Elastic-plastic Boundary Research Articles

Bearing Performance of a Helical Pile for Offshore Photovoltaic under Horizontal Cyclic Loading

For an offshore photovoltaic helical pile foundation, significant horizontal cyclic loading is imposed by wind and waves. To study a fixed offshore PV helical pile’s horizontal cyclic bearing performance, a numerical model of the helical pile under horizontal cyclic loading was established using an elastic–plastic boundary interface constitutive model of the clay soil. This model was compared with a monopile of the same diameter under similar conditions. The study examined the effects of horizontal cyclic loading amplitude, period, and vertical loads on the horizontal cyclic bearing performance. The results show that under horizontal monotonic loading, the bearing capacities of a helical pile and monopile in a serviceability limit state are quite similar. However, as the amplitude of horizontal cyclic loading increases, soil stiffness deteriorates significantly, leading to greater horizontal displacement accumulation for both types of piles. The helical pile’s bearing capacity under horizontal cyclic loadings is approximately 60% of that under monotonic loading. With shorter cyclic loading periods, horizontal displacement accumulates rapidly in the initial stage and stabilizes over a shorter duration. In contrast, longer cyclic loading periods lead to slower initial displacement accumulation, but the total accumulated displacement at stabilization is greater. When vertical loads are applied, the helical pile exhibits more stable horizontal cyclic bearing performance than the monopile.

Fatigue and Autofrettage Analysis of Steel Sleeve Based on Precision Fit under Ultra High Pressure

Abstract In order to ensure precision fit between steel sleeve and plunger, copper sleeve and the other parts of the ultra high pressure plunger pump, as well as increase the fatigue life of steel sleeve, this paper made the analysis of work process and fatigue life of ultra high pressure autofrettage steel sleeve of plunger pump based on both analytical method and FEM. The elastic-plastic boundary radius, radial stress and plastic zone displacement were obtained based on the elastic-plastic mechanics analysis of ultra high pressure steel sleeve. The functional relationship built related to precision fit among autofrettage pressure, inner diameter expectation and displacement could ensure the machining dimension of inner diameter of steel sleeve and realize the precise control of inner diameter of steel sleeve. The analytical method and FEM for calculating fatigue life was also proposed, which are verified by experiment. The research shows that machining dimension is determined by inner diameter expectation in the autofrettage process to ensure precision fit; autofrettage treatment can reduce the working stress level of the steel sleeve and extend the fatigue life remarkably. These conclusions contribute to guide the design of steel sleeve.

Application of efficient algorithm based on block Newton method to elastoplastic problems with nonlinear kinematic hardening

PurposeThe purpose of this study is to present the effectiveness and robustness of a numerical algorithm based on the block Newton method for the nonlinear kinematic hardening rules adopted in modeling ductile materials.Design/methodology/approachElastoplastic problems can be defined as a coupled problem of the equilibrium equation for the overall structure and the yield equations for the stress state at every material point. When applying the Newton method to the coupled residual equations, the displacement field and the internal variables, which represent the plastic deformation, are updated simultaneously.FindingsThe presented numerical scheme leads to an explicit form of the hardening behavior, which includes the evolution of the equivalent plastic strain and the back stress, with the internal variables. The features of the present approach allow the displacement field and the hardening behavior to be updated straightforwardly. Thus, the scheme does not have any local iterative calculations and enables us to simultaneously decrease the residuals in the coupled boundary value problems.Originality/valueA pseudo-stress for the local residual and an algebraically derived consistent tangent are applied to elastic-plastic boundary value problems with nonlinear kinematic hardening. The numerical procedure incorporating the block Newton method ensures a quadratic rate of asymptotic convergence of a computationally efficient solution scheme. The proposed algorithm provides an efficient and robust computation in the elastoplastic analysis of ductile materials. Numerical examples under elaborate loading conditions demonstrate the effectiveness and robustness of the numerical scheme implemented in the finite element analysis.

