Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.

On the calibration and verification of Voronoi-based discontinuous deformation analysis for modeling rock fracture

Since its introduction,discontinuous deformation analysis(DDA)has been widely used in different areas of rock mechanics.By dividing large blocks into subblocks and introducing artificial joints,DDA can be applied to rock fracture simulation.However,parameter calibration,a fundamental issue in discontinuum methods,has not received enough attention in DDA.In this study,the parameter calibration of DDA for intact rock is carefully studied.To this end,a subblock DDA with Voronoi tessellation is presented first.Then,a modified contact constitutive law is introduced,in which the tensile and shear meso-strengths are modified to be independent of the bond lengths.This improvement can prevent the unjustified preferential failure of short edges.A method for imposing confining pressure is also introduced.Thereafter,sensitivity analysis is performed to investigate the influence of the calculated parameters and meso-parameters on the mechanical properties of modeled rock.Based on the sensitivity analysis,a unified calibration procedure is suggested for both cases with and without confining pressure.Finally,the calibration procedure is applied to two examples,including a biaxial compression test.The results show that the proposed Voronoi-based DDA can simulate rock fracture with and without confining pressure very well after careful parameter calibration.

The Deformation Analysis of the 3D Alignment Control Network Based on the Multiple Congruence Models

In the construction and maintenance of particle accelerators,all the accelerator elements should be installed in the same coordinate system,only in this way could the devices in the actual world be consistent with the design drawings.However,with the occurrence of the movements of the reinforced concrete cover plates at short notice or building deformations in the long term,the control points upon the engineering structure will be displaced,and the fitness between the subnetwork and the global control network may be irresponsible.Therefore,it is necessary to evaluate the deformations of the 3D alignment control network.Different from the extant investigations,in this paper,to characterize the deformations of the control network,all of the congruent models between the points measured in different epochs have been identified,and the congruence model with the most control points is considered as the primary or fundamental model,the remaining models are recognized as the additional ones.Furthermore,the discrepancies between the primary S-transformation parameters and the additional S-transformation parameters can reflect the relative movements of the additional congruence models.Both the iterative GCT method and the iterative combinatorial theory are proposed to detect multiple congruence models in the control network.Considering the actual work of the alignment,it is essential to identify the competitive models in the monitoring network,which can provide us a hint that,even the fitness between the subnetwork and the global control network is good,there are still deformations which may be ignored.The numerical experiments show that the suggested approaches can describe the deformation of the 3D alignment control network roundly.

General Kinetostatic Modeling and Deformation Analysis of a Two-Module Rod-Driven Continuum Robot with Friction Considered

Continuum robots actuated by flexible rods have large potential applications,such as detection and operation tasks in confined environments,since the push and pull actuation of flexible rods withstand tension and compressive force,and increase the structure's rigidity.In this paper,a generalized kinetostatics model for multi-module and multi-segment continuum robots considering the effect of friction based on the Cosserat rod theory is established.Then,the model is applied to a two-module rod-driven continuum robot with winding ropes to analyze its deformation and load characteristics.Four different in-plane configurations under the external load term as S1,S2,C1,and C2 are defined.Taking a bending plane as an example,the tip deformation along thex-axis of these shapes is simulated and compared,which shows that the load capacity of C1 and C2 is generally larger than that of S1 and S2.Furthermore,the deformation experiments and simulations show that the maximum error ratio without external loads relative to the total length is no more than 3%,and it is no more than 4.7%under the external load.The established kinetostatics model is proven sufficient to accurately analyze the rod-driven continuum robot with the consideration of internal friction.

