Elastic-plastic Constitutive Relation Research Articles

Research on ship-ice collision model and ship-bow fatigue failure Mechanism based on elastic-plastic ice constitutive relation

Collisions between sea ice and ships can damage the hull structure and pose a threat to crew safety in severe cases. The modelling of ice materials is crucial, but it is difficult to study ice-ship interactions. In this study, an ice constitutive model including the temperature factor was verified through experiments and numerical simulations of uniaxial and triaxial compression. Furthermore, the effects of salinity and porosity on the compressive strength of ice were studied using experiments and numerical simulations. The mechanical behaviour of sea ice was then simulated using the constitutive model mentioned above. A numerical model of collisions between polar ships and sea ice was established to investigate the ice-breaking processes of ships under different working conditions. The collision force and the level of structural damage were obtained. The influences of the initial pore size, hull speed, bow angle, and bow shape on the collision force and structural damage in the ship-ice collision process were analysed. Finally, fatigue damage to the bow structure at different ice thicknesses and speeds was calculated. The present results provide a reference for the structural design and optimisation of polar ships to a certain extent and improve the theory of ship-ice collisions.

Large-scale field test on the shear behavior of concrete pipe-silty soil interfaces in pipe jacking: A case study

With the rapid advancement of urbanization, research on the shear behavior of concrete pipe-silty soil interfaces in pipe jacking has a high engineering application value. In this study, a large-scale field direct shear test apparatus and the corresponding test method were designed and proposed to investigate the shear properties of the concrete-silty soil interfaces in pipe jacking. A series of in-situ direct shear tests were conducted at five normal stress levels under four interface contact conditions. The results show that the shear stress-displacement relationships of the interfaces conform to the typical elastic-plastic constitutive relations, the shear strength-normal stress relationships of the interfaces can be well fitted by the Mohr-Coulomb failure criterion, and the interface shear properties are influenced by soil properties, normal stress, lubrication conditions and stagnation time. Without lubrication, the concrete-silty soil interfaces have a shear stress-displacement curve shape similar to that of the test results obtained from indoor direct shear tests, but their ductility and shear strengths are lower. Under lubrication conditions, the paraffin wax and thixotropic slurry can both effectively diminish the interface friction angle, thereby reducing the concrete-silty clay interface friction coefficient by 62.8% and 72.2% and reducing the concrete-silty sand interface friction coefficient by 60.8% and 59.2%, respectively. Based on the macroscopic and microscopic images observed in the tests, the lubrication mechanisms of the lubricants were analysed. The research results can provide a reference for the prediction of jacking force and construction disturbance in adjacent pipe jacking projects.

Micromechanics of kink-band formation in bimetallic layered composites

Bimetallic layered composites with ultrathin layers possess high strength and hardness, and excellent shock resistance and radiation damage tolerance. However, they are prone to deformation localization and readily form kink-bands when subjected to layer parallel compression. Following this, we carried out extensive plane strain finite element finite deformation analyses to understand and rationalize the experimentally observed kink-band formation in these composites. In the calculations, both constituent materials were assumed to follow a rate-independent isotropic elastic-plastic constitutive relation with an ad-hoc thickness dependent yield strength. Our results demonstrate that in these composites, layer refinement, together with the strength differential between the layers of the constituent materials, is sufficient to trigger kink-banding. Importantly, this phenomenon occurs even in the absence of elastically stiff layers, geometrical imperfections (such as waviness of the layers), and extreme plastic anisotropy within the layers. Additionally, we performed parametric studies to investigate the individual effects of layer thickness, strength differential between the two constituent materials, and strain-hardenability of the materials on kink-band formation. The outcomes of our parametric studies reveal that the strain-hardenability of the constituent materials stabilizes the formation of kink-bands. Furthermore, it leads to a transition from the abrupt formation of through-width kink-bands to the onset and propagation of stable inclined wedge-shaped kink-bands, similar to the experimental observations.

