Tangent Modulus Research Articles

Numerical Thermal Analysis of Greased Rolling Bearing Considering Surface Topography and Plastic Deformation

ABSTRACTIn numerical studies of grease lubrication, thermal effect is often neglected and surface plastic deformation is almost not considered. This paper has developed a deterministic thermal plasto‐elastohydrodynamic lubrication (PEHL) model for grease‐lubricated rolling bearing. The influence of tangent modulus, rheological index and texture orientation on lubrication characteristics and temperature rise is analysed. The results show that increasing the rheological index of grease and decreasing the wavelength factor are obviously positive for improving lubrication behaviour. Since surface plastic deformation in the EHL state is at nanoscale, film thickness, friction coefficient and temperature rise of solid surfaces decline slightly with the decrease of tangent modulus.

Restoration of Corneal Stiffness in Rabbits Following Withdrawal of Travoprost.

To evaluate if the effect of travoprost on corneal material stiffness could be restored after drug withdrawal. Seventy-two rabbits were randomly allocated into three groups: medicine (M), medicine withdrawal (MW), and blank (B). Within the M and MW groups, treatment with travoprost was administered to the right eyes (MT and MWT) over a period of 12 weeks. Subsequently, the M group was killed, but the MW group underwent an additional 12-week period for treatment withdrawal. No treatment was given to the contralateral eyes (MC and MWC) in the M and MW groups. A separate blank control (BC) group remained untreated for the entire 24-week duration. In each group, corneas from 18 rabbits were tested mechanically under inflation conditions to estimate their tangent modulus (Et). The corneas of the remaining six rabbits underwent electron microscopy analysis, which focused on fibril diameter and interfibrillar spacing. Central corneal thickness (CCT) of the treated eyes (MT and MWT groups) decreased with 12 weeks of travoprost treatment (P < 0.05). The CCT in the MWT group increased after 12 weeks of withdrawal but was still lower than that in the BC group (P < 0.05). The Et of the MT group was significantly lower than that of the MC group at mean tissue stresses of 2, 4, and 6 kPa (P < 0.05). Conversely, no significant difference in Et values was observed between the MWT, MWC, and BC groups, indicating recovery after treatment cessation. Furthermore, the stromal interfibrillar spacing of the treated MT group was significantly larger (P < 0.05) than that of the control MC group, but no disparity was noted among the MWT, MWC, and BC groups following treatment withdrawal. Additionally, there were no significant differences in the mean diameter of collagen fibrils among all groups (all P > 0.05). Travoprost treatment appears to soften corneal tissue, decrease tissue thickness, and reduce the density of stromal collagen fibers by increasing the interfibrillar spacing. These changes were partially reversed after treatment cessation. Travoprost could further inhibit corneal growth, so its use in childhood and adolescence should be carefully considered. Additionally, the effect of travoprost in reducing corneal stiffness may lead to underestimations of intraocular pressure (IOP) measurement and hence overestimations in the effect of treatment in lowering IOP.

Mechanical characterization of a 3D printed lattice core sandwich structure

AbstractSandwich structures have garnered interest as versatile structures for applications in advanced engineering structures. To fabricate sandwich structures, plastics have replaced conventional materials; however, most of these plastics remain in the environment beyond their functional lifespan. This study describes the fabrication of sustainable hybrid sandwich structures with 3D printed poly‐lactic acid (PLA) cores and self‐reinforced polyethylene terephthalate (srPET) face sheets. The mechanical responses of the hybrid sandwich structures with three types of lattice cores, S‐90, S‐45, and S‐V, were compared with those of the parent material sandwich structures after performing bending and impact tests. The face sheet in the hybrid sandwich structure transferred the load to the core without failure. The hybrid sandwich structure containing the S‐90 core exhibited a higher fracture strength (52.4 MPa) and tangent modulus of elasticity (2860 MPa) than those of the other structures. S‐V exhibited the highest fracture strains of 3.3% and 5% for parent material and hybrid sandwich structures, respectively. This study highlights the sandwich structures with excellent mechanical properties for structural applications.Highlights Novel sandwich structures with 3D printed PLA cores are fabricated. Three‐point bending and low‐velocity impact tests are performed. Failure occurred in the core, but the Sr‐PET face sheets did not deform. Hybrid sandwich structures significantly improve mechanical performance.

