPs.The results show that GNPs shape has a little influence on the thermal conductivity of GNP/Al composites,and composites with elliptic GNPs have the highest thermal conductivity.In addition,with increasing the aspect ratio of GNPs,the thermal conductivity of GNP/Al composites increases and finally tends to be stable.The GNPs configuration strongly influences the thermal conductivity of GNP/Al composites,and the thermal conductivity of the composites with layered GNPs is the highest among the five configurations.The effective thermal conductivity is sensitive to volume fraction of GNPs.Ideally,when the volume fraction of layered GNPs reaches 1.54%,the thermal conductivity of GNP/Al composites is as high as 400 W/m K.The findings of this study could provide a good theoretical basis for designing high thermal conductivity GNP/Al composites.

A deterministic FE contact analysis of 3D rough surfaces with textures and comparison with classic statistical contact models

Accurate contact calculations of real rough surfaces are fundamental but complicated. The model-based methods are convenient and straightforward. But these methods ignore some factors and may lead to less accurate results. This is especially true when considering multi-scale topographic features of engineering rough surfaces. Based on artificially generated rough surfaces, the deterministic contact analysis of two 3D rough surfaces is conducted by the finite element method(FEM). The calculations show that when the separation between surfaces reduces, results of classic model-based methods are quite different from those of this study, especially when the roughness distribution and textures are considered. As friction pairs are working under increasing harsh conditions, the accurate contact calculation in this paper will be of great significance.

Research on failure criterion of composite based on unified macro- and micro-mechanical model

A new unified macro- and micro-mechanics failure analysis method for composite structures was developed in order to take the effects of composite micro structure into consideration. In this method, the macro stress distribution of composite structure was calculated by commercial finite element analysis software. According to the macro stress distribution, the damage point was searched and the micro-stress distribution was calculated by reformulated finite-volume direct averaging micromechanics （FVDAM）, which was a multi-scale finite element method for composite. The micro structure failure modes were estimated with the failure strength of constituents. A unidirectional composite plate with a circular hole in the center under two kinds of loads was analyzed with the traditional macro-mechanical failure analysis method and the unified macro- and micro-mechanics failure analysis method. The results obtained by the two methods are consistent, which show this new method＇s accuracy and efficiency.