Elastic-plastic torsion of a two-layer rod

We study the elastic-plastic torsion of a two-layer rod under the action of torque in this article. It is assumed that the rod consists of two layers. Each layer has its own elastic properties, but the plastic properties of both layers are the same. The contact boundary of the layers is located along the oh axis. The lateral boundary of the rod is stress-free, displacements and stresses are continuous at the interface. The components of the stress tensor at a point are calculated using contour integrals derived from conservation laws calculated along the lateral boundary. Next, the second invariant of the stress tensor is compared with the yield strength. At those points where the yield point is reached, the plastic state is realized, in the rest -elastic. This allows you to build a boundary between the plastic and elastic regions. This technique provides a way to calculate elastic-plastic boundaries for the main rolling profiles of rods. This is supposed to be done in subsequent works. We remind you that earlier, with the help of conservation laws, the main boundary value problems for a plastic two-dimensional medium, elastic-plastic torsion of isotropic rods and elastic media for bodies of finite dimensions were solved.solutions.

A post-peak dilatancy model for soft rock and its application in deep tunnel excavation

The dilation angle is the most commonly used parameter to study nonlinear post-peak dilatancy (PPD) behavior and simulate surrounding rock deformation; however, simplified or constant dilatancy models are often used in numerical calculations owing to their simple mathematical forms. This study developed a PPD model for rocks (rock masses) based on the Alejano–Alonso (A–A) dilatancy model. The developed model comprehensively reflects the influences of confining pressure (σ3) and plastic shear strain (γp), with the advantages of a simple mathematical form, while requiring fewer parameters and demonstrating a clear physical significance. The overall fitting accuracy of the PPD model for 11 different rocks was found to be higher than that of the A–A model, particularly for Witwatersrand quartzite and jointed granite. The applicability and reliability of the PPD model to jointed granites and different scaled Moura coals were also investigated, and the model was found to be more suitable for the soft and large-scale rocks, e.g. deep rock mass. The PPD model was also successfully applied in studying the mechanical response of a circular tunnel excavated in strain-softening rock mass, and the developed semi-analytical solution was compared and verified with existing analytical solutions. The sensitivities of the rock dilatancy to γp and σ3 showed significant spatial variabilities along the radial direction of the surrounding rock, and the dilation angle did not exhibit a monotonical increasing or decreasing law from the elastic–plastic boundary to the tunnel wall, thereby presenting the σ3-or γp-dominated differential effects of rock dilatancy. Tunnel deformation parabolically or exponentially increased with increasing in situ stress (buried depth). The developed PPD model is promising to conduct refined numerical and analytical analyses for deep tunneling, which produces extensive plastic deformation and exhibits significant nonlinear post-peak behavior.

Mechanical Modeling of Tube Bending Considering Elastoplastic Evolution of Tube Cross-Section.

Aluminum alloy tubes are widely used in various industries because of their excellent performance. Up to now, when the tube is bent, the elastoplastic deformation evolution mechanism of the cross-section has not been clear, and no direct analytical proof has been found. In this paper, based on the bilinear material model assumption, a new mechanical model of tube plane bending deformation is constructed. The analytical model can describe in detail the evolution mechanism of elastic–plastic deformation on the cross-section of the tube after bending deformation, the position of the elastic–plastic boundary, the position of the radius of the strain neutral layer, and the relationship between the bending moment over the section and the bending radius. According to this model, the deformation law of the tube cross-section during bending is elucidated. The results are as follows: (1) the deformation evolution of the cross-section of the bending deformed tube calculated by the analytical model is in good agreement with the finite element model (FEM) of pure bending. (2) By comparing the results of the analytical model with FEM results, and the processing test of the self-designed four-axis free bending forming tube bender, the bending moments are in good agreement. (3) Compared with the bending moments calculated by several other analytical models of tube bending, this model has a relatively small deviation value.