The strength and hydraulic conductivity characteristics of sewage sludge ash and natural soil mixtures – a sustainable alternate landfill liner material

ABSTRACT This paper examines the feasibility of the natural soil and sewage sludge ash (SSA) mixtures, which satisfy the criteria to be used as landfill liners. The effect of SSA content on hydraulic conductivity and strength characteristics of natural soil and SSA mixtures has been investigated through a series of laboratory tests. The results demonstrate that mixtures exhibit an increase in both hydrodynamic diffusion coefficient and strength with the increasing SSA content. With the content of SSA from 0% to 5%, the values of the hydrodynamic diffusion coefficient ( D ) ranged from 3.5 × 10−10 to 15 × 10−10 cm2/s. The increase in the hydrodynamic diffusion coefficient is minor for low SSA content and significant for SSA content exceeding 5%. The inclusion of 5% SSA content results in a hydrodynamic diffusion coefficient that is approximately three times higher than that observed in natural soil. The results were obtained from soil triaxial tests, revealing that the mixtures containing SSA exhibited a significant increase in both the initial tangent modulus and the ultimate principal stress difference compared to those of natural soil. The SSA content with the highest value exhibits maximum initial tangent modulus and ultimate principal stress. The comprehensive analysis of the strength and hydraulic diffusion conductivity of the mixtures demonstrates that the incorporation of 3% SSA results in a significant enhancement in strength, while marginally increasing hydrodynamic diffusion coefficients. Therefore, it can be inferred that the utilization of mixtures containing 3% SSA content as a liner material is suitable.

Elastoplastic plate shakes down under repeated impulsive loadings

When subjected to repeated dynamic impacts at identical load level, a metallic monolithic beam/plate may reach a stable state wherein measurable deformation ceases (i.e., shakedown in elastic state) after undergoing a sequence of elastoplastic deformations, which has been termed as “pseudo-shakedown” (P-S) (Jones, 1973; Shen and Jones, 1992). While the response of a single beam/plate under repeated low-velocity impacts has been thoroughly studied, its dynamic behavior under high-velocity impacts, such as explosive or alternating impulsive loads, is difficult to measure experimentally, due mainly to high costs and setup challenges. In the current study, the method of metallic foam projectile impact was employed to produce repeated impulsive loadings on a fully-clamped elastoplastic monolithic plate made of L907A (a Chinese standard shipbuilding steel). Its dynamic responses, including mid-point deflection versus time histories, final deflections, and deformation modes after each impact, were systematically measured. The phenomenon of dynamic shakedown was observed. To further explore this phenomenon, the method of finite elements (FE) was employed to simulate the repeated impulsive impact test, and its prediction accuracy was validated against experimental results. Unlike an elastoplastic (e.g., steel) monolithic plate subjected to repeated low-velocity impacts, which exhibits zero plastic energy dissipation in the P-S (pseudo-shakedown) state, the same plate under repeated high-velocity impacts shows a small level of plastic energy dissipation in the P-S state, mainly due to more extreme loading conditions. The initial impact momentum, yield strength, and tangent modulus of the material the plate is made of significantly affect both the stable deflection in the P-S state and the number of impacts needed to reach it, while the elastic modulus has limited influence. A modified dimensionless impulse loading number, accounting for the strain-hardening effect, is proposed. An approximately linear relationship between stable deflection in the P-S state and impulsive loading is found in dimensionless form.

Design of the testing procedure for investigation of Eryx conicus dermal armour characteristics

The aim of this work is to develop an experimental method suitable for the mechanical testing of highly non-standard biological samples such as snake skin with osteoderms. The objective of the method is to determine, whether the osteoderms provide a protective function for the animal in its natural environment. For this purpose, a simulation of rodents biting the skin based on uni-axial compressive loading using a synthetic tooth as a penetrator was developed with an emphasis on integration with X-ray scanners to facilitate in-situ testing. To identify and characterise the structure of snake skin and to prove the protective function of osteoderms, all samples were subjected to high resolution X-ray computed tomography. The results of the experiments are presented in the form of stress-strain curves and a map of the tangent modulus.