Finite–Discrete Element Method Prediction of Advanced Fractures in Extra-Thick Coal Seams Based on a Constitutive Model of Rock Deformation–Fragmentation Failure Process

Roof fall is a frequent and destructive disaster in the working face of extra-thick coal seams. The important technology for disaster elimination is roof grouting, and the key to its success is to accurately predict the distance of the advanced fractures based on a reasonable rock constitutive relationship. In this paper, the constitutive relationship reflecting the progressive failure process of rock was established, including the elastic–plastic constitutive relation of intact rock, the fracture constitutive relation of non-penetrating fracture, and the shear friction constitutive relation of penetrating fracture. On this basis, the finite–discrete element method (FDEM) numerical calculation method was developed. Taking Yushupo Coal mine with a 16-m-thick coal seam as an example, the numerical results showed that the fractures in the roof appear 15~35 m ahead of the working face, and the maximum value of advance bearing pressure is between 16 and 30 MPa. Meanwhile the laboratory test results showed that the compressive strength of the grouted coal is 14.91 MPa after solidification for 7d. The above data mean that the grouting slurry can solidify the broken roof into a whole without roof fall disaster. At the same time, the rock pressure of the extra-thick coal seam can effectively crush the top coal, which is conducive to the top-coal caving operation. The in situ test shows that when the pre-grouting is carried out in the range of 20~30 m in front of the working face, the roof fall disaster can be effectively avoided, which is consistent with the numerical simulation results. It shows the rationality of the FDEM numerical method and the constitutive model of rock deformation–fragmentation failure process.

Constitutive model for solid-like, liquid-like, and gas-like phases of granular media and their numerical implementation

Granular media, a macroscopic amorphous matter composed of mesoscopic discrete particles, exhibits different behaviour characteristics (e.g., solid-, liquid-, and gas-like phases) depending on the volume fraction and loading conditions. Therefore, it poses a significant challenge to three-phase modelling and analysis. In this study, a description of multiple phases in granular media is realised by establishing the transition criteria and parameter conversion relations between different phases, using the already established theories of the elastic-plastic constitutive relation in solid mechanics, the viscoplastic constitutive relation in rheology, and the kinetic theory of granular flow. The new model realises the coexistence of different phases and the conversions therebetween. Smoothed discrete particle hydrodynamics are introduced to discretise the new theoretical model, and the correspondence between the smoothed and actual particles for different phases and discrete formulas under different models are described in detail. Two typical cases are used for numerical tests: the collapse of one side of a three-dimensional granular column and the collapse and flow of a granular column on an inclined surface. The calculated morphology of granular flow, distributions of velocity vectors, scaling law of spreading range under different height-width ratios, and the transient characteristics of particle spreading all accord well with the experimental results. Furthermore, quasi-static, slow, fast, and other phases of particle motions are well captured. Thus, we verify the feasibility of the new model and method for the multiple-phase simulation of granular media.

Study on sealing performance of bolted flange structure after creep based on ABAQUS

In this paper, a finite element analysis model is established based on ABAQUS software and DN600 bolted flange connection structure is the research object. The elastic-plastic constitutive relation is adopted for the flange and bolt materials, and the user subroutine of Creep is written in Fortran language according to the creep constitutive equations. Each component can meet the requirements of strength and seal evaluation, and it is found that after creep, the seal stress of gasket decreases significantly, and the stress increases almost linearly from the inside to the outside of the gasket. After cooling and heating, the stress is redistributed. The residual pre-tightening force of bolt is increased, and the flange deflection angle is slowed down, which improves the sealing performance. The study of gasket sealing performance in this paper has a positive guiding significance for preventing leakage accidents.

Anisotropic elastic-plastic behavior of architected pyramidal lattice materials

The initial and subsequent yield surfaces for architected pyramidal lattice materials are investigated analytically. Considering lattice struts as elastic-perfectly plastic thin beams subjected to both axial force and bending moment, a set of nonlinear elastic-plastic constitutive relations for a strut is proposed. Moreover, we phenomenologically present anisotropic pressure-dependent yield functions for pyramidal lattices. Comparison of planar yield surfaces of pyramidal lattices predicted by analytical approach to the ones obtained from phenomenological models shows a good agreement for the type of external loads and range of strains investigated in this study. Investigating the normality between the plastic strain vectors and yield surfaces, the obtained results demonstrate the associative nature of the flow rule. We have also emphasized on utilizing hollow-tapered struts as the constituent of pyramidal lattices. To this end, we analytically found that hollow-tapered struts can remarkably improve the effective stiffness and yield strength of bending-dominant pyramidal lattices.