Dynamic process analysis of the Niumiangou landslide triggered by the Wenchuan earthquake using the finite difference method and a modified discontinuous deformation analysis

The Niumiangou landslide was the largest landslide triggered by the 2008 Wenchuan earthquake,which was significantly affected by the amplification effect of seismic acceleration.The ringshear experiments indicated that the materials in the source area of the Niumiangou landslide were subjected to friction degradation under a big shear displacement,which may result in rapid movement of the landslide.In order to better understand the landslide movement and study the effect of the friction degradation on movement mechanisms,the dynamic process of Niumiangou landslide was simulated with a new numerical method,which combines the finite difference method(FDM)and the discontinuous deformation analysis(DDA).First,the FDM was used to study the initiation time,amplification effect and velocity of the landslide.Afterwards,these initiation velocities were applied to the blocks in the DDA model by corresponding coordination in the FDM model.A displacementdependent friction model of the sliding surface was incorporated into DDA code to further understand the kinetic behavior of the landslide.The results show that the displacement-dependent friction strongly decreases the friction coefficient of sliding surface under a big displacement,which can obviously promote the run-out and velocity of landslide.The model output well matches the topographic map formed by the landslide.This implies that the proposed model can be applied to the simulation of earthquake-induced landslides with amplification effect,and the friction degradation model is important to clarify the movement mechanism of high-speed and long-distance landslides.

Deformation Analysis and Fixture Design of Thin-walled Cylinder in Drilling Process Based on TRIZ Theory

Thin-walled cylindrical workpiece is easy to deform during machining and clamping processes due to the insufficient rigidi.Moreover,it’s also difficult to ensure the perpendicularity of flange holes during drilling process.In this paper,the element birth and death technique is used to obtain the axial deformation of the hole through finite element simulation.The measured value of the perpendicularity of the hole was compared with the simulated value to verify then the rationality of the simulation model.To reduce the perpendicularity error of the hole in the drilling process,the theory of inventive principle solution(TRIZ)was used to analyze the drilling process of thin-walled cylinder,and the corresponding fixture was developed to adjust the supporting surface height adaptively.Three different fixture supporting layout schemes were used for numerical simulation of drilling process,and the maximum,average and standard deviation of the axial deformation of the flange holes and their maximum hole perpendicularity errors were comparatively analyzed,and the optimal arrangement was optimized.The results show that the proposed deformation control strategy can effectively improve the drilling deformation of thin-walled cylindrical workpiece,thereby significantly improving the machining quality of the parts.

A new nano-scale surface marking technique for the deformation analysis of Mg-based alloys

In this work a new nanoscale surface marking technique,namely electron beam damage induced surface marking(EBDISM),is developed and tested for the first time on a fine-grained pure Mg surface.This technique utilizes focused high-energy electron beam of a scanning electron microscope to“burn”dense arrays of nano-scale grid patterns on the sample surface,and it is proved to be very effective for identifying and measuring localised deformation behaviours.However,the surface marking deposited by EBDISM is not permanent and it tends to deteriorate overtime.Cheap,easy to use and versatile,the EBDISM technique has a huge potential for quantitative measurement of strain field and nano-scale deformation analysis.

Methods of configuration test and deformation analysis for large airship

In recent years, high-altitude aerostats have been increasingly developed in the direction of multi-functionality and large size. Due to the large size and the high flexibility, new challenges for large aerostats have appeared in the configuration test and the deformation analysis. The methods of the configuration test and the deformation analysis for large airship have been researched and discussed. A tested method of the configuration,named internal scanning, is established to quickly obtain the spatial information of all surfaces for the large airship by the three-dimensional(3D) laser scanning technology. By using the surface wrap method, the configuration parameters of the large airship are calculated. According to the test data of the configuration, the structural dimensions such as the distances between the characteristic sections are measured. The method of the deformation analysis for the airship contains the algorithm of nonuniform rational B-splines(NURBS) and the finite element(FE)method. The algorithm of NURBS is used to obtain the reconfiguration model of the large airship. The seams are considered and the seam areas are divided. The FE model of the middle part of the large airship is established. The distributions of the stress and the strain for the large airship are obtained by the FE method. The position of the larger deformation for the airship is found.