Determining the bilinear flow stress of thin films by comparing load/depth and sink-in/pile-up behavior between nanoindentation and FEM

Abstract It is known from the literature that the load-depth curve obtained by nanoindentation cannot uniquely determine the plastic flow stress behaviour of the material. In this study, the sink-in/pile-up of nanoindentation is another important information for predicting the elastic-plastic behaviour of thin film. Therefore, by comparing load/depth behaviour and sink-in/pile-up from nanoindentation with finite element analysis, the bilinear flow stress of the coating can be determined. Commercial TiN coatings are currently used as an example for this study. The bilinear flow stress of TiN can be determined by this method: the elastic modulus of 343.007 GPa, the yield stress of 10.458 GPa and the tangent modulus of 214.080 GPa. In addition, the stress of loading and unloading during the nanoindentation of the thin film was also investigated.

Exploring the influence of rock bridge angle on the rock secant modulus.

Rock can undergo shape deformation and damage due to the influence of joint fissures, and the range of damage caused by joints at different rock bridge angles varies. To study the influence of rock bridge angle on the size effect of rock secant modulus, this paper adopts the principle of regression analysis and combines numerical simulation to carry out relevant research. The research results indicate that: (1) As the rock bridge angle increases, the secant modulus gradually decreases, following a power function relationship. (2) As the rock size increases, the secant modulus shows a trend of first decreasing and then stabilizing, following a power function relationship. (3) As the rock bridge angle increases, the characteristic tangent modulus and characteristic size gradually decrease, following a power function relationship. On this basis, we obtained their relationship formulas separately.

Development of Soft Computing-based Predictive Tools for Estimating the Young Modulus of Weak Rocks

The deformation characteristics of rocks are of vital importance in addressing most geomechanical issues as they are one of the most critical input parameters in rock engineering analyses. For this reason, robust forecasting models are required when analysing the stability of tunnels, slopes, mine galleries, and other underground excavations. In this research, novel predictive models are proposed to estimate the tangential Young modulus (Eti) of weak rocks. To achieve this, an extensive literature review is performed to obtain a comprehensive database including critical physico-mechanical properties of various weak rocks. Thanks to the advantages of soft computing methods such as genetic algorithm (GA), adaptive neuro-fuzzy inference system (ANFIS), artificial neural networks (ANN) and multivariate adaptive regression splines (MARS), novel predictive models are established. The effectiveness of the developed predictive models is investigated using various statistical measures and it is concluded that empirical models utilizing ANN and ANFIS methodologies are the most effective tools for estimating the Eti of weak rocks. In addition, a practical design chart is also developed for assessing the Eti of weak rocks.

Monomer Trapping Synthesis Toward Dynamic Nanoconfinement Self-healing Eutectogels for Strain Sensing.

The rapid advancement in attractive platforms such as biomedicine and human-machine interaction has generated urgent demands for intelligent materials with high strength, flexibility, and self-healing capabilities. However, existing self-healing ability materials are challenged by a trade-off between high strength, low elastic modulus, and healing ability due to the inherent low strength of noncovalent bonding. Here, drawing inspiration from human fibroblasts, a monomer trapping synthesis strategy is presented based on the dissociation and reconfiguration in amphiphilic ionic restrictors (7000-times volume monomer trapping) to develop a eutectogel. Benefiting from the nanoconfinement and dynamic interfacial interactions, the molecular chain backbone of the formed confined domains is mechanically reinforced while preserving soft movement capabilities. The resulting eutectogels demonstrate superior mechanical properties (1799% and 2753% higher tensile strength and toughness than pure polymerized deep eutectic solvent), excellent self-healing efficiency (>90%), low tangential modulus (0.367MPa during the working stage), and the ability to sensitively monitor human activities. This strategy is poised to offer a new perspective for developing high strength, low modulus, and self-healing wearable electronics tailored to human body motion.

Hyperelastic Material Modeling Using First- and Second-Order Differential Operations with Complex Step Derivative Approximation

This study proposes a method for calculating hyperelastic materials’ stress and tangent modulus using a generalized complex-step derivative approximation. This method is accurate and requires only the operational code of the strain energy density function. Moreover, because it uses only standard complex operations in Fortran, no prior preparation is required, making the method convenient and practical. The effectiveness of the method was confirmed by applying it to the implementation of isotropic and anisotropic hyperelastic models.

