A Proposed Algorithm to Compute the Stress-Strain Plastic Region and Displacement of a Deep-Lying Tunnel Considering Intermediate Stress and Strain-Softening Behavior

Past studies on deep-lying tunnels under the assumption of plane strain have generally neglected the influence of intermediate principal stress even though this affects the surrounding rocks in the plastic zone. This study proposes a finite difference method to compute the stress strain plastic region and displacement of a tunnel based on the Drucker–Prager (D–P) yield criterion and non-associated flow rule and considering the influences of intermediate principal stress and the strain-softening behavior of surrounding rock. The computed results were compared with those of other well-known solutions and the accuracy and validity of the method were confirmed through some examples. Parameter analysis was conducted to investigate the effects of intermediate principal stress on stress-strain, the plastic region, the ground response curve, and the dilatability of surrounding rock. The results showed that the plastic radius , the residual radius , and radial displacement of surrounding rock first decreased and then increased with increasing intermediate principal stress coefficient b from 0 to 1, with the minimums occurring at b = 0.75. On the contrary, the peak and rate of variation of the dilatancy coefficient first increased and then decreased with increasing b and the dilatancy coefficient gradually transitioned from nonlinear to linear variation. Meanwhile, the inhibition of the plastic radius and radial displacement gradually weakened with increasing support pressure, whereas the dilatancy coefficient of the tunnel opening gradually increased.

The Stability Analysis of Heituwan Tailings Pond Based on Strength Reduction Method

To analyze the stability of Heituwan tailings pond after vacuum well point dewatering treatment, a unit thickness numerical 3D model was built based on field survey data and physical mechanical properties tests; and the model was analyzed by FEM numerical software according to strength reduction method. The properties of stress and strain, the plastic region, and the deformation properties are acquired by numerical stimulation, and the simulation result was compared withe the in-situ monitoring data. The results show that the safety factor does not meet the requirements of the standard; and most of the landfill made of manganese tailing has developed into plastic status; the deformation is more obvious where the tailing store is higher and closer to roller compacted rockfill dam; the manganese tailing landfill near the roller compacted rockfill dam should be grouted by cement to meet the requirements of continued use.

Verifying the Movable Elastoplastic Boundary Method by Using Galin’s Problem

Galin’s solution for the problem of biaxial tension of a plate with a hole completely covered by the plastic region appears to be a pearl recognized by the world scientific community. This solution serves as a test for all sorts of approximate approaches to solving elastoplastic problems, including the semi-analytical iterative method being developed by the author, focused on solving more complex problems such as the Kirsch problem in the elastoplastic formulation. The proposed iterative approach for a semi-analytical solution involves an explicit analytical expression for stresses in the plastic region and an iterative numerical solution in the elastic region with a refined border. The paper shows the convergence of the results based on the iterative procedure for the elastoplastic region boundary approaching its analytical position, which follows from the analytical solution of Galin’s elastoplastic problem. Consideration has also been given to obtaining results on the determination of the boundary between the elastic and plastic regions using a competing approximate perturbation method. The advantage of the proposed method lays in not limited modifications in parameters due to the requirement for small differences while formulating a problem from the axisymmetric case as seen in the perturbation method.

COMBINED EXTRUSION OF GLASSES WITH A CONICAL BOTTOM. KINEMATIC AND STRESS STATES OF THE PLASTIC REGION LOCATED UNDER THE CONICAL SURFACE OF THE PUNCH

For extrusion of glasses with a conical bottom using the method of plastic flow by A. L. Vorontsov, the kinematic and stress states of the extruded metal in the area of the plastic deformation center located under the conical surface of the punch were determined. The resulting formulas will be used to determine the stress state in the region of the hearth located under the central flat part of the punch-son՚s working end. In the future, the results of this mechanical and mathematical analysis will also make it possible to investigate the question of the presence of the taper of the punch, which is optimal in terms of strength.

The Application of Standard Nonlinear Solid Material Models in Modelling the Tensile Behaviour of the Supraspinatus Tendon

Tendons transmit forces from muscles to bones through joints. Typically, tendons and muscles work together to innovate a particular type of motion. Therefore, in order for the tendons to find attachment to the bones, they are naturally adapted as much thinner strands than the muscles that they serve. Thus, they are often subjected to much higher stresses than the muscles that they actually serve in any given action. As a result, tendons are susceptible to injuries that may lead to a permanent dysfunction in joint mobility due to the fact that the scar tissue that forms after healing does not often have the same mechanical properties of the original tissue. It is, therefore, very important to understand the mechanical response of tendons. This paper examines the performances of two viscoelastic standard nonlinear models in modelling the elastic and plastic behaviour of the tendon in the light of a well-known hyperelastic Yeoh model. The use of the Yeoh model is more for validating the performances of the viscoelastic models within the elastic region rather than for comparison purposes. Yeoh model’s selection was based on its superior performance in modelling the elastic phase of soft tissue as reported in previous studies combined with its simplicity. The results show that the two standard nonlinear solid models perform extremely well both in fitting accuracies and in correlating stress results. The most promising result is the fact that the two standard nonlinear models can model tendon behaviour in the nonlinear plastic region. It is also noted that the two standard nonlinear models are physically insightful since their optimisation parameters can be easily interpreted in terms of tendon elasticity and viscoelastic parameters.