Analysis of undrained cylindrical cavity contraction in anisotropic soils under constant total vertical stress condition

A semi-analytical solution to cylindrical cavity contraction in anisotropic soils under constant total vertical stress and undrained condition is presented in this paper. The elastoplastic constitutive relationship for the problem considered is obtained via Hooke’s law in the elastic stage and the anisotropic modified Cam-Clay model in the plastic stage. By employing an auxiliary parameter to transform the equilibrium equation from Eulerian scheme into Lagrangian scheme, the problem reduces to an initial value problem with the vertical strain and the effective radial, circumferential, vertical stresses as four basic unknowns. The governing equations of this problem in the plastic region are solved as an initial value problem with the mechanical states of soil at the elastic-plastic boundary as the initial values. Parametric analyses show that, owing to the large deformation in the vertical direction, the material particle at cavity surface reaches the critical state much more quickly under constant total vertical stress condition than that under plane strain condition. The distribution of stress components does not manifest a critical-state region as a traditional plane strain solution does. Also, the overconsolidation ratio has an obvious influence on contraction responses. The proposed solution is expected to provide a more accurate prediction of stress and displacement around a drilled wellbore and to other similar geotechnical problems.

Combined approach for fatigue crack characterisation in metals

In this work a comprehensive characterisation of the fatigue crack growth of an Al 2024 alloy is presented. A powerful Christopher-James-Patterson (CJP) model is used for multi-parameter characterisation of the crack state at a few different locations through the fatigue crack growth. The CJP model of crack tip displacements and stress fields was proposed in order to better capture the influences on the applied elastic stress field of the plastic enclave that is generated around a growing fatigue crack. The model does this through a set of elastic stresses applied at a notional elastic-plastic boundary, and it has been shown to accurately model plastic zone shape and size, whilst its ability to predict the effective range of stress intensity factor during a fatigue cycle has been verified. Thus, the model can predict the driving force component of the crack and additional components that account for different shielding mechanisms. CJP model is combined with full-field non-contact Digital Image Correlation (DIC) so that the model can be fed at any moment with real experimental information. The results are then correlated with Paris law data for Al 2024 alloy through Scanning Electron Microscopy (SEM) observations of the fracture surface. In this work the effect of crack length and load level are thoroughly studied and validated with fatigue crack growth rate measurements.

Densification effects on the fracture in fused silica under Vickers indentation

This study investigates the effects of densification on the deformation and fracture in fused silica under Vickers indentation by both the finite element analysis (FEA) and experimental tests. A refined elliptical constitutive model was used, which enables us to investigate the effects of the evolution of yield stress under pure shear and elastic properties with densification. The densification distribution was predicted and compared with experiments. The plastic deformation and indentation stress fields were used to analyze the initiation and morphology of various crack types. The formation mechanism of borderline cracks was revealed for the first time. This study reveals that the asymmetry of the densification distribution and elastic-plastic boundary significantly influences the cracking behavior. Under the Vickers indentation, conical cracks have the largest penetration depth. When these cracks emerge from a region far from the impression, they extend with constant radii to form circles on the sample surface. Otherwise, they tend to be initiated at the centers of the indenter-material contact edges before propagating towards the impression corners with increasing radii. Therefore, the borderline cracks consisting of successive partial conical cracks can form at a low load and makes them the first type of crack to appear.

Analytical model for three-dimensional non-uniform temperature field and welding stress of thick plates via friction stir weld

The non-uniform thermal field for thick plates jointed by friction stir welding (FSW) easily causes the complex stress state and affects the mechanical behaviour of welded components. The transient non-uniform temperature field for thick plates by FSW is analytically studied based on the heat conduction problem solved by three-dimensional Green’s function. The asymmetric volumetric heat source model is developed by considering the flux distributions in the thickness direction, which is used to obtain the semi-analytical temperature field for welded plates with nonhomogeneous boundary conditions. Then, the analytical model for welding stress is proposed for thick plates by FSW according to the non-uniform temperature field in the weld. The elastic-plastic boundary and the variations of welding stress in the thickness direction are discussed based on the temperature gradient in the welding process. The non-uniform stress distribution in the weld may be analytically predicted in the welding process. The residual stress in the weld is numerically calculated in the cooling process and compared with experiment data to verify the models for the non-uniform temperature field and stress distribution of thick plates. The results show that the three-dimensional temperature field may be used effectively to provide insights into the mechanical response by FSW.