Experimental Study on Static and Dynamic Characteristics of Sand–Clay Mixtures with Different Mass Ratios

The alteration of soil static and dynamic characteristics induced by clay content constitutes a crucial issue in the realm of disaster prevention and mitigation within geotechnical engineering. The static and dynamic characteristics of mixed soils with varying sand–clay contents were investigated through the design and implementation of static and dynamic triaxial tests. The relationship between clay content and soil resistance to liquefaction was investigated, with an analysis of the influence of clay content on soil strength and static liquefaction performance. Furthermore, the study examined the soil’s resistance to liquefaction under dynamic constitutive and cyclic loading conditions for soils with varying clay content. Results indicate that stress–strain curves for samples with varying clay content exhibit a consistent trend, with the lowest tangent modulus and peak strength observed in samples containing 30% clay. Increasing clay content diminishes soil’s resistance to liquefaction under static loading conditions. Higher confining pressures correspond to larger tangent moduli and peak deviating stresses in triaxial shear tests. Dynamic shear modulus decreases as clay content increases, whereas damping ratio decreases accordingly. Soil gradation significantly affects liquefaction-induced deformation, with the sample containing 30% clay experiencing the fastest increase in pore water pressure during testing failure, accompanied by fewer cyclic loading cycles until failure occurs. Improving soil gradation and adjusting the sand–clay ratio are beneficial for enhancing both soil strength and its resistance to liquefaction.

A Mathematical Model for Postimplant Collagen Remodeling in an Autologous Engineered Pulmonary Arterial Conduit.

This study was undertaken to develop a mathematical model of the long-term in vivo remodeling processes in postimplanted pulmonary artery (PA) conduits. Experimental results from two extant ovine in vivo studies, wherein polyglycolic-acid (PGA)/poly-L-lactic acid tubular conduits were constructed, cell seeded, incubated for 4 weeks, and then implanted in mature sheep to obtain the remodeling data for up to two years. Explanted conduit analysis included detailed novel structural and mechanical studies. Results in both studies indicated that the in vivo conduits remained dimensionally stable up to 80 weeks, so that the conduits maintained a constant in vivo stress and deformation state. In contrast, continued remodeling of the constituent collagen fiber network as evidenced by an increase in effective tissue uniaxial tangent modulus, which then stabilized by one year postimplant. A mesostructural constitute model was then applied to extant planar biaxial mechanical data and revealed several interesting features, including an initial pronounced increase in effective collagen fiber modulus, paralleled by a simultaneous shift toward longer, more uniformly length-distributed collagen fibers. Thus, while the conduit remained dimensionally stable, its internal collagen fibrous structure and resultant mechanical behaviors underwent continued remodeling that stabilized by one year. A time-evolving structural mixture-based mathematical model specialized for this unique form of tissue remodeling was developed, with a focus on time-evolving collagen fiber stiffness as the driver for tissue-level remodeling. The remodeling model was able to fully reproduce (1) the observed tissue-level increases in stiffness by time-evolving simultaneous increases in collagen fiber modulus and lengths, (2) maintenance of the constant collagen fiber angular dispersion, and (3) stabilization of the remodeling processes at one year. Collagen fiber remodeling geometry was directly verified experimentally by histological analysis of the time-evolving collagen fiber crimp, which matches model predictions very closely. Interestingly, the remodeling model indicated that the basis for tissue homeostasis was maintenance of the collagen fiber ensemble stress for all orientations, and not individual collagen fiber stresses. Unlike other growth and remodeling models that traditionally treat changes in the external boundary conditions (e.g., changes in blood pressure) as the primary input stimuli, the driver herein is changes to the internal constituent collagen fiber themselves due to cellular mediated cross-linking.

Mechanical Response Characteristics and Tangent Modulus Calculation Model of Expansive-Clay Unloading Stress Path

Mechanical Response Characteristics and Tangent Modulus Calculation Model of Expansive-Clay Unloading Stress Path

Tensile properties of glaucomatous human sclera, optic nerve, and optic nerve sheath.

