Strain Energy Research Articles

Energy redistribution in railway transition zones by geometric optimisation of a novel transition structure

Railway transition zones are critical regions in railway infrastructure that are subjected to excessive operation-driven degradation due to energy concentration within these zones. This work presents a heuristic approach to optimise the geometry of the transition structure and investigate its influence on the strain energy distribution in the railway transition zones (RTZs), with a specific focus on embankment-bridge transitions equipped with a newly proposed ’Safe Hull-Inspired Energy Limiting Design (SHIELD)’ transition structure. For this purpose, a number of three-dimensional finite element models are used to analyze different geometric profiles of SHIELD in a systematic manner. By altering SHIELD’s geometry across longitudinal, transversal, and vertical directions, the influence of the different geometric profiles on the total strain energy distribution across the trackbed layers (ballast, embankment, and subgrade) is studied in terms of spatial and temporal variations. The results establish the contribution of geometry to energy redistribution in all three directions and present an optimum geometry for the type of transition under study. It is found that among all the profiles, the longitudinal geometric profile of SHIELD has the most significant impact on the strain energy distribution, while the transversal profile primarily influences the ballast layer, and the alteration of vertical profiles enhance the local redistribution of strain energy in the vicinity of the transition interface. The preliminary optimisation (heuristic approach) presented in this work provides the starting point for full-scale optimisation to obtain tailored shapes of transition structures such that there is neither a concentration of energy nor an obstruction in the flow of energy in RTZs.

Comparison of Laminar and Turbulent K–Omega Shear Stress Transport Models Under Realistic Boundary Conditions Using Clinical Data for Arterial Stenosis

Abstract Early diagnosis of cardiovascular diseases (CVDs), including arterial stenosis, enables targeted treatments that reduce CVD mortality. It is vital to improve the accuracy of early diagnostic tools. Current computational studies of stenosis use mathematical models, such as laminar and k–omega shear stress transport (SST) models, available in ansys (Fluent and CFX), openfoam, and comsol software packages. Users can adjust boundary conditions, such as inlet velocity and outlet pressure using user-defined functions (UDFs) with different expressions and constant values. However, currently there is no rule over what to impose at these boundaries, and previous studies have used various assumptions, such as rigid artery wall, one-way fluid–structure interaction (FSI) or two-way FSI, and the blood's Newtonian or non-Newtonian material properties. This variety in construction has associated deviations of the models from the clinical data and lessens the value of the models as potential diagnostic or predictive tools for medical practitioners. In this study, we examine arterial stenosis models, with severities of 20%, 40%, and 50%, compared with the healthy artery analyzed in terms of strain energy to the artery wall. Additionally, we investigate elastic walls using one-way FSI, comparing with laminar and k–omega SST. These boundary conditions are based on clinical data. The results regarding the strain energy (mJ) behavior along the artery wall show that the k–omega SST model outperforms the laminar model for short arterial segments and under the Newtonian assumption with a no-slip boundary wall and turbulent flow.

Preparation and Application of a Novel Liquid Oxygen-Compatible Epoxy Resin of Fluorinated Glycidyl Amine with Low Viscosity

A liquid oxygen-compatible epoxy resin of fluorinated glycidyl amine (TFEPA) with a low viscosity of 260 mPa·s in a wide range of temperatures, from room temperature to 150 °C, was synthesized and used to decrease the viscosity of phosphorus-containing bisphenol F epoxy resins. And the forming process and application performances of this resin system and its composite were investigated. The viscosity of the bisphenol F resin was decreased from 4925 to 749 mPa·s at 45 °C by mixing with 10 wt.% TFEPA, which was enough for the filament winding process. Moreover, the processing temperature and time windows were increased by 73% and 186%, respectively. After crosslinking, the liquid oxygen compatibility was preserved, and its tensile strength, elastic modulus, and breaking elongation at −196 °C were 133.31 MPa, 6.59 GPa, and 2.36%, respectively, which were similar to those without TFEPA. And the flexural strength and modulus were 276.14 MPa and 7.29 GPa, respectively, increasing by 21.73% in strain energy at flexural breaking, indicating an enhanced toughness derived from TFEPA. Based on this resin system, the flexural strength and toughness of its composite at −196 °C were 862.73 MPa and 6.88 MJ/m3, respectively, increasing by 4.46% and 10.79%, respectively.

