Modeling time-dependent mechanical behavior of hard rock considering excavation-induced damage and complex 3D stress states

To investigate the long-term stability of deep rocks,a three-dimensional(3D)time-dependent model that accounts for excavation-induced damage and complex stress state is developed.This model comprises three main components:a 3D viscoplastic isotropic constitutive relation that considers excavation damage and complex stress state,a quantitative relationship between critical irreversible deformation and complex stress state,and evolution characteristics of strength parameters.The proposed model is implemented in a self-developed numerical code,i.e.CASRock.The reliability of the model is validated through experiments.It is indicated that the time-dependent fracturing potential index(xTFPI)at a given time during the attenuation creep stage shows a negative correlation with the extent of excavationinduced damage.The time-dependent fracturing process of rock demonstrates a distinct interval effect of the intermediate principal stress,thereby highlighting the 3D stress-dependent characteristic of the model.Finally,the influence of excavation-induced damage and intermediate principal stress on the time-dependent fracturing characteristics of the surrounding rocks around the tunnel is discussed.

3D DEM simulation of hard rock fracture in deep tunnel excavation induced by changes in principal stress magnitude and orientation

To achieve the loading of the stress path of hard rock,the spherical discrete element model(DEM)and the new flexible membrane technology were utilized to realize the transient loading of three principal stresses with arbitrary magnitudes and orientations.Furthermore,based on the deep tunnel of China Jinping Underground Laboratory II(CJPL-II),the deformation and fracture evolution characteristics of deep hard rock induced by excavation stress path were analyzed,and the mechanisms of transient loading-unloading and stress rotation-induced fractures were revealed from a mesoscopic perspective.The results indicated that the stressestrain curve exhibits different trends and degrees of sudden changes when subjected to transient changes in principal stress,accompanied by sudden changes in strain rate.Stress rotation induces spatially directional deformation,resulting in fractures of different degrees and orientations,and increasing the degree of deformation anisotropy.The correlation between the degree of induced fracture and the unloading magnitude of minimum principal stress,as well as its initial level is significant and positive.The process of mechanical response during transient unloading exhibits clear nonlinearity and directivity.After transient unloading,both the minimum principal stress and minimum principal strain rate decrease sharply and then tend to stabilize.This occurs from the edge to the interior and from the direction of the minimum principal stress to the direction of the maximum principal stress on theε1-ε3 plane.Transient unloading will induce a tensile stress wave.The ability to induce fractures due to changes in principal stress magnitude,orientation and rotation paths gradually increases.The analysis indicates a positive correlation between the abrupt change amplitude of strain rate and the maximum unloading magnitude,which is determined by the magnitude and rotation of principal stress.A high tensile strain rate is more likely to induce fractures under low minimum principal stress.

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.

Three-Dimensional Analysis of Rolling by Twin Shear Stress Yield Criterion

Using the twin shear stress yield criterion, the surface integral of the co-line vectors, and the integration depending on upper limit, Kobayashi＇s three-dimensional velocity field of rolling was analyzed and an analytical expression of rolling torque and single force was obtained. Through redoing the same experiment of rolling pure lead as Sims, the calculated results by the above expression were compared with those of Kobayashi and Sims formulae. The results show that the twin shear stress yield criterion is available for rolling analysis and the calculated results by the new formula are a little higher than those by Kobayashi and Sims ones if the reduction ratio is less than 30%.

Autologous nerve graft repair of different degrees of sciatic nerve defect:stress and displacement at the anastomosis in a three-dimensional finite element simulation model

In the repair of peripheral nerve injury using autologous or synthetic nerve grafting, the mag- nitude of tensile forces at the anastomosis affects its response to physiological stress and the ultimate success of the treatment. One-dimensional stretching is commonly used to measure changes in tensile stress and strain; however, the accuracy of this simple method is limited. There- fore, in the present study, we established three-dimensional finite element models of sciatic nerve defects repaired by autologous nerve grafts. Using PRO E 5.0 finite element simulation software, we calculated the maximum stress and displacement of an anastomosis under a 5 N load in 10-, 20-, 30-, 40-mm long autologous nerve grafts. We found that maximum displacement increased with graft length, consistent with specimen force. These findings indicate that three-dimensional finite element simulation is a feasible method for analyzing stress and displacement at the anas- tomosis after autologous nerve grafting.