We characterized the tensile behavior of sclera, optic nerve (ON), and ON sheath in eyes from donors with glaucoma, for comparison with published data without glaucoma. Twelve freshly harvested eyes were obtained from donors with history of glaucoma, of average age 86 ± 7 (standard deviation) years. Rectangular samples were taken from anterior, equatorial, posterior, and peripapillary sclera, and ON sheath, while ON was in native form and measured using calipers. Under physiological temperature and humidity, tissues were preconditioned at 5% strain before loading at 0.1mm/s. Force-displacement data were converted into engineering stress-strain curves fit by reduced polynomial hyperelastic models and analyzed by tangent moduli at 3% and 7% strain. Data were compared with an age-matched sample of 7 published control eyes. Optic atrophy was supported by significant reduction in ON cross section to 73% of normal in glaucomatous eyes. Glaucomatous was significantly stiffer than control in equatorial and peripapillary regions (P < 0.001). However, glaucomatous ON and sheath were significantly less stiff than control, particularly at low strain (P < 0.001). Hyperelastic models were well fit to stress-strain data (R2 > 0.997). Tangent moduli had variability similar to control in most regions, but was abnormally large in peripapillary sclera. Tensile properties were varied independently among various regions of the same eyes. Glaucomatous sclera is abnormally stiff, but the ON and sheath are abnormally compliant. These abnormalities correspond to properties predicted by finite element analysis to transfer potentially pathologic stress to the vulnerable disk and lamina cribrosa region during adduction eye movement.

Numerical approximation for algorithmic tangent moduli for nonlinear viscoelastic model with CSDA method

This work revisits the notion of complex step derivative approximation (CSDA) and presents its use in constitutive model of a class of nonlinear viscoelastic materials. The effectiveness of a CSDA is evaluated by putting it through a series of straightforward examples. After that, the idea of the CSDA is put to use in order to carry out a numerical evaluation of the algorithmic tangent moduli of a viscoelastic constitutive model. The performance of the constitutive models is evaluated through the use of three different numerical tests, and the results are compared to those that were achieved by the application of an analytical method. In comparison to other numerical differentiation techniques, It has been found that the CSDA scheme is the most computationally efficient and robust method of numerical differentiation, regardless of the size of the finite difference interval.

Study on unified strength theory and elastic–plastic stress update algorithm

The unified strength theory with the two-piecewise linear equations is more convenient and concise to calculate the strength of materials. It can fully explore the potential in the strength of materials and improve the economic benefits of engineering design. This study combines the semi-implicit return mapping algorithm and the Aitken accelerated iteration scheme and develops a plastic constitutive algorithm for isotropic softening materials based on the unified strength theory. The combining method can simplify the stress update and make the calculation of consistent tangent modulus easier. Furthermore, it can avoid solving the partial derivatives of the plastic flow rule and overcome the stress-deviating problem. The self-developed constitutive algorithm is used to simulate the elastic–plastic excavation process of a deep-lying circular tunnel. The numerical simulation results match well with the theoretical solution, verifying the correctness of the self-developed constitutive algorithm. Based on the self-developed constitutive algorithm, the stability of an underground mining stope is comprehensively analyzed, and its structural parameters are optimized. The research reveals the mechanism of stope instability, provides a reliable scientific basis for the mining design and decision-making, ensures the safe and efficient production of the stope, and achieves the expected goal.

Buckle propagation failure of subsea pipelines; experimental, analytical, and numerical simulations