Manganese Partitioning and its Effect on Residual Stress

The residual stress in low‐carbon high‐strength steel is not effectively relaxed during alloy carbide precipitation but is fully relaxed during manganese partitioning. The specific microscopic mechanisms responsible for this observed phenomenon have yet to be fully elucidated. This study employs first‐principles calculations in conjunction with experiments to demonstrate that alloy carbide precipitation leads to the formation of dense dislocation tangles that hinder carbon diffusion and carbide precipitation. Conversely, manganese partitioning aids carbon diffusion by altering dislocation morphology while also causing plastic deformation. The simultaneous occurrence of partitioning plasticity and precipitation plasticity during manganese partitioning results in a more significant relaxation of residual stress compared to alloy carbides precipitation: The plasticity coefficient for alloy carbide precipitation is 1.303 × 10−5, while the plasticity coefficient for manganese partition is 2.691 × 10−5. During alloy carbide precipitation, the elastic strain energy decreases to 43.48% of its initial value, whereas it can be further reduced to 25.29% after manganese partitioning.

A novel fatigue life model for MCrAlY coated superalloys considering interfacial microstructure evolution

MCrAlY coatings, extensively utilized for safeguarding turbine blades against oxidation and erosion, encounter impediments due to inter-diffusion between the coating and substrate, thereby exacerbating fatigue life degradation at elevated temperatures. In this study, we introduce a novel approach involving the modification of critical depth in interfacial strain energy density to elucidate the impact of interfacial microstructure evolution on mechanical properties. Building upon this concept, we propose a fatigue life prediction model, which incorporates the dynamic evolution of interfacial structure and mechanical characteristics. Validation against empirical data underscores the commendable precision of the model. Our inquiry not only advances the comprehension of mechanical-chemical coupled behaviors but also yields significant insights for the optimization and maintenance of turbine blades.

A multi-objective optimization approach to design bistable collapsible tubular mast

The collapsible tubular mast (CTM) is a deployable structure made of two omega shaped shells, with each omega composed of three arc segments. In the bistable CTM (Bi-CTM), in addition to the strain energy well associated with the stable deployed state, another strain energy well can be found corresponding to the stable coiled state. The arcs’ geometries influence the existence of the second strain energy well and the associated stable coiled radius, responsible for the boom’s packaging efficiency. Besides packaging efficiency, factors like bending stiffness are also contingent on the geometries of the arcs, leading to significant trade-offs among these metrics. In this work, we propose a multi-objective optimization (MOO) to find optimal compromises that balance these conflicting requirements of a CTM. Particularly, a coupling analytical models and evolutionary algorithms (EA) technique is presented, utilizing and bench-marking various state-of-the-art EAs. The MOO approach gives as output the Pareto front, a set of the non-dominated design points, which showcases different trade-offs solutions tailorable for specific space-applications. Different design points are presented and discussed based on higher-level considerations.

Comparing Earthquake Cycles on Normal and Reverse Faults Based on Simulations With a Dynamic Elasto‐Plastic Model

AbstractShear stress levels on reverse faults are anticipated to be several times higher than on normal faults with the same pore pressure ratio. In addition, ruptures on normal faults release gravitational potential energy, whereas earthquakes on reverse faults expend work in uplifting rocks. In this study, I investigate the significance of these differences for earthquake cycles and I question whether the source of energy driving earthquakes is the same on reverse and normal faults. Based on the assumption that normal and reverse faults have the same background frictional properties and pore pressure states, I use numerical simulations with a two‐dimensional dynamic elastic‐plastic model to show that due to stress differences, earthquakes on reverse faults tend to occur less frequently, produce more coseismic slip and stress drop and involve higher slip rates than ruptures on normal faults with equivalent dimensions. The analysis also shows differences in the energy changes associated with earthquake cycles on reverse and normal faults. However, the earthquakes on both fault types result from abrupt release of elastic strain energy, which proceed and essentially drive variations in gravitational potential energy. Thus, ruptures on both normal and reverse faults are consistent with elastic rebound theory.

