Stress Field Research Articles

Residual Strain and Joint Pressurization Maintain Collagen Tension for On-Joint Lumbar Facet Capsular Ligaments.

Modeling the lumbar facet capsular ligament's mechanical behavior under various physiological motions has often been a challenge due to limited knowledge about the on-joint in situ ligament state arising from attachment to the bone or other internal loads. Building on prior work, this study presents an enhanced computational model of the lumbar facet capsular ligament by incorporating residual strain and joint pressurization strain, factors neglected in prior models. Further, the model can predict strain and stress distribution across the ligament under various spinal motions, highlighting the influence of the ligament's attachment to the bone, internal synovial fluid pressurization, and distribution of collagen fiber alignment on the overall mechanical response of the ligament. Joint space inflation was found to influence the total observed stress and strain fields, both at rest and during motion. A significant portion of the ligament was found to be in tension, even in the absence of external load. Additionally, the model's ability to account for residual strain offers a more realistic portrayal of the collagen fibers and elastin matrix's role in ligament mechanics. We conclude that (1) computational models of the lumbar facet capsular ligament should not assume that the ligament is unloaded when the joint is in its neutral position, and (2) the ligament is nearly always in tension, which may be important in terms of its long-term growth and remodeling.

High-resolution measurement of contact stresses and friction in indentation and machining by full-field photoelasticity

An experimental study has been made of the sliding plastic contact in wedge indentation and machining of ductile metals. The use of full-field photoelasticity has allowed direct determination of interface pressure and shear stress distribution along the tool (indenter) and workpiece sliding contact at micron-scale resolution. Sapphire, a transparent photoelastic material that possesses sufficiently high hardness to indent and machine metals, is used as the tool material. It is shown that the Coulomb friction model applies only at the edges of the contact where the interface pressure falls below a certain value associated with the material's flow stress. Within the plastic contact zone, the mode of friction as well as the relationship between interface pressure and shear stress are very complex. In both cases, it is shown that shear stress neither remains constant nor varies in proportion to the pressure. It is proposed that the complex nature of friction and stress field at the sliding contact can be understood through simultaneous observations of the metal plastic flow at and near the interface. Using in situ measurements of the velocity field near the interface and local stress distribution at the contact from photoelasticity, friction contribution to the overall work is calculated and shown to be substantial (greater than one-third) in the case of machining.

Re-orientation of principal stresses during tunnel excavation: Model development and support strategy

The safety and stability during the excavation and production of the tunnel is a key issue that must be addressed in tunneling engineering, which is pronounced under principal stress re-orientation. A mechanical model is therefore developed to determine the boundary curve of the failure zone of a supported circular tunnel under rotating the principal stress direction. Meanwhile, the effects of various environmental factors on the pattern of the failure zone are quantitatively analyzed. Subsequently, two critical morphological indexes are determined to elucidate the uniformity of the failure zone and the functional relationship between these two morphological indices and the environmental factors, respectively. Furthermore, technical approaches and control measures for maintaining the surrounding rock are put forward. In particular, the “long and short” coordinated hierarchical support technology has been recommended and is validated through a comparison of the designed schemes and several engineering cases. The results indicate that the proposed support technology resulted in a gradual reduction of the “butterfly wings” pattern and a more consistent failure zone in the surrounding rock. These findings are useful to ensure the overall stability and anti-interference performance of the surrounding rock of a tunnel under the complicated stress field, especially with regards to the deflection of principal stress.

Mode-III fracture of four cracks emanating from an elliptical hole in one-dimensional orthorhombic quasicrystals with piezoelectric effect

In this study, a new generalized conformal mapping is introduced using the generalized complex variable method, focusing on the investigation of the anti-plane problem of an elliptical hole with four cracks in one-dimensional (1D) orthogonal piezoelectric quasicrystals. Under the consideration of electrically impermeable and electrically permeable boundary conditions, the governing equations of the anti-plane problem in 1D orthogonal piezoelectric quasicrystals are successfully simplified into an eighth-order partial differential equation and a fourth-order partial differential equation by introducing a potential function. Based on this, analytical solutions for the stress field and electric field are obtained, and the exact solution for the stress intensity factor (SIF) is derived. In addition, formulas for the electric displacement intensity factor (EDIF) and energy release rate are provided. Subsequently, the influence of geometric parameters and external loads on the field intensity factors and energy release rate is analyzed through numerical examples, providing a theoretical basis for engineering mechanics analysis.