Slope deformation partitioning and monitoring points optimization based on cluster analysis

The scientific and fair positioning of monitoring locations for surface displacement on slopes is a prerequisite for early warning and forecasting.However,there is no specific provision on how to effectively determine the number and location of monitoring points according to the actual deformation characteristics of the slope.There are still some defects in the layout of monitoring points.To this end,based on displacement data series and spatial location information of surface displacement monitoring points,by combining displacement series correlation and spatial distance influence factors,a spatial deformation correlation calculation model of slope based on clustering analysis was proposed to calculate the correlation between different monitoring points,based on which the deformation area of the slope was divided.The redundant monitoring points in each partition were eliminated based on the partition's outcome,and the overall optimal arrangement of slope monitoring points was then achieved.This method scientifically addresses the issues of slope deformation zoning and data gathering overlap.It not only eliminates human subjectivity from slope deformation zoning but also increases the efficiency and accuracy of slope monitoring.In order to verify the effectiveness of the method,a sand-mudstone interbedded CounterTilt excavation slope in the Chongqing city of China was used as the research object.Twenty-four monitoring points deployed on this slope were monitored for surface displacement for 13 months.The spatial location of the monitoring points was discussed.The results show that the proposed method of slope deformation zoning and the optimized placement of monitoring points are feasible.

A continuous/discontinuous deformation analysis(CDDA)method based on deformable blocks for fracture modeling

In the framework of finite element meshes,a novel continuous/discontinuous deformation analysis(CDDA)method is proposed in this paper for modeling of crack problems.In the present CDDA,simple polynomial interpolations are defined at the deformable block elements,and a link element is employed to connect the adjacent block elements.The CDDA is particularly suitable for modeling the fracture propagation because the switch from continuous deformation analysis to discontinuous deformation analysis is natural and convenient without additional procedures.The SIFs(stress intensity factors)for various types of cracks,such as kinked cracks or curved cracks,can be easily computed in the CDDA by using the virtual crack extension technique(VCET).Both the formulation and implementation of the VCET in CDDA are simple and straightforward.Numerical examples indicate that the present CDDA can obtain high accuracy in SIF results with simple polynomial interpolations and insensitive to mesh sizes,and can automatically simulate the crack propagation without degrading accuracy.

Simulation of blast induced crater in jointed rock mass by discontinuous deformation analysis method

Rock blasting is a dynamic process accom panied with the propagations of shock waves and the dispersion of the explosion gas.This paper adopts the discontinuous deformation analysis(DDA)method to simulate the rock blasting process.A dynamic parameter adjustment and the non-reflecting boundary condition are implemented in the DDA method.The sub-block DDA method to simulate fracture problems is used.The blasting process in jointed rock mass is simulated by application of the explosion gas pressure on the expanding borehole walls and induced connected fracture surfaces around the boreholes.The blast craters with different overburdens are derived.The whole process including the explosion gas dispersion,borehole expansion,rock mass failure and cast,and the formation of the final blasting piles in rock blasting are well reproduced numerically.Parametric study for different overburdens is carried out,and the results are analyzed and discussed.

Dam deformation analysis based on BPNN merging models

Hydropower has made a significant contribution to the economic development of Vietnam,thus it is important to monitor the safety of hydropower dams for the good of the country and the people.In this paper,dam horizontal displacement is analyzed and then forecasted using three methods:the multi-regression model,the seasonal integrated auto-regressive moving average(SARIMA)model and the back-propagation neural network(BPNN)merging models.The monitoring data of the Hoa Binh Dam in Vietnam,including horizontal displacement,time,reservoir water level,and air temperature,are used for the experiments.The results indicate that all of these three methods can approximately describe the trend of dam deformation despite their different forecast accuracies.Hence,their short-term forecasts can provide valuable references for the dam safety.

Contact-Stress-Based Stress Recovery Methods for Discontinuous Deformation Analysis