Finite Element Analysis of Well Pads in Basra Province

After the year 2003, the oil / gas sector evolved and gained investment. International companies of different origins utilized heavy drilling rigs (to achieve high drilling depths) and entered our region. Meanwhile, some drilling problems were recorded, accompanied by well-pad failure cases. This research aims to study the behavior of well-pads with different geometric configurations, under the effects of drilling rigs with various characteristics, within the Basra province. Four case studies have been selected to represent four fields, namely: Siba, Zubair, West Qurna-2, and Zubair-Mishrif fields. The finite element method is utilized to conduct a stress analysis process, adopting an elastic–plastic constitutive relation for soil, based on Drucker-Prager's yield criterion. The maximum contact pressure applied on soil (under the working loads) is compared to its bearing capacity. When a rigid method is used to calculate the contact pressure, it is compared with the ultimate soil-bearing capacity, as calculated by Reddy and Srinivasan's method for cohesive soils, with allowable bearing capacity taken from the Peck, Hanson, and Thornburn's method for cohesionless soils. The contact pressure calculated via the finite element method is compared with the ultimate soil-bearing capacity calculated using the same method, based on a settlement of 50 mm. The extreme values of the bending moments and shear forces developed in the well-pad sections (under the factored loads), are compared with the section capacities calculated by using the ultimate strength design method. Regarding the geotechnical side, the results indicate insufficient safety factors against soil shear failure for some cases, especially for cohesive soil profiles. For cohesionless soil profiles, the provided safety factors are sufficient. The finite element method reveals higher contact pressures compared to the conventional rigid method. For cohesionless soil profiles, the Peck, Hanson, and Thornburn's method, gives a bigger safety margin than the finite element method. The immediate settlement values are almost tolerable. Regarding the structural side, it has been identified that a uniform section is adopted for all locations of each pad, for individual wells. In most cases, the provided reinforcing steel is less than the minimum code requirement. This leads to a violation of the section capacity of bending, at least near the cellar. The beam shear capacity is rarely violated. Using strip footings beneath the rig skids, permits utilizing a heavy section that satisfies the requirements of structural safety, without violating the economic considerations.

Modeling of contact fatigue damage behavior of a wind turbine carburized gear considering its mechanical properties and microstructure gradients

Carburized gears are commonly used in heavy-duty machines such as wind turbines, ships and high-speed rails. The gradient characteristics of mechanical properties and microstructure from the case to the core and the complex subsurface stress state in service make it very challenging to understand the contact fatigue performance of the carburized gears. In this study, a numerical model considering the effects of mechanical properties and microstructure gradients is developed to investigate the contact fatigue damage behavior of a wind turbine carburized gear. The hardness gradient in the case depth is modelled using Thomas empirical equation. The microstructure gradient is considered in terms of the grain size variation adopting the technique of Voronoi tessellation. The damage-coupled elastic-plastic material constitutive relations are developed to capture the intergranular mechanical response and the progressive fatigue damage under repeated gear meshing. The results indicate that the shear stress reversal is not uniformly distributed along the grain boundaries of the same depth. The critical subsurface depth of crack initiation and the fatigue damage evolution obtained from the calculation model compare well to the experimental and numerical results readily available in literature. With the developed framework, the influences of normal load and case carburization on the fatigue damage behavior of the carburized gear are also investigated and discussed in detail.

Numerical analysis of the influence factors of plastic failure in the cracked nozzle region of reactor pressure vessel

The integrity of reactor pressure vessel (RPV) is greatly affected by pressurized thermal shock (PTS). Once crack appears in the nozzle region, the stress concentration around the crack tips may lead to crack propagation, and finally cause a serious security problem. When the transient temperature is above the nil-ductility reference temperature, elastic–plastic constitutive relations are considered in the fracture mechanics analysis. The temperature-related properties of the materials are introduced into a 3-D finite element model to establish the temperature field and stress field of a real RPV. Since the test and safety inspection for RPV with defects under PTS loads are quite difficult and dangerous, the process of the ductile crack propagation is simulated by the extended finite element method (XFEM), and the critical crack sizes for different base wall thicknesses are determined. Then, the quantitative analysis of the effect of the crack position on the ultimate bearing capacity is carried out. For the crack tips with different shapes, the crack propagation law and the shape effect on the ultimate bearing capacity of the whole structure are also analyzed. According to their crack propagation paths and damage degrees, a good agreement is obtained.

Effect of Seismic Frequency Spectra on Surrounding Rock Damage Evolution of Large Underground Caverns

To explore the distribution and evolution of the surrounding rock of underground caverns of hydropower stations, the dynamic compression tests for granite sample were carried out and the dynamic constitutive relation suitable to computer programming was established in terms of strain‐based static elastic‐plastic damage constitutive relation. By inputting five earthquakes of various frequency spectra, the fully nonlinear dynamic analysis was performed for some large underground caverns in the gorge and mountain region in Sichuan Province in China with the explicit difference method. The simulation results show that, as the input seismic waves become strong gradually, the damage zone generally extends deeply from the middle of side walls. The damage zone reaches the maximum value in areas immediately after the seismic acceleration peak arrives and keeps constant thereafter. According to the initial analysis, if the dominant frequency of input wave approaches the natural frequency of underground caverns, the maximum area of damage zone will increase. Those findings may provide practical data for earthquake‐resistant design and construction.