The seismic behaviour of precast concrete interior joints with different connection methods in assembled monolithic subway station

The study investigated the performance of a specific full-scale precast concrete interior joint using many connected methods (e.g. grouted sleeves, anchorage arrangements, corbels) in the core region of joint, whilst a monolithic cast-in-place concrete specimen served as a control. The important indexes in terms of failure mode, hysteretic behavior, strength, deformation performance, and stiffness degradation were investigated under low-reversed cyclic loading. The new cross-lapping connection of concrete slab was presented and the position of the interface between two layers of lamination slab was optimized. The experimental and analysis results indicated that, (1) the precast concrete specimens were capable of matching peaking strength and deformation performance of the monolithic cast-in-place joint, while the displacement ductility and failure modes of two joints were different; (2) the elastic–plastic boundary of 1/550 which was used to evaluate precast structures should be carefully selected in the design; (3) an effective range for the thickness ratio of upper layer (post-pouring concrete) and lower layer (precast concrete) was presented; (4) a new cross-lapping connection for bend-up reinforcement at the ends of the semi-precast slab was performed for another optional method.

Undrained cylindrical cavity expansion in modified cam-clay soil: A semi-analytical solution considering biaxial in-situ stresses

This paper presents a semi-analytical solution for undrained cylindrical cavity expansion in modified Cam-clay soils under biaxial in-situ stresses based on the small strain and large strain assumptions in the elastic and plastic regions, respectively. The cylindrical cavity expansion problem is treated as a boundary value problem and formulated by solving a system of first-order differential equations with four stress components as basic unknown variables. The validity of the proposed solution is examined by comparing with the existing solution, where the in-situ stress is uniform. Extensive parametric studies are conducted to investigate the effects of biaxial in-situ stresses on the stress distribution, the expansion process and the shape and size of elastic-plastic boundary. The results indicate that the elastic-plastic boundary is in the shape of an ellipse due to the shear stress induced by biaxial in-situ stresses. The major axis of the elliptical elastic-plastic boundary is in accordance with the direction of the larger in-situ stress. The present solution is free of the limitation that the cavity expands under the uniform in-situ stress, therefore it is expected to provide a more general method for practical geotechnical and petroleum problems.

Study on the subsurface damage mechanism of optical quartz glass during single grain scratching

The single grain scratching SPH simulation model was established to study the subsurface damage of optical quartz glass. Based on the analysis of the stress, strain and scratching force during scratching, the generation and propagation of subsurface cracks were studied by combining with the scratch elastic stress field model. The simulation results show that the cracks generate firstly at the elastic-plastic deformation boundary in front of the grain (φ = 28°) due to the influence of the maximum principal tensile stress. During the scratching process, the median crack closes to form the subsurface damage by extending downward, the lateral crack promotes the brittle removal of the material by extending upward to the free surface, and microcracks remain in the elastic-plastic boundary at the bottom of the scratch after scratching. The depth of subsurface crack and plastic deformation increases with rising scratching depth. The increase of scratching speed leads to the greater dynamic fracture toughness, accompanied by a significant decrease of the maximum depth of subsurface crack and the number of subsurface cracks. The subsurface residual stress is concentrated at the bottom of the scratch, and the residual stress on both sides of the scratch surface would generate and propogate the Hertz crack. When the scratching depth is less than 1.5 μm or the scratching speed is greater than 75 m/s, the residual stress value and the depth of residual stress are relatively small. Finally, the scratching experiment was carried out. The simulation analysis is verified to be correct, as the generation and propagation of the cracks in the scratching experiment are consistent with the simulation analysis and the experimental scratching force indicates the same variation tendency with the simulation scratching force. The research results in this paper could help to restrain the subsurface damage in grinding process.