Research on the correlation between roughness parameters and contact stress on tooth surfaces and its dominant characteristics

The contact performance of the tooth surface is a crucial factor affecting the operational lifespan of gears. There is a significant correlation between tooth surface topography and contact stress, as well as fatigue performance. To investigate the influence of different topography parameters on tooth surface contact stress, this paper performs analytical calculations on asperity contacts of rough tooth surfaces based on reconstruction modeling. Through efficient calculations, sufficient correlation analysis data is obtained. The neural network analysis method is used to measure the degree of influence of roughness parameters on tooth surface contact performance. Research on the correlation between micro-topography parameters and maximum contact stress on tooth surfaces, as well as regression analysis, is conducted. The results show that: (1) Considering rough surfaces, the tooth surface contact stress field exhibits two stress peaks in the near-surface layer and sub-surface layer, with a maximum Mises stress increase of up to 30 % compared to a smoother surface. (2) In the case of low roughness (Sa < 0.2 μm), the amplitude of the maximum Mises stress peak in the near-surface layer is close to that in the sub-surface layer. However, as the roughness amplitude increases, the amplitude of the near-surface stress peak increases sharply. (3) Ranking the roughness parameters based on their influence on contact stress, the main parameters characterizing contact performance are identified as Spk, Vmp, and Sq. The peak characteristics of the surface are the decisive factors affecting fatigue extremes, which are stronger than the traditional surface roughness parameter Sq. This paper establishes a direct correlation model between tooth surface topography parameters and contact stress, providing a foundation for simplifying stress calculations considering complex topographies and offering new insights for fatigue-resistant design of tooth surfaces.

Research on the thermo-hydro-mechanical coupling simulation and deformation spatiotemporal evolution for the entire process of oil shale in-situ mining

The ground surface deformation (GSD) caused by oil shale in-situ mining poses a threat to land resources and human's lives and property. This study, for the first time, conducts a full stratum simulation of the Fuyu oil shale in-situ pyrolysis pilot base, analyzing the evolution characteristics of the temperature field, stress field, and deformation field of the entire stratum profile during the heating and cooling processes of convective heating mining. Considering the changes in the pore structure, thermophysical, and mechanical properties of the stratum, the environmental geological effects of rock deformation during in-situ mining were identified. Simulation results show that after heating, the temperature within 80 cm of the heating well reaches above the initial pyrolysis temperature of 350 °C for oil shale organic matter, and there is a significant stress concentration near the heat source. In the simulation, ground displacement rises in a wave-like manner during heating, quickly subsides after cooling, and finally stabilizes. Eventually, the entire stratum exhibited subsidence, with a subsidence amount of 0.59 cm. The spatiotemporal deformation trend obtained from SBAS-InSAR real-time monitoring results is similar to the simulation results. By comparing the monitoring results with the simulation results, the synergistic deformation mechanism of underground and ground surface co-deformation during in-situ mining of geochemical reactions in the study area was analyzed. The deformation rate is determined by the thermal hysteresis phenomenon and the temperature difference between the heated fluid and the rock layer. This provides scientific support for the geological effect evaluation of oil shale in-situ mining, which helps to improve mining safety and efficiency.