Research on the strength influence and crack evolution law of layered backfill based on macro and meso mechanical response

This article analyzes the effects of inclined angle (IA), filling times (FTs) and cement tailings ratio (CTR) on the uniaxial compressive strength (UCS) and crack development law of layered cemented backfill (LCB) using various research methods, including indoor experiments, numerical simulation, and computed tomography (CT) scanning. The research shows: (1) In the indoor experiments, it was observed that increasing the IA, increasing the number of FTs, and decreasing the CTR had a significant weakening effect on the UCS of the specimens. The greater the IA, the more pronounced the separation and dislocation of the layered contact surface, resulting in a significant increase in macroscopic cracks at the bottom. As the FTs increases, the center of gravity of the failure of the LCB gradually moves downwards. This causes the damage and failure time to advance, and the peak stress to change from one main crack to multiple main cracks. (2) During the numerical simulation, compressive stress accumulates and increases around the pores in the layered contact surface. Microcrack aggregation occurs on the contact surface, and downward expansion and extension. The peak strain energy decreases as the IA increases with the FTs. The number of shear cracks increased more at 20° to 30° than at 0° to 20°. The strain energy of the 0° specimen is the highest, while that of the 30° specimen is the lowest. (3) The CT scan shows that the LCB is affected by stress conduction hysteresis. When the bottom backfill is in the stage of crack evolution, the top backfill is in the stage of compaction.When the LCB reaches the peak stress, both the bottom and middle layers of the backfill lose load-bearing capacity, and the top layer of the backfill has no cracks. This paper provides reference value and research ideas for the destruction of backfill that contain layered defective structures.

Comparison of Experimental and Numerical Investigation of Mono-Composite and Metal Leaf Spring

The automotive industry is increasingly focused on reducing vehicle weight, leading to the widespread adoption of composite materials with high strength-to-weight ratios in both aviation and automotive sectors. These materials are gradually replacing traditional options like steel. Leaf springs, one of the oldest and most common suspension components, continue to be widely used in vehicles. This study aims to replace conventional multi-leaf steel springs with mono-composite leaf springs while preserving the same load-carrying capacity and stiffness. Composite materials, such as glass fiber and epoxy resin, provide advantages including higher elastic strain energy storage, superior strength-to-weight ratios, and enhanced corrosion resistance compared to steel. Consequently, the weight of leaf springs can be reduced without sacrificing performance. The steel and mono-composite leaf springs were modeled using Catia software, and their performance was evaluated using ANSYS 15.0 software.

Differential growth and shape formation of a flower-shaped structure

Morphogenesis, which is a complex interplay of biological, chemical, and physical processes, facilitates differential growth in various biological systems, particularly in plant organs, such as petals and leaves. Although recent studies have increasingly delved into the mechanical aspects of these biological structures, there remains a lack of a comprehensive quantitative understanding of shape formation induced by differential growth in plant organs. Thus, this study addressed this gap by employing a multifaceted approach encompassing theoretical analyses and comprehensive finite element analysis of the effect of differential growth on the shape of a cylinder into a flower shape. Based on the derivation of the strain energy expressions for the axisymmetric and asymmetric configurations, the shape function of the growing flower-like structures were calculated through mathematical optimization. The findings of this study shed light on the influence of the growth function, geometric characteristics, and material properties. As the wave number increased, the final configuration tended to have smaller waves, whereas a longer cylinder buckled more easily and the thickness had a minimal effect. This study offers insights that can pave the way for innovative geometrical designs, thereby providing inspiration for applications on both micro-and macroscales, such as in the realms of self-assembly of soft robotics and flexible electronics.