Discontinuous deformation analysis(DDA)has been widely applied for the simulation of block systems that have many discontinuous surfaces.The penalty method is utilized to ensure that there are no penetrations between blocks.A linear polynomial function for displacement leads to a constant stress for a block,which cannot precisely describe the stress field within the block.Therefore,a high-order polynomial displacement function and a flue mesh are always used to improve the precision of the stress field.However,these means are not practical for simulating block systems that have many contacts.In this paper,the contact-stress-based stress recovery methods are proposed for DDA.High-precision solutions for the contact stresses on the boundaries of the blocks are utilized.The first-order Gaussian point of a block is the block's centroid,where the constant stress obtained via DDA is of higher precision.The high-precision solutions for the stresses are utilized in the least squares method to recover a single block's inner stress field.The proposed methods enhance the resolution of the stress field inside a single block without increasing the computational effort in the main iterative process for displacement in DDA.Numerical examples are simulated using both the finite element method(FEM)with a fine mesh and the proposed DDA program.The recovered DDA results can accurately describe the distribution of the stresses in a single block and,in some areas,have the same precision as the FEM results.Moreover,the precision of the proposed methods improves as the gradient of the contact stress on the boundary decreases.

Parallelization of spherical discontinuous deformation analysis(SDDA) for geotechnical problems based on cloud computing environment

The computational efficiency of the traditional serial spherical discontinuous deformation analysis(SDDA) program has limited its application in geotechnical engineering problems that need a large number of spheres. The cloud computing technology is used to parallel the SDDA program for the first time in this research. The most computationally intensive portions of the SDDA program, i.e., contact detection and matrix solution, are parallelized with proposed algorithms. The accuracy of the cloud-based parallel SDDA program(CB-PSDDA) is verified first. Further efficiency tests show that significant speedup can be obtained with an 8-server configuration and the computing scale can be up to several tens of thousands of particles. The cloud-based parallelized SDDA program increases its potential in applications of deformation and failure analysis of large-scale and realistic geotechnical engineering problems.

Bending and stress analysis of polymeric composite plates reinforced with functionally graded graphene platelets based on sinusoidal shear-deformation plate theory

The bending and stress analysis of a functionally graded polymer composite plate reinforced with graphene platelets are studied in this paper.The governing equations are derived by using principle of virtual work for a plate which is rested on Pasternak’s foundation.Sinusoidal shear deformation theory is used to describe displacement field.Four different distribution patterns are employed in our analysis.The analytical solution is presented for a functionally graded plate to investigate the influence of important parameters.The numerical results are presented to show the deflection and stress results of the problem for four employed patterns in terms of geometric parameters such as number of layers,weight fraction and two parameters of Pasternak’s foundation.

Research on Deformation and Force of Bridge Pile Foundation on High and Steep Slope in Mountainous Area

With the rapid development of my country’s economy, the demand for infrastructure construction is also increasing. However, in most areas of China, the terrains are mountainous and hilly. Some projects have to be built on steep slopes. Choosing viaducts or half-bridges on high-steep slopes is not only conducive to the protection of the surrounding environment, but also conducive to the stability of the slope. Bridges usually choose the form of pile foundation-high pier bridge. This paper uses numerical simulation to study and analyze the bridge pile foundation of the slope section. Relying on actual engineering, use the finite element software ABAQUS6.14 to establish a three-dimensional finite element model to study the bearing mechanism and mechanical characteristics of the pile foundation under vertical load, horizontal load and inclined load, discuss the influence of the nature of the soil around the pile and the stiffness of the pile body on the deformation and internal force of the bridge pile foundation in the slope section. The analysis results show that the horizontal load has a great influence on the horizontal displacement of the pile, but has a small influence on the vertical displacement, and the vertical load is just the opposite. Inclined load has obvious “p-Δ” effect. The increase in soil elastic modulus and pile stiffness will reduce the displacement of the pile foundation, but after reaching a certain range, the displacement of the pile foundation will tend to be stable. Therefore, in actual engineering, if the displacement of the pile foundation fails to meet the requirements, the hardness of the soil and the stiffness of the pile can be appropriately increased, but not blindly.