Nonlinear contact between pipeline’s outer wall and slip-on buckle arrestor’s inner wall during buckling process

In order to theoretically study the buckle propagation of subsea pipelines with slip-on buckle arrestors, a two-dimensional ring model was set up to represent the pipeline and a nonlinear spring model was adopted to simulate the contact between pipeline’s inner walls and between pipeline’s outer wall and slip-on buckle arrestor’s inner wall during buckle propagation. In addition, some reverse springs are added to prevent the wall of left and right sides separating from the inner wall of slip-on buckle arrestors. Considering large deformation kinematics relations and the elastic-plastic constitutive relation of material, balance equations were established with the principle of virtual work. The variation of external pressure with respect to the cross-sectional area of pipelines was analyzed, and the lower bound of the crossover pressure of slip-on buckle arrestors was calculated based on Maxwell’s energy balance method. By comparing the theoretical results with experiment and finite element numerical simulation, the theoretical method is proved to be correct and reliable.

Fatigue properties of catalyst coated membranes for fuel cells: Ex-situ measurements supported by numerical simulations

The interactions between catalyst layers and membrane are known to have significant impact on the mechanical properties of the composite catalyst coated membrane (CCM) materials used in fuel cells. The mechanical fatigue durability of such composite CCM materials is investigated herein, and compared to the characteristics of pure membranes. Ex-situ uniaxial cyclic tension tests are conducted under controlled environmental conditions to measure the fatigue lifetime, defined by the number of stress cycles that the specimen can withstand before mechanical failure. The sensitivity of the CCM fatigue lifetime to the applied stress is determined to be higher than that of the pure membrane, and varies significantly with environmental conditions. The experimental results are then utilized to develop a finite element based CCM fatigue model featuring an elastic–plastic constitutive relation with strain hardening. Upon validation, the model is used to simulate the fatigue durability of the CCM under cyclic variations in temperature and relative humidity, which is critical for fuel cells but cannot be effectively measured ex-situ. When combined, the experimental and numerical methods demonstrated in this work provide a novel, convenient approach to determine the CCM fatigue durability under various hygrothermal loading conditions of relevance for fuel cell design and operation.

Plastic limit load of Grade 91 steel pipe containing local wall thinning defect at high temperature

This paper aims to predict the plastic limit load of Grade 91 pipe at high temperature by experimental and numerical analysis methods. The elastic–plastic constitutive relation of P91 considering creep damage at high temperature is proposed and the effectiveness is verified by high-temperature instantaneous tensile test after creep of P91 sample. Then, using the elastic–plastic constitutive relation considering creep damage, the plastic limit loads of P91 pipe containing local wall thinning (LWT) defect at high temperature have been calculated by finite element (FE) method and the accuracy is checked by high-temperature burst experiment after creep of T91 pipe containing LWT. Finally, the fracture analysis and metallographic analysis of Grade 91 sample and pipe containing LWT defect are performed. The results show that the elastic–plastic constitutive relation of P91 considering creep damage proposed by this paper can well describe the elastic–plastic behavior of P91 under creep condition and is useful to calculate the plastic limit load of P91 pipe containing LWT. The failures of P91 tensile samples and T91 pipes containing LWT defect are both plastic fracture. This research would provide an optional method for structure integrity analysis of the pipe containing LWT defect at high temperature.

Evaluation of stress integration algorithms for elastic–plastic constitutive models based on associated and non-associated flow rules

This paper presents in-depth analyses of four stress integration algorithms for finite deformation elastic–plastic constitutive relations. In particular, the four integration schemes were developed for both non-Associated Flow Rule (non-AFR) and Associated Flow Rule (AFR) in the continuum level of plasticity theory. The four integration schemes are (1) fully implicit backward Euler, (2) semi explicit convex cutting plane, (3) fully explicit classical forward Euler and (4) fully explicit forward Euler named Next Increment Corrects Error (NICE-1), which were implemented into the user material subroutines of finite element software ABAQUS. Analysis on numerical accuracy was carried out by using uniaxial tensile simulations at various orientations and time increments. The same analysis was also conducted for uniaxial tension/compression tests to investigate the effect of time increment on the calculated hardening curve. Finally, cylindrical cup deep drawing (manufacturing process which stamps a cylindrical cup) simulations were performed to compare computation time and accuracy for both AFR and non-AFR schemes for the evaluation of more realistic forming application. From the systematic comparative analyses, the following conclusions are made; (1) Caution should be exercised when finding an optimum time increment for explicit integration schemes. (2) The computation time and accuracy for both AFR and non-AFR are not much different when identical integration scheme is used. (3) For the simulation of large scale sheet metal forming applications, the explicit type stress integration algorithm can be a more practical choice considering that it does not deteriorate the computational accuracy and efficiency compared to the fully implicit algorithm.