Evaluation of Cracks Embedded in Zones With Large Scale Plasticity in Subsea HPHT Equipment – Comparing FAD and Driving Force Approaches

Fracture mechanics assessments for pressure vessels are performed to determine critical flaw sizes and/or estimate the fatigue life of a growing crack as a means of establishing inspection intervals for the equipment. In most cases the evaluation is performed based on methods described in API 579-1/ASME FFS-1 and BS7910. The approaches described in these standards are mostly based on a linear elastic fracture mechanics approach. Even though plasticity can be accounted for by using a failure assessment diagram (FAD); however, even with this approach the effect of plastic strain around the crack is not explicitly considered. This paper presents an approach as per API 579, Annex 9G.5 which recommends utilizing a driving force method whereby the J-integral is directly evaluated from an elastic-plastic finite element model. The main goal is to study differences between the FAD approach against the elastic-plastic J-integral approach wherein the crack is modeled explicitly. Simplified representative geometries are considered for this study. Two scenarios for the plastic zone are considered a) crack present during initial loading with no residual plastic strain and b) crack in a residual stress zone. Different crack sizes are considered for this comparison study ranging from small cracks completely embedded within the plastic region and larger cracks with partial embedment. The paper presents comparison studies which highlight the key differences between different analysis approaches with the aim of identifying the most conservative assessment method for different crack geometries.

COMBINED EXTRUSION OF GLASSES WITH A CONICAL BOTTOM. KINEMATIC AND STRESS STATES OF THE PLASTIC REGION IN CONTACT WITH THE CONICAL SURFACE OF THE MATRIX

For the extrusion of glasses with a conical bottom using the method of plastic flow by A. L. Vorontsov, the kinematic and stress states of the extruded metal in the area of the plastic deformation zone in contact with the conical surface of the matrix were determined. The results are combined with the results obtained earlier for the cylindrical region located under the forming glass wall. The resulting formulas will be used to determine the stress state in the areas of the focus located under the end of the punch. The derived formula for the maximum pressure on the matrix wall is necessary for calculating the matrix strength and making an informed decision about the need for its banding.

COMBINED EXTRUSION OF GLASSES WITH A CONICAL BOTTOM. KINEMATIC AND STRESS STATES OF A CYLINDRICAL PLASTIC REGION LOCATED UNDER THE FORMING GLASS WALL

For extrusion of glasses with a conical bottom using the method of plastic flow by A. L. Vorontsov, the kinematic and stress states of the extruded metal in the area of the plastic deformation center located under the formed wall of the glass and adjacent to the cylindrical section of the matrix were determined. The resulting formulas will be used to determine the stress state in the areas of the focus located under the punch end.

Numerical Simulation Investigation on Well Performance Integrated Stress Sensitivity and Sand Production

For unconsolidated sanding wells, the interaction between sanding and pressure-dependent permeability as oil is produced from the bottom of the well puts higher challenges on the evaluation and prediction of well performance. Therefore, it is essential to assess the oil well performance considering the synthetic effect of stress-sensitive and produced sand particles. In this paper, a new stress-sensitive factor is proposed to describe the relationship between stress and permeability in the numerical model. Also, based on the rectangular plastic region by the sand migration near the perforation, a quantitative expression of the sanding area for numerical model calculation was established. Combined with a quantitative description of these two key parameters, a sand-producing horizontal well model is established to evaluate production performance. In this model, the area of sand production near the wellbore is considered as the inner area with increased permeability while the outer zone remains the original reservoir. Besides, the model was verified by the production data from the sand-producing horizontal well in the oilfield. Furthermore, sensitivity parameters (such as stress sensitivity, the size of sanding zone, well location, and reservoir boundaries) are used to make the analysis of well productivity, which provides a theoretical basis for petroleum engineers to adjust the development plan for horizontal wells in the weakly consolidated sandstone reservoir.

Effect of Plastic Anisotropy on the Collapse of a Hollow Disk under Thermal and Mechanical Loading

Plastic anisotropy significantly affects the behavior of structures and machine parts. Given the many parameters that classify a structure made of anisotropic material, analytic and semi-analytic solutions are very useful for parametric analysis and preliminary design of such structures. The present paper is devoted to describing the plastic collapse of a thin orthotropic hollow disk inserted into a rigid container. The disk is subject to a uniform temperature field and a uniform pressure is applied over its inner radius. The condition of axial symmetry in conjunction with the assumption of plane stress, permits an exact analytic solution. Two plastic collapse mechanisms exist. One of these mechanisms requires that the entire disk is plastic. According to the other mechanism, plastic deformation localizes at the inner radius of the disk. Additionally, two special solutions are possible. One of these solutions predicts that the entire disk becomes plastic at the initiation of plastic yielding (i.e., plastic yielding simultaneously initiates in the entire disk). The other special solution predicts that the plastic localization occurs at the inner radius of the disk with no plastic region of finite size. An essential difference between the orthotropic and isotropic disks is that plastic yielding might initiate at the outer radius of the orthotropic disk.