The Effect of Microstructural and Geometric Inhomogeneities Induced by Laser for Forming Strain Analysis on Sheet Metal Formability

A commercially available laser marking system based on diode-pumped Nd:YVO4 laser was used for creating grid patterns for forming strain analysis of a dual-phase steel. The aim was to determine and analyze the influence of laser working parameters on the formability of sheet material by means of an in-depth characterization of this induced microstructural and geometric inhomogeneity. The electrochemical etching served as the reference method without the negative effect of generating inhomogeneity. The formability was evaluated using the cupping test according to Erichsen. While the quantification of geometric inhomogeneity was based on the determination of the notch factor, light microscopy and microhardness measurement were used for the evaluation of microstructural inhomogeneity. Furthermore, on the basis of the results an empirical regression model was established which described in terms of quantity the relationship between the examined factors such as laser power, pulse frequency and scanning speed as well as the command variable and the mark depth. The results showed that microstructural inhomogeneity in the used marking parameters due to their locally very limited formation did not have an appreciable influence on the mechanical properties. In contrast to this, the induced geometric inhomogeneity had a marked influence on the material formability.

Failure of levees induced by toe uplift:Investigation of post-failure behavior using material point method

Levees are essential structures in flood defense systems,and their failures can lead to devastating consequences on the surrounding territories.One of the failure mechanisms mostly controlled by the foundation soil stratigraphy is the instability of the land side slope,triggered by the development of high uplift pressures in the foundation.This complex phenomenon has been investigated experimentally with centrifuge tests or large-scale tests and numerically with the limit equilibrium method(LEM)and the finite element method(FEM).In this work,we applied a multiphase formulation of the material point method(MPM)to analyze the development of toe uplift instability mechanism,from the onset of failure to large displacements.The numerical model is inspired by an experiment carried out in a geotechnical centrifuge test by Allersma and Rohe(2003).The comparison with the experiment allows for understanding critical pore pressure triggering large displacements in the foundation soils.Moreover,we numerically evaluated the impact of different values of foundation soils’hydraulic conductivity on the failure mechanism.The results show that hydraulic conductivity mainly influences the time of failure onset and the extension of shear localization at depth.Finally,the advantages of using large displacement approaches in the safety assessment of earth structures are discussed.Unlike FEM,there are no issues with element distortions generating difficulties with numerical convergence,allowing for full postfailure reproduction.This capability permits precise quantification of earth structure damages and post-failure displacements.The ensuing reinforcement systems’design is no longer over-conservative,with a significant reduction in associated costs.

Fault activity characteristics in the northern margin of the Tibetan Plateau before the Menyuan Ms6.4 earthquake

Fault deformation characteristics in the northern margin of the Tibetan Plateau before the Menyuan Ms6.4 earthquake are investigated through time-series and structural geological analysis based on cross-fault observation data from the Qilian Mountaine Haiyuan Fault belt and the West Qinling Fault belt. The results indicate: 1) Group short-term abnormal variations appeared in the Qilian Mountaine Haiyuan Fault belt and the West Qinling Fault belt before the Menyuan Ms6.4 earthquake. 2) More medium and short-term anomalies appear in the middle-eastern segment of the Qilian Mountain Fault belt and the West Qinling Fault belt, suggesting that the faults' activities are strong in these areas. The faults' activities in the middle-eastern segment of the Qilian Fault belt result from extensional stress, as before the earthquake, whereas those in the West Qinling Fault belt are mainly compressional. 3) In recent years, moderate-strong earthquakes occurred in both the Kunlun Mountain and the Qilian Mountain Fault belts, and some energy was released. It is possible that the seismicity moved eastward under this regime. Therefore, we should pay attention to the West Qinling Mountain area where an Ms6-7 earthquake could occur in future.

Practical studies on rockfall simulation by DDA

In this paper,simulations of real rockfall by discontinuous deformation analysis (DDA) are conducted.In the simulations,the energy losses of rockfall are categorized into three types,i.e.the loss by friction,the loss by collision,and the loss by vegetation.Modeling of the energy loss using absolute parameters is conducted by the DDA method.Moreover,in order to verify the applicability and validity of the proposed DDA,field tests on rockfall and corresponding simulations of rockfall tests by DDA are performed.The simulated results of rockfall velocity and rockfall jumping height agree well with those obtained from the field tests.Therefore,the new technique properly considers the energy-absorption ability of slope based on vegetation condition and shape of the rockfall,and provides a new method for the assessment and preventive design of rockfall.