Critical evaluation of borehole ovalization analysis against hydrofracturing profiles in argillaceous formations

This paper introduces and evaluates the effectiveness of borehole ovalization analysis, a methodology designed to predict the natural stress field by examining deformations in vertical boreholes. The reliability of this approach has undergone rigorous testing across multiple boreholes within soft argillaceous formations, revealing several key observations. First, the results obtained demonstrate a notable correlation with hydrofracturing measurements, enhancing the overall credibility of the methodology. Second, the ratio of horizontal to vertical stress (σH/σh) is found to be contingent on the selected value of the breakout angle (θ), introducing a nuanced variable into the predictive framework. This insight emphasizes the importance of considering breakout angle variability in stress field predictions. Finally, the cohesion of the rock mass emerges as a pivotal factor that significantly influences the estimation of the horizontal stress magnitude (σH). This finding underscores the necessity of accounting for rock mass cohesion when applying borehole ovalization analysis for stress field predictions. Additionally, this paper conducts a meticulous comparative analysis by contrasting its results with findings from three hydrofracturing profiles conducted in distinct boreholes. Through this comparative approach, a more comprehensive understanding of the methodology's strengths and limitations is unveiled, contributing to the ongoing discourse on accurate stress field predictions in subsurface geomechanics.

Numerical simulation and properties analysis of Ta10W alloy joints prepared by electron beam welding

Vacuum electron beam welding has the characteristics of concentrated energy, controllable heat input, almost no pollution, and a small heat-affected zone. In this study, the Ta10W alloy was successfully connected by electron beam welding (EBW), and numerical simulations were employed to examine the distribution of temperature and stress fields throughout the welding process. Additionally, the influence of EBW on the microstructure and corrosion resistance of the welded joints was scrutinized. Findings indicate that the welding heat process led to a reduction in grain boundary energy, thereby facilitating thermal activation processes that contributed to grain growth. Grain boundary migration and possible dynamic crystallization led to the appearance of the coarse columnar crystal structure in the welded joint. A three-dimensional, nonlinear, transient, thermo-mechanically coupled finite element model was developed for the electron beam welding of Ta10W alloy. The shape characteristics and size of the weld and transient thermal cycles calculated by numerical simulations were in reasonable agreement with experimental results. Electron beam welding reduced the corrosion resistance of the Ta10W alloy, and the corrosion product was mainly composed of Ta, O and Na.

Forming mechanism of single-channel multilayer laser cladding Fe60 process under different laser heat source operating mode

Continuous wave (CW) and pulsed wave are the two principal modes of operation used to control the laser heat source. Different laser heat source operating modes have an essential impact on the rapid cooling and heating temperature change rate during the cladding process, which directly determines the cladding layer quality. The laser cladding process is meaningful to quantitatively reveal the mechanism of single-channel multilayer cladding and forming under different laser heat source operating modes. In this article, a multi-field coupled 3D numerical model of the single-channel multilayer cladding process under different laser operating modes was proposed, and the thermal physical parameters of the cladding material were computed on the basis of Calculation of Phase Diagrams method. The mechanism of the impact of distinct operating modes on the multi-field coupled ephemeral evolution process of laser cladding was investigated by using the solid/liquid interface tracking technique, which comprehensively considers the light powder interaction between the powder waist beam and the laser beam under different operating modes. The temperature, flow, and stress fields were computationally solved for a single-channel multilayer cladding process. On the foundation of this study, the impact mechanism of pulse duty cycle and pulse frequency on the cladding behavior of single-channel and multilayers during pulsed laser cladding were dissected. The macroscopic morphology and microstructure of the cladding layer were observed by KEYENCE VH-Z100R ultra-deep field electron microscope, and the feasibility of the model was confirmed. This study provides a significant theoretical rationale for enhancing the cladding quality under different laser operating modes.