Deformation analysis of geosynthetic-encased stone column-supported embankments using cavity expansion model

This article presents an analytical solution to predict the deformation of geosynthetic-encased stone columns (GESCs) and the surrounding soil in GESC-supported embankments, taking into account the effect of anisotropy of surrounding soil. Based on the theory of cylindrical cavity expansion, the elastoplastic constitutive relationship of the surrounding soil is described by the K 0-based Modified Cam-Clay (K 0-MCC) model, analysing the relationship between the radial displacement and the elastic-plastic boundary displacement. According to elastoplastic model of stone column materials, the relationship between stress and deformation of the stone column is analysed via the radial stress and the vertical stress equilibrium. This method has been verified by the existing numerical data of GESC-supported embankments and shows a good agreement. As for the isotropic in situ stress state, the K 0-MCC model-based solution of this study reduces to the MCC model-based solution of previous studies. However, the results show that the predictions generated from the isotropic model underestimate the deformation of the surrounding soil. Parametric studies are conducted to investigate the impact of the embankment fill height, the geosynthetic reinforcement stiffness, anisotropy of the soil, overconsolidation ratio, area replacement ratio, initial pore water pressure and encasement length on the deformation of GESC-supported embankments.

Mathematical modeling of rotating disk states

We consider the problem of a rapidly rotating disk in the elastic-plastic state. The piecewise linear plasticity condition in general form is chosen. It is believed that all plastic curves have the common point of intersection which corresponds to uniaxial tension. For external parameters, we obtain the conditions that determine the probability of inception of plastic zones. It is shown that plastic zones could incept in the center of the disk and/or on the boundary of it. The problem in the plastic zone is statically determinate. The case when the plastic zone occupies some central part (core) of the disk, where one regime of plastic condition is fulfilled, is considered. In order to estimate the stress state inside the elastic zone of the disk, equivalent stress which is equal to the chosen plasticity function is defined. In order to define the relationship between plastic deformations and stresses, the piecewise linear plastic potential being equal to the plasticity function is chosen. The plastic incompressible body is considered. The associated flow rule can be integrated so that the problem of getting displacements turns into quasistatic one. The problem of determining displacements in the plastic region leads to a first-order differential equation with respect to the radial component of the displacement vector. Therefore the continuity condition for displacements at the elastic-plastic boundary and the assumption that the displacements in the center of the disk are equal to zero leads to an overdetermined problem. So, only the continuity condition for displacements at the elasto-plastic boundary is accepted. It is assumed that plastic deformations at the elastic-plastic boundary are equal to zero. It is shown that displacements at the center of the disk are equal to zero automatically for all piecewise linear conditions of plasticity apart from the Tresca yield criterion. For the Schmidt–Ishlinskii yield criterion, all deformations at the center of the disk attain finite values. Meanwhile, for other piecewise linear conditions, plastic deformations at the center of the disk attain infinitely large values. This explains the discontinuity of displacements at the center of the disk for the Tresca yield criterion. The calculation results are presented as graphs of stresses, displacements, and deformations.

Drained cylindrical cavity expansion in modified Cam-clay soil under biaxial in-situ stresses

A drained solution is derived for cylindrical cavity expansion in modified Cam-clay soils under biaxial in-situ stresses. The problem is formulated by solving a system of first-order differential equations using an auxiliary variable, which provides semi-analytical expressions for stresses and specific volume. The solution validity is examined through comparisons with the existing solution and the finite element simulation. The results show that the elastic-plastic boundary of cylindrical cavity expanding under biaxial in-situ stresses is an ellipse, due to the existence of shear stress. Besides, the stress distribution and the stress path change significantly with the variation of radial direction.