Three-Dimensional Thermo-Elastic-Plastic Finite Element Method Modeling for Predicting Weld-Induced Residual Stresses and Distortions in Steel Stiffened-Plate Structures

The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this purpose, three-dimensional thermo-elastic-plastic finite element method computations are performed with varying plate thickness and weld bead length (leg length) in welded plate panels, the latter being associated with weld heat input. The finite element models are verified by a comparison with experimental database which was obtained by the authors in separate studies with full scale measurements. It is concluded that the nonlinear finite element method models developed in the present paper are very accurate in terms of predicting the weld-induced initial imperfections of steel stiffened plate structures. Details of the numerical computations together with test database are documented.

Strip Layer Method for Analysis of the Three-Dimensional Stresses and Spread of Large Cylindrical Shell Rolling

As the traditional forging process has many problems such as low efficiency, high consumption of material and energy, large cylindrical shell rolling is introduced. Large cylindrical shell rolling is a typical rotary forming technology, and the upper and lower rolls have different radii and speeds. To quickly predict the three-dimensional stresses and eliminate fishtail defect, an improved strip layer method is developed, in which the asymmetry of the upper and lower rolls, non-uniform deformation and stress, as well as the asymmetrical spread on the end surface are considered. The deformation zone is divided into a certain number of layers and strips along the thickness and width, respectively. The transverse displacement model is constructed by polynomial function, in order to increase the computation speed greatly. From the metal plastic mechanics principle, the three-dimensional stress models are established. The genetic algorithm is used for optimization calculation in an industrial experiment example. The results show that the rolling pressure, the normal stresses, the upper and lower friction stress distributions are not similar with those of a general plate rolling. There are two relative maximum values in rolling pressure distribution. The upper and lower longitudinal friction stresses change direction nearby the upper and lower neutral points, respectively. The fishtail profile of spread on the end surface is predicted satisfactorily. The reduction could be helpful to eliminate fishtail defect. The large cylindrical shell rolling example illustrates the calculation results acquired rapidly are good agreements with the finite element simulation and experimental values of previous study. A highly effective and reliable three-dimensional simulation method is proposed for large cylindrical shell rolling and other asymmetrical rolling.

Three-Dimensional Stress Fields in Finite Thickness Plate with Hole Under Shear Load

The theoretical solutions are obtained for the three-dimensional(3-D)stress field in an infinite isotropic elastic plate with a through-the-thickness circular hole subjected to shear load at far field by using Kane and Mindlin′s assumption based on the stress function method.Based on the present solutions,the characteristics of 3-D stress field are analyzed and the emphasis is placed on the effects of the plate thickness and Poisson′s ratio on the deviation of the present 3-D in-plane stress from the related plane stress solutions,the stress concentration and the out-of-plane constraint.The present solutions show that the stress concentration factor reaches its peak value of about 8.9% which is higher than that of the plane stress solutions.As expected,the out-of-plane stress constraint factor can reach 1on the surface of the hole when the plate is a very thick one.

CONVOLUTION OF THE IMPACT THREE-DIMENSIONAL ELASTO-DYNAMICS AND DYNAMIC STRESS INTENSITY FACTOR FOR AN ELLIPTIC CRACK

This paper presents a formulation for three-dimensional elasto-dynamics with an elliptic crack based on the Laplace and Fourier transforms and the convolution theorem. The dynamic stress intensity factor for the crack is determined by solving a Fredholm integral equation of the first kind. The results of this paper are very close to those given by the two-dimensional dual integral equation method.

Three-Dimensional Thermal-Stress Analysis of Semi-infinite Transversely Isotropic Composites

By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local thermal and force loadings.The material plane of isotropy is assumed to be parallel to the limiting surface of the halfspace.By reducing the original thermoelasticity equations to the governing ones for individual stress-tensor components,the effect of material anisotropy in the stress field is analyzed with regard to the feasibility requirement,i.e.,the finiteness of the stress field at a distance from the disturbed area.As a result,the solution is constructed in the form of explicit analytical dependencies on the force and thermal loadings for various kinds of transversely isotropic materials and agrees with the basic principles of the continua mechanics.The solution can be efficiently used as a benchmark one for the direct computation of temperature and thermal stresses in transversely isotropic semi-infinite domains,as well as for the verification of solutions constructed by different means.