Establishment and Solution of a Finite Element Gas Exchange Model in Greenhouse-Grown Tomatoes for Two-Dimensional Porous Media with Light Quantity and Light Direction

An accurate gas utilization model is essential for precisely detecting plant photosynthetic capacity. Existing equipment for measuring the plant photosynthetic rate typically considers the key parameters of mesophyll cell conductance and a photosynthetic model based on the carbon reaction process under direct light conditions. However, the light environment signals received by the plant canopy not only vary significantly in incidence angles, but the effective light intensity also differs greatly from the measured values under vertical incidence conditions. To reduce the deviation between existing photosynthetic models and the actual photosynthetic efficiency of leaves, this study employs the gas diffusion method from engineering, using the finite element approach. Based on elastic mechanics and seepage mechanics, the internal stress field control equation of tomato leaves and the two-phase flow equation under a CO2 porous medium were derived. A mathematical model of porous gas–liquid two-phase fluid-solid coupling was established, solved, and analyzed. Preliminary verification was conducted through tests. The results show that in the initial stage of CO2 entering the leaf, the gas flow velocity is higher because of the larger pressure gradient between the pore and the leaf. In this stage, the gas diffusion rate is higher. As the intake time increases, the pressure gradient gradually decreases, and the inlet velocity slows down. Consequently, the diffusion rate gradually reduces. Because of the coupling of light quantity and light direction, the gas diffusion rate significantly increases compared with the uncoupled model. Additionally, a diffusion model that does not consider fluid–solid coupling will overestimate the gas flow rate as the depth of gas entry increases. Therefore, the internal gas diffusion model must account for the effect of coupling on the diffusion rate.

Statistical distribution of static stress resolved onto geometrically-rough faults

The in-situ stress state within fault zones is technically challenging to characterize, requiring the use of indirect methods to estimate. Most work to date has focused on understanding average properties of resolved stress on faults, but fault non-planarity should induce spatial variations in resolved static stress on a single fault. Assuming a particular stochastic model for fault geometry (band-limited fractal) gives an approximate analytic solution for the probability density function (PDF) on fault stress that depends on the mean fault orientation, mean stress ratio, and roughness level. The mean stress is shown to be equal to the planar fault value, while deviations are described by substituting a second-order polynomial expansion of the stress ratio into the inverse distribution on fault slope. The result is an analytical expression for the PDF of shear-to-normal stress ratio on 2-D rough faults in a uniform background stress field. Two end-member distributions exist, one approximately Gaussian when all points on the fault are well away from failure, and one reverse exponential, which occurs when the mean stress ratio approaches the peak. For the range of roughness values expected to apply to crustal faults, stress deviations due to geometry can reach nearly 100% of the background stress level. Consideration of such a distribution of stress on faults suggests that geometric roughness and the resulting stress deviations may play a key role in controlling earthquake behavior.

Residual stress evaluation in innovative layer-level continuous functionally graded materials produced by Powder Bed Fusion-Laser Beam

AbstractThe main objective of this study is to evaluate residual stresses in AISI 316L and 18Ni Maraging 300 functionally graded materials with continuous variation of composition within a single layer using the contour method. The manufacture of this kind of layer-level continuous functionally graded materials by employing a Powder Bed Fusion-Laser Beam system utilizing a blade/roller-based powder spreading technique has only been recently devised and a proper residual stress analysis is still required. In fact, as the mechanical properties of additively manufactured samples are significantly influenced by the direction of construction, the same holds true for the direction along which the compositional variation is made. Furthermore, in this study, the impact of solution annealing and aging heat treatment, which are necessary for enhancing the mechanical properties of martensitic steel, on residual stresses was explored. Additionally, the effect of adopting material-differentiated process parameters was investigated. The results indicated that each specimen displayed areas of tensile stress concentration on the upper and lower surfaces, balanced by compression in the center. The application of heat treatment led to a decrease in the maximum tensile stress of 8% and provided a uniform and significant stress reduction within the maraging steel. Finally, the implementation of material-specific process parameters for the three composition zones in conjunction with the heat treatment resulted in a reduction in the maximum residual stress of 35% and also a significantly lower residual stress field throughout the specimen.

The Influence of Cement Thickness within the Cap on Stress Distribution for Dental Implants.