This research program investigates buckle propagation in subsea pipeline systems, The study aims to understand and predict propagation pressure (PP ), essential for ensuring the structural integrity and safe operation of these pipelines, hypothesizing that incorporating strain hardening effects into the strain energy approach can significantly enhance the prediction of propagation pressure (PP ) and that geometric parameters, particularly the diameter-to-thickness (D/t) ratio, play a major role in PP prediction. Accurate PP prediction is essential for ensuring the structural integrity and safe operation of these pipelines. The investigation is conducted through analytical, experimental, numerical, and machine learning approaches. A new analytical solution for PP is proposed, incorporating strain hardening effects using a strain energy approach. Experimental tests conducted using a hyperbaric chamber cover a wide range of pipeline configurations and materials, including steel, aluminum, and stainless steel. Complementing experimental data, numerical simulations using finite element methods facilitate parametric dependence analysis and the visualization of results through 3D charts. More than 600 FE models were simulated to investigate the influence of geometric and material parameters on PP . The findings from both experimental and numerical analyses indicated that the geometric and material properties have a significant impact on PP , specifically, the diameter-to-thickness (D/t) ratio, yield stress (σy ), and tangent modulus (E′). Furthermore, Machine Learning (ML) techniques have been used to predict the PP value and have concluded that the Random Forest (RF) technique outperformed the K-Nearest Neighbors (KNN), and Multi-layer Perceptron (MLP) neural network techniques. Overall, this study concludes that analytical, numerical, and machine learning approaches offer valuable insights into buckle propagation in subsea pipelines, contributing to improved safety and reliability in offshore oil and gas operations.

From Biomechanical Properties to Morphological Variations: Exploring the Interplay between Aortic Valve Cuspidity and Ascending Aortic Aneurysm.

Background: This research explores the biomechanical and structural characteristics of ascending thoracic aortic aneurysms (ATAAs), focusing on the differences between bicuspid aortic valve aneurysms (BAV-As) and tricuspid aortic valve aneurysms (TAV-As) with non-dilated aortas to identify specific traits of ATAAs. Methods: Clinical characteristics, laboratory indices, and imaging data from 26 adult patients operated on for aneurysms (BAV-A: n = 12; TAV-A: n = 14) and 13 controls were analyzed. Biomechanical parameters (maximal aortic diameter, strain, and stress) and structural analyses (collagen fiber organization, density, fragmentation, adipocyte deposits, and immune cell infiltration) were assessed. Results: Significant differences in biomechanical parameters were observed. Median maximal strain was 40.0% (control), 63.4% (BAV-A), and 45.3% (TAV-A); median maximal stress was 0.59 MPa (control), 0.78 MPa (BAV-A), and 0.48 MPa (TAV-A). BAV-A showed higher tangential modulus and smaller diameter, with substantial collagen fragmentation (p < 0.001 vs. TAV and controls). TAV-A exhibited increased collagen density (p = 0.025), thickening between media and adventitia layers, and disorganized fibers (p = 0.036). BAV-A patients had elevated adipocyte deposits and immune cell infiltration. Conclusions: This study highlights distinct pathological profiles associated with different valve anatomies. BAV-A is characterized by smaller diameters, higher biomechanical stress, and significant collagen deterioration, underscoring the necessity for tailored clinical strategies for effective management of thoracic aortic aneurysm.

Deformation Analysis of Existing Buildings Affected by Shield Tunnels Based on Intelligent Inversion and Measured Data

In the construction of urban underground shield tunnels, uneven deformation can easily occur when the shield passes through soft soil and other poor strata. Such deformation has a significant impact on surface settlement and may cause potential safety hazards to the surrounding existing buildings, directly affecting the safety of urban operation. When simulating and predicting surface settlements, the small-strain soil hardening model can more accurately characterize the mechanical parameters of soil. Nevertheless, its parameters are numerous and complicated to determine accurately, so parameter inversion is needed to determine the accurate parameters of the soft soil layer in order to more accurately predict the surface settlement. This study uses the EFAST method to analyse the sensitivity of the HSS model parameters of soft soil strata. It is determined that the parameters that have the most significant impact on the surface settlement are the reference tangent modulus, rebound modulus, and effective cohesion. Then, XGBoost’s fast calculation speed and high precision of SSA inversion are used to inverse and optimize the parameters with high sensitivity. Finally, according to the parameters of the soft soil layer obtained from inversion and measured data, the settlement deformation and safety behaviour of existing buildings are analysed. Combined with the actual shield tunnel project in a city along a river, the inversion calculation shows that the overall average error of the transverse monitoring section is 1.04 mm, and the average maximum error of each monitoring point in the overall shield process is 2.87 mm. The prediction effect is significantly improved compared with the original parameters. The accuracy of the inversion of soil layer parameters is verified from the perspective of time and space. The average settlement of the river embankment foundation is 2.5 mm. Compared with the original parameter data, the prediction results have been greatly improved, and the settlement deformation results are more consistent with the measured data.