Study on the effects of electrode volume fraction and electrode particle radius on dynamic electrochemical-thermal-aging coupling characteristics of lithium cell based on cylindrical cell design method

Electrode volume fraction and electrode particle radius are important electrode parameters for the lithium cell design and deeply influence the electrochemical-physical processes inside lithium cell, which is still insufficiently clear. In order to obtain the effects of electrode parameters on lithium cell, a combine method of the dynamic electrochemical-thermal-aging coupling model and cylindrical cell design was proposed. Simulation was conducted at charge rate 1C. Cell temperature, current density and Solid-Electrolyte-Interface at ambient temperature 25 °C, and total strain energy density and lithium plating at ambient temperature −5 °C were analyzed. As electrode volume fraction or electrode particle radius increases, maximum temperature and maximum temperature difference of lithium cell increase. When electrode volume fraction increases from 0.3 to 0.7, maximum temperature of cell increases by 2.6 °C at least. Current density peak increases with the increase of the positive electrode volume fraction or electrode particle radius. When electrode volume fraction increases from 0.3 to 0.7, current density peak increases by 44 %∼74 %. As electrode volume fraction increases, total strain energy density Ws decreases in the early stage of charge, while increases in the late stage of charge. As the negative (or positive) electrode particle radius increases, Ws of the negative (or positive) electrode increase, while Ws of the positive (or negative) electrode decreases. Solid-Electrolyte-Interface thickness increases with the increase of the electrode volume fraction or electrode particle radius. The effect range of negative electrode volume on lithium plating is 0.5 ∼ 0.7. The lithium metal thickness increase with the increase of the positive electrode volume fraction. As the negative or positive electrode particle radius increases, the lithium metal thickness increase or decrease, respectively.

Evolution of Atomic-Level Interfacial Fracture Mechanics in Magnesium-Zinc Compounds Used for Bioresorbable Vascular Stents.

Bioresorbable magnesium-metal vascular stents are gaining popularity due to their biodegradable nature and good biological and mechanical properties. They are also suitable candidate materials for biodegradable stents. Due to the rapid degradation rate of Mg metal vascular scaffolds, a Mg/Zn bilayer composite was formed by a number of means, such as magnetron sputtering and physical vapor deposition, thus delaying the degradation time of the Mg metal vascular scaffolds while providing good radial support for the stenotic vessels. However, the interlaminar compounds at the metal interface have an essential impact on the mechanical properties of the bi-material interface, especially the cracking and delamination of the Mg matrix Zn coating vascular stent in the radially expanded process layer. Intermetallic compounds (IMCs) are commonly found in dual-layer composites, such as Mg/Zn composites and multi-layer structures. They are frequently overlooked in simulations aiming to predict mechanical properties. This paper analyses the interfacial failure processes and evolutionary mechanisms of interfacial fracture mechanics of a Mg/Zn interface with an intermetallic compound layer between coated Zn and Mg matrix metallic vascular stents. The simulation results show that the fracture mode in the Mg/Zn interface with an intermetallic compound involves typical ductile fracture under static tensile conditions. The dislocation line defects mainly occur on the side of the Mg, which induces the Mg/Zn interfacial crack to expand along the interface into the pure Mg. The stress intensity factor and the critical strain energy release rate decrease as the intermetallic compound layer's thickness gradually increases, indicating that the intensity of stress and the force of the crack extending and expanding along the crack tip are weakened. The presence of intermetallic compounds at the interface can significantly strengthen the mechanical properties of the material interface and alleviate the crack propagation between the interfaces.