The purpose of this finite element analysis (FEA) was to evaluate the stress distribution within the prosthetic components and bone in relation to varying cement thicknesses (from 20 to 60 μm) utilized to attach a zirconia crown on a conometric cap. The study focused on two types of implants (Cyroth and TAC, AoN Implants, Grisignano di Zocco, Italy) featuring a Morse cone connection. Detailed three-dimensional (3D) models were developed to represent the bone structure (cortical and trabecular) and the prosthetic components, including the crown, cement, cap, abutment, and the implant. Both implants were placed 1.5 mm subcrestally and subjected to a 200 N load at a 45° inclination on the crown. The results indicated that an increase in cement thickness led to a reduction in von Mises stress on the cortical bone for both Cyroth and TAC implants, while the decrease in stress on the trabecular bone (apical zone) was relatively less pronounced. However, the TAC implant exhibited a higher stress field in the apical area compared to the Cyroth implant. In summary, this study investigated the influence of cement thickness on stress transmission across prosthetic components and peri-implant tissues through FEA analysis, emphasizing that the 60 μm cement layer demonstrated higher stress values approaching the material strength limit.

Finite element analysis of a rubber bearing base isolator under vertical and horizontal loads using a nonlinear hyper-viscoelastic material model

This research is devoted to developing a finite element model using Abaqus code for the computer simulation of an in-house developed and manufactured rubber bearing subjected to static vertical and cyclic horizontal loads. A high-damping rubber compound was designed. The material behavior of the rubber was assumed to be described by the hyper-viscoelastic model. Both linear (Prony series) and nonlinear (strain hardening power law) viscoelastic relationships were used in conjunction with the Ogden-Roxburgh equation to take the addition of the stress softening phenomenon or Mullins effect into consideration. The parameters of the material model were determined using MCalibration code in which an optimization technique was used, and data obtained in experiments carried out on test specimens were fitted into the selected model. The results of the simulations were compared with their corresponding experimental data carried out on the rubber bearing. The force-displacement behavior, stress and strain fields, and computed energy were presented and discussed. It is shown that the nonlinear viscoelastic model accompanied by the Mullins effect gives the best results. Moreover, the model could accurately predict the energy variations during the earthquake loading.

Non-contact ultrasonic vibration-assisted laser metal deposition manufacturing Fe-based powder: Numerical simulation and experimental investigation

Fe-based powder was manufactured on 42CrMoA steel substrate using non-contact ultrasonic vibration-assisted(UVA) laser metal deposition(LMD) process with different exciting distances(d), and the temperature field and stress field distribution, microstructure and mechanical properties of the deposited layers were investigated. The results show that the distribution of temperature field was more uniform, especially at the bottom of the molten pool, and the gradient of temperature field decreased. Compared with the condition without UVA, the residual stress peak value of the tensile stress area decreased significantly after UVA applied. When d=80 mm, the peak tensile stress and compressive stress were 90.5 MPa and 72.6 MPa, respectively, which were reduced by 45.6 % and 25.2 % compared with the condition without UVA. The length of the columnar crystals and the region of the columnar crystals decreased at the interface after UVA applied. The application of UVA can significantly improved the microhardness of deposition layer. With the reduction of the residual stress at the interface and the improvement of uniformity, the tensile properties of the deposit were also significantly improved. The highest tensile strength was 1281.3 MPa when d=80 mm, which was 30.12 % higher than that without UVA.

Development and experimental validation of a thermo-metallurgical-mechanical model of the laser metal deposition (LMD) process

The current paper presents the development and experimental validation of a thermo-metallurgical-mechanical model for a multi-pass Laser Metal Deposition (LMD) process, with the objective of accurately predicting the resultant constituent phases and residual stresses. The thermal model is calibrated using temperature readings and is shown to accurately capture the transient temperature field and extent of the fusion zone associated with the multi-pass LMD process. The metallurgical model incorporates the kinetics of ongoing solid-state phase transformations (SSPTs) and tempering reactions. The predictions are validated via hardness measurements, demonstrating a very good agreement with the predictions. The developed mechanical model predicts the residual stress field, which is validated using X-ray diffraction measurements, and the comparison also shows a very good agreement between the predictions and measurements. The validated numerical model is then used to explore alternative LMD strategies showing that the choice of deposition strategy can significantly impact resultant constituent phases and residual stresses.