A new analytical-numerical solution to analyze a circular tunnel using 3D Hoek-Brown failure criterion

In this study, a new analytical-numerical procedure is developed to give the stresses and strains around a circular tunnel in rock masses exhibiting different stress-strain behavior. The calculation starts from the tunnel wall and continues toward the unknown elastic-plastic boundary by a finite difference method in the annular discretized plastic zone. From the known stresses in the tunnel boundary, the strains are calculated using the elastic-plastic stiffness matrix in which three dimensional Hoek-Brown failure criterion (Jiang and Zhao 2015) and Mohr-Coulomb potential function with proper dilation angle (i.e., non-associated flow rule) are employed in terms of stress invariants. The illustrative examples give ground response curve and show correctness of the proposed approach. Finally, from the results of a great number of analyses, a simple relationship is presented to find out the closure of circular tunnel in terms of rock mass strength and tunnel depth. It can be valuable for the preliminary decision of tunnel support and for prediction of tunnel problems.

The stress-strain state of the double-layer spherical construction taking into account the porous structure of inner layer and heterogeneity of outer layer

The mathematical model describing the stress-strain state of a double-layer spherical body is constructed. The inner layer of the considered body has a porous structure, and the outer layer has nonhomogeneous elastic properties. Deforming of the porous medium under the specified uniformly distributed compressive loads is divided into two stages: elastic deforming of the porous medium and inelastic deforming of the compressed matrix having hardening elastic-plastic properties. The mathematical model describing the stress and displacement fields for a double-layer spherical body is constructed within the framework of the centrally symmetric formulation. The analytical relations that define the stress and displacement fields for both layers at the first stage of deforming are obtained. The analytical expressions that describe the stressstrain states in the elastic and plastic deforming zones of the inner layer with a fully compressed matrix, as well as the outer layer are found. The equation for defining the radius, which separates the elastic and plastic deforming zones of the inner layer at the second stage of deforming is obtained. The consistency conditions at the elastic-plastic boundary were chosen as follows: 1) the continuity conditions of the radial component of stresses and displacements; 2) the equality to zero of plastic deformations on the radial component of stresses and displacements. The continuity conditions of the radial component of stresses and displacements were chosen as consistency conditions on the boundary between the layers.

Nanoindentation of Fused Quartz at Loads Near the Cracking Threshold

Nanoindentation with triangular pyramidal indenters with centerline-to-face angles of 35.3°, 45°, 55°, 65.3° and 75° at loads in the range 1–500 mN was conducted on fused quartz to explore how cracks first form and develop in brittle materials during sharp indentation contact. The cracking behavior was documented using high resolution scanning electron microscopy and serial cross sectioning by focused ion beam milling. Results show that cracking is enhanced by sharper indenters and that there is a distinct threshold load below which no cracking is observed. The threshold increases rapidly with indenter angle. A series of indentations made at increasing load with the 45° indenter shows that the first cracks to form are relatively straight radials that emanate outward from the corners of the indentation. However, underneath the indent they do not connect to the hardness impression but rather terminate at what appears to be the elastic-plastic boundary. With increasing load, the radial cracks extend outward and downward, but at an intermediate load they branch to the sides beneath the hardness impression to form lateral cracks. Cracking does not appear to initiate from pre-existing flaws, but is generated from processes associated with plastic deformation beneath the indenter. Results are discussed in terms of prevailing ideas on the origin of the cracking threshold.

A Study of Elastic-Plastic Boundary Propagation in a Tube of Elastic-Perfectly Plastic Material Under Dynamic Loadings of Different Types

The dynamics of distribution of the border between areas of elasticity and plasticity for a hollow thick-walled cylinder under the influence of the internal pressure applied instantly is investigated in this work. Proof of the accuracy of the obtained numerical solution is provided. A more general regime loading a tube is examined.