The Expression of Stress and Strain at the Tip of Three-Dimensional Notch

The singularity of stress and strain at the tip of three-dimensional notch isanalysed by the power expansion method .the eigenquation of the notch is gainedthrough the boundary conditions of the notch, the eigenvalues under different innerangles of the notch are obtained, the expression of stress and strain at the tip of thenotch is finally derived .

Stream Surface Strip Element Method and Simulation of Three-Dimensional Deformation of Continuous Hot Rolled Strip

A new method,the stream surface strip element method,for simulating the three-dimensional deformation of plate and strip rolling process was proposed.The rolling deformation zone was divided into a number of stream surface(curved surface)strip elements along metal flow traces,and the stream surface strip elements were mapped into the corresponding plane strip elements for analysis and computation.The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal were respectively constructed to be a quartic curve and a quadratic curve,of which the lateral distributions were expressed as the third-power spline function,and the altitudinal distributions were fitted in the quadratic curve.From the flow theory of plastic mechanics,the mathematical models of the three-dimensional deformations and stresses of the deformation zone were constructed.Compared with the streamline strip element method proposed by the first author of this paper,the stream surface strip element method takes into account the uneven distributions of stresses and deformations along altitudinal direction,and realizes the precise three-dimensional analysis and computation.The simulation example of continuous hot rolled strip indicates that the method and the model accord with facts and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.

Numerical study of three-dimensional wave-induced longshore current's effects on sediment spreading of the Huanghe River mouth

A three-dimensional wave radiation stress is introduced into the hydrodynamic sediment coupled model COHERENS-SED, which has been developed through introducing wave-enhanced bottom shear stress, wave dependent surface drag coefficient, wave-induced surface mixing, SWAN, damping function of sediment on turbulence, sediment model and depth-dependent wave radiation stress to COHERENS. The COHERENS-SED is adopted to study the effects induced by wave-induced three-dimensional longshore current on suspended sediment spreading of the Huanghe River （Yellow River） mouth. Several different cases divided by setting different wave parameters of inputting boundary waves are carried out. The modeling results agree with measurement data. In terms of simulation results, it is easy to know that three-dimensional wave radiation stress plays an obvious role when inputting boundary wave height is stronger than 3 m. Moreover, wave direction also affects the sediment spreading rules of the mouth strongly too.

Dynamic Stress Analysis of the Leg Joints of Self-Elevating Platform

Since a self-elevating platform often works in water for a long time, the lattice leg is largely influenced by wave and current. The amplitude of leg joint stresses is a very important factor for the fatigue life of the platform. However, there are not many researches having been done on the mechanism and dynamic stress analysis of these leg joints. This paper focuses on the dynamic stress analysis and suppression methods of the leg joints of self-elevating platforms. Firstly, the dynamic stresses of the lattice leg joints are analyzed for a self-elevating platform by use of the 5th-order Stokes wave theory. Secondly, the axial and bending stresses are studied due to their large contributions to total stresses. And then, different joint types are considered and the leg-hull interface stiffness is analyzed for the improvement of the joint dynamic stress amplitude. Finally, some useful conclusions are drawn for the optimization design of the self-elevating platform.

A simplified three-dimensional extension of Hoek-Brown strength criterion

The Hoek-Brown(HB)strength criterion has been applied widely in a large number of projects around the world.However,this criterion ignores the intermediate principal stress s2.Many evidences have demonstrated that the rock strength is dependent on s2.Thus it is necessary to extend the HB criterion into a three-dimensional(3D)form.In this study,the effect of s2 on the strength of rocks is identified by reviewing the true triaxial tests of various rock types reported in the literature.A simple 3D strength criterion is developed.The modified criterion is verified by the true triaxial tests of 13 rock types.The results indicate that the modified criterion can achieve a good fit to most of rock types.It can represent a series of criteria as b varies.For comparisons,several existing 3D versions of the HB criterion are selected to predict the strengths of these rock types.It is indicated that the proposed criterion works better than other criteria.A substantial relationship between parameter b and the unconfined compressive strength is established,which guarantees that the proposed criterion can still work well even in the absence of true triaxial test data.