Three-Dimensional Numerical Analysis of Compound Lining in Complex Underground Surge-Shaft Structure

The mechanical behavior of lining structure of deep-embedded cylinder surge shaft with multifork tunnel is analyzed using three-dimensional nonlinear FEM. With the elastic-plastic constitutive relations of rock mass imported and the implicit bolt element and distributed concrete cracking model adopted, a computing method of complex surge shaft is presented for the simulation of underground excavations and concrete lining cracks. In order to reflect the interaction and initial gap between rock mass and concrete lining, a three-dimensional nonlinear interface element is adopted, which can take into account both the normal and tangential characteristics. By an actual engineering computation, the distortion characteristics and stress distribution rules of the dimensional multifork surge-shaft lining structure under different behavior are revealed. The results verify the rationality and feasibility of this computation model and method and provide a new idea and reference for the complex surge-shaft design and construction.

Implicit Algorithm of Hybrid Hardening Elastic-Plastic Constitutive Relation and its Application in Autofrettage Residual Stress Analysis

Implicit Algorithm of Hybrid Hardening Elastic-Plastic Constitutive Relation and its Application in Autofrettage Residual Stress Analysis

비국부 이론을 이용한 입자 강화 복합재 이중후방응력 소성 구성방정식 모델 및 전단밴드 분석

2개의 상으로 구성된 입자 강화 복합재에 대한 균질화와 내부 상태 변수에 대해 2차 미분항이 포함된 비구역적 이론을 적용하여 탄소성 구성 방정식을 제안하였다. 열역학과 소성 포텐셜을 통해 내부 상태 변수에 대한 전개식 또한 본 논문에 포함되었다. 연속체 결함 모델을 이용, 결함 인자에 따른 물성 저하 현상도 감안되었으며 이중 후방응력이 조합된 전개식 또한 제시하였다. 일부 예에 대한 수치해석 결과, 비구역적 변수의 영향이 증가할수록 전단밴드는 감소하나 반면 특정 후방응력 전개가 지배적일수록 소성변형 집중이 증가함이 관찰되었다. 더욱이 두 개의 강소성 상으로 이루어진 복합재의 경우 강성이 높은 게재물의 비중이 증가함에 따라 전단밴드 형성이 용이한 것으로 나타났다. 그 밖에 제어변수들의 변화에 따른 전단밴드 형성에 대한 분석 결과는 Rice 소성 불안정성 분석결과와 잘 일치함 또한 밝혀졌다.

Numerical Analysis of the Mechanical Properties of Batter Piles under Inclined Loads

AbstractA three-dimensional elastic-plastic finite element model based on the elastic-plastic constitutive relation of the non-associated flow Mohr-Coulomb criterion is constructed to analyze the influence of inclination angles of loads and piles on the mechanical properties of batter piles under inclined loads. The results indicate that (1) the stiffness of batter pile depends on both its axial and horizontal stiffness under a smaller inclined load and does not become maximum under an axial force because of the existing stiffness balance in the axial and horizontal directions. (2) The relationship between the ultimate compressive bearing capacity of batter pile and the load inclination angle exhibits an M shape. The peak of this capacity appears near a small load inclination angle rather than under axial load. (3) The stiffness and bearing capacity of batter pile increase with pile inclination under positive inclined loads, whereas the results show the opposite behavior under negative inclined loads. (4)...

Analysis of parameters in granular solid hydrodynamics for triaxial compression tests

Granular materials are omnipresent in industries and in nature. For small strains, elastic-plastic and hypoplastic constitutive relations are widely used in engineering practice, but they are not a significant reflection of the underlying physics. Under a unified thermodynamics framework explaining the physics of materials, granular solid hydrodynamics (GSH) was an extension towards describing granular materials, not only solid-like, but also fluid-like behaviors. In this paper, the fundamentals of GSH are briefly treated and then simplified to analyze quasistatic deformations in triaxial compressions. The calculated stress-strain relations and volumetric strain are compared with experimental results. The influences of the major parameters in GSH, especially their cross coupling influences, are analyzed and their physical meanings are further clarified. After parameters were calibrated, the calculated stress values in the characteristic stress state are found to be within 22% of tested values. Meanwhile, the energy dissipation during triaxial compression is analyzed. The above results support and partially quantify GSH.