Graph Neural Networks for Geometry Design in Plastic Regime

In this work, we extend MeshGraphNets to simulate collisions involving plastic material, previously limited to hyperelastic, addressing higher non-linearities and energy dissipation. While previous work estimated only the displacement field, our approach also resolves the complete tensor stress field, under different boundary conditions and geometries.

Failure assessment of eccentric circular holes under compressive loading

AbstractThe present work aims to investigate the failure size effect on flattened disks containing an eccentric circular hole under mode I loading conditions. For this purpose, uniaxial compression tests are carried out on polymethyl methacrylate (PMMA) samples with holes. Depending on the hole radius and eccentricity, the energy release rate is either an increasing or decreasing function of the crack length, thus affecting the stability of crack propagation. Experimental results are interpreted and discussed through the coupled stress and energy criterion of Finite Fracture Mechanics. The approach lies on the assumption of a finite crack advance and it is implemented through the numerical estimation of the stress field and the Incremental Energy Release Rate functions. Finally, stability and crack speed propagation are discussed under the assumption of Linear Elastic Fracture Mechanics. Theoretical predictions reveal in agreement with experimental results thus demonstrating that the Coupled Criterion effectively captures the failure condition.

Magnetic field and initial stress on a rotating photothermal semiconductor medium with ramp type heating and internal heat source

This manuscript addresses a significant research gap in the study by employing a mathematical model of photo thermoelastic wave propagation in a rotator semiconductor medium under the effect of a magnetic field and initial stress, as well as ramp-type heating. The considered model is formulated during the photothermal theory and in two-dimensional (2D) electronic-elastic deformation. The governing equations represent the interaction between the primary physical parameters throughout the process of photothermal transfer. Computational simulations are performed to determine the temperature, carrier density, displacement components, normal stress, and shear stress using the application of Lame’s potential and normal mode analysis. Numerical calculations are carried out and graphically displayed for an isotropic semiconductor like silicon (Si) material. Furthermore, comparisons are made with the previous results obtained by the others, as well as in the presence and absence of magnetic field, rotation, and initial stress. The obtained results illustrate that the rotation, initial stress, magnetic field, and ramp-type heating parameter all have significant effects. This investigation provides valuable insights into the synergistic dynamics among a magnetization constituent, semiconducture structures, and wave propagation, enabling advancements in nuclear reactors' construction, operation, electrical circuits, and solar cells.

Modeling and Assessment of Temperature and Thermal Stress Field of Asphalt Pavement on the Tibetan Plateau

The Qinghai–Tibet Plateau (QTP) is the highest altitude plateau in the world, characterized by strong solar radiation and large diurnal temperature differences and so on, which brings a great negative impact on the temperature and thermal stress field of asphalt pavement. The purpose of this study is to analyze the temperature field and thermal stress status of asphalt pavement in the QTP to provide a reference for pavement design and maintenance in high-altitude areas. The finite element method was applied to establish the temperature field model to study the distribution and variation of pavement temperature. On this basis, the influence of cooling amplitude on pavement thermal stress was studied during cold waves. In addition to this, the key internal factors affecting the thermal stress of pavement, such as surface thickness, surface temperature shrinkage coefficient, surface modulus, and base modulus, were analyzed by an orthogonal test. It was found that temperature and solar radiation have a significant effect on the pavement temperature field. When the cold wave came, the cooling rate had a considerable impact on the thermal stress of the pavement, that is, every 5 °C increase in cooling rate would increase the thermal stress by more than 50%. The temperature shrinkage coefficient and surface modulus of the surface layer material had the greatest influence on the pavement thermal stress. The thermal stress could be reduced by more than 0.4 Mpa for every 5 × 10−6/°C reduction in the surface temperature shrinkage coefficient or every 1000 Mpa reduction in the surface modulus. This study can provide a reference for improving the temperature field and thermal stress field of asphalt pavement in the plateau area.