Three-dimensional photoelasticity analysis of Nitinol Patellar Concentrator for treating patellar fractures

Objective: To analyze the biomechanical elements of Nitinol Patellar Concentrator (NT-PC) in heating commi nuted patellar fractures. Methods: The epoxy resin three dimensional photoelasticity pobal model was loaded with Nitinol Patellar Connector and frozen. After dividing layer, photographing and tracing, iterative method was used to calculate the stress value of every tuteed node. Rasults: Stress values of 1 262 nodes scattered in 12 layers were obtained The stress distribution indicated that an overall stress field was yield when the NT-PC fixated the patellar model, and there existed fixative stress in the facies articularis and distal pole of the patellar model. Conclusion: The NT-PC has evident therapeutic effect for the comminuted patellar fractures. The existing stress is helpful in maintaining anatomical reduction and enhancing fracture healing.

Three-dimensional surface model analysis in the gastrointestinal tract

The biomechanical changes during functional loading and unloading of the human gastrointestinal （GI） tract are not fully understood. GI function is usually studled by introducing probes in the GI lumen. Computer modeling offers a promising alternative approach in this regard, with the additional ability to predict regional stresses and strains in inaccessible locations. The tension and stress distributions in the GI tract are related to distensibility （tension-strain relationship） and smooth muscle tone. lore knowledge on the tension and stress on the GI tract are needed to improve diagnosis of patients with gastrointestinal disorders. A modeling framework that can be used to integrate the physiological, anatomical and medical knowledge of the GI system has recently been developed. The 3-D anatomical model was constructed from digital images using ultrasonography, computer tomography （CT） or magnetic resonance imaging （IRI）. Different mathematical algorithms were developed for surface analysis based on thin-walled structure and the finite element method was applied for the mucosa-folded three layered esophageal model analysis. The tools may be useful for studying the geometry and biomechanical properties of these organs in health and disease. These studies will serve to test the structurefunction hypothesis of geometrically complex organs.

Analysis of Three-dimensional Crack Propagation by Using Displacement Discontinuity Method

A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the two contacted surfaces of the crack must be satisfied.A simple iterative method was adopted in order to consider three different states of cracks.Under the assumption that the advance of the point on the crack front would occur only in the normal plane which is through this edge point,the maximum energy release rate criterion is modified to be used as the criterion for the crack growth.With discretization,the process of crack propagation can be seen as the advance of the vertices of the crack front.The program MCP3D was developed based on these theories to simulate the 3D quasi-static crack propagation.A numerical example of a penny-shaped crack subject to tension and compression in an infinite elastic media was analyzed with MCP3D,and the results in comparison with others' show that the present method for 3D crack propagation is effective.

Three-dimensional FDEM numerical simulation of failure processes observed in Opalinus Clay laboratory samples

This study presents the first step of a research project that aims at using a three-dimensional （3D） hybridfinite-discrete element method （FDEM） to investigate the development of an excavation damaged zone（EDZ） around tunnels in a clay shale formation known as Opalinus Clay. The 3D FDEM was first calibratedagainst standard laboratory experiments, including Brazilian disc test and uniaxial compression test. Theeffect of increasing confining pressure on the mechanical response and fracture propagation of the rockwas quantified under triaxial compression tests. Polyaxial （or true triaxial） simulations highlighted theeffect of the intermediate principal stress （s2） on fracture directions in the model： as the intermediateprincipal stress increased, fractures tended to align in the direction parallel to the plane defined by themajor and intermediate principal stresses. The peak strength was also shown to vary with changing s2. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

基于CFD和热阻网络法的C型舱LEG船温度场分析及热应力计算

为解决C型舱LEG船进行温度场计算时,CFD方法难以计入结构细节以及热阻网络法处理热对流精度较低的问题,提出将2种方法相结合的船体结构温度场计算方法。在CFD计算时,只考虑主要结构,将计算结果作为热阻网络法的输入,而在热阻网络法中考虑结构细节。实船计算结果显示,该方法高效可靠,避免了2种方法的缺点,可以合理地求解船体结构的温度场,是一种工程上实用的方法。计算还表明,对于温度梯度大的关键结构区域,结构强度评估需要考虑热应力。