Phenyl, propyl polysiloxane modified epoxy resin II: The co-continuous phase, concurrently strengthening and toughening mechanism

The applications of epoxy resins are restricted in certain areas due to their brittleness, while improving the epoxy toughness always compromises their strength. We reported a phenyl, propyl polysiloxane modified epoxy resins with excellent tensile strength and toughness before. In this study, the mechanism of strengthening and toughening are studied and elaborated. Compared to cured EP resin (EP), cured P/E resin (P/E20) significantly improved the tensile strength, elongation at break, impact strength, and critical strain energy release rate (GIc) by 45 %, 248 %, 18 %, and 512 %, respectively. Fracture analysis of the P/E20 revealed the appearance of parabolic markings, typical and convincing evidence of ductile fracture, indicating good toughness of the resin. AFM height and Young's modulus plots reveal the complex details of the dimples and the co-continuous phases, which provide the strong evidence to explain the reinforcement and toughening mechanism.

Allylic Epoxides Increase the Strain Energy of Cyclic Olefin Monomers for Ring-Opening Metathesis Polymerization.

Ring-opening metathesis polymerization (ROMP) is an effective method for synthesizing functional polymers, but since the technique typically relies on high ring strain cyclic olefins, the most common monomers are norbornene derivatives. The reliance on one class of monomer limits the obtainable properties of ROMP polymers. In this work, we investigate new bicyclic monomers synthesized via epoxidation of commercial dienes. DFT estimates of these monomers' ring strains suggests a significant increase in strain for cyclic olefins containing allylic epoxides. We found that the eight-membered (3,4-COO) and five-membered (CPO) cyclic olefins were particularly effective for ROMP. CPO was of especially intriguing due to its excellent polymerizability when compared to the limited reactivity of other five-membered rings. Unlike polynorbornenes, the resulting polymers of both monomers displayed glass transition temperatures well below room temperature. Interestingly, poly(3,4-COO) showed both high stereo- and regioregularity while poly(CPO) showed little regularity. Both polymers could be readily modified via post-polymerization ring-opening of the reactive allylic epoxides. With a high epoxide density in poly(CPO), CPO is an exciting new ROMP monomer that is easily synthesized, can be polymerized to high conversion at room temperature, and may be facilely modified to yield a wide range of functional materials.

Allylic Epoxides Increase the Strain Energy of Cyclic Olefin Monomers for Ring‐Opening Metathesis Polymerization

Ring‐opening metathesis polymerization (ROMP) is an effective method for synthesizing functional polymers, but since the technique typically relies on high ring strain cyclic olefins, the most common monomers are norbornene derivatives. The reliance on one class of monomer limits the obtainable properties of ROMP polymers. In this work, we investigate new bicyclic monomers synthesized via epoxidation of commercial dienes. DFT estimates of these monomers’ ring strains suggests a significant increase in strain for cyclic olefins containing allylic epoxides. We found that the eight‐membered (3,4‐COO) and five‐membered (CPO) cyclic olefins were particularly effective for ROMP. CPO was of especially intriguing due to its excellent polymerizability when compared to the limited reactivity of other five‐membered rings. Unlike polynorbornenes, the resulting polymers of both monomers displayed glass transition temperatures well below room temperature. Interestingly, poly(3,4‐COO) showed both high stereo‐ and regioregularity while poly(CPO) showed little regularity. Both polymers could be readily modified via post‐polymerization ring‐opening of the reactive allylic epoxides. With a high epoxide density in poly(CPO), CPO is an exciting new ROMP monomer that is easily synthesized, can be polymerized to high conversion at room temperature, and may be facilely modified to yield a wide range of functional materials.

Investigating Mechanical Characteristics of Rocks Under Freeze–Thaw Cycles Using Grain-Based Model

AbstractBased on the discrete element method (DEM), a water-contained grain-based model (GBM) is developed in this study to evaluate the effects of freeze–thaw cycles (FTCs) on the mechanical characteristics of the rock. A set of freeze–thaw and uniaxial compression tests is carried out to explore the impact of micro damage caused by FTCs on the mechanical prosperities of rock samples. By monitoring the development and distribution of micro-cracks during freeze–thaw test and uniaxial compression test, the damage mechanism of FTCs is revealed from a microscopic perspective, which shows that FTCs deteriorate the strength and brittleness parameters as exponential functions. The parametric analysis is carried out to explore the influence of porosity and mineral components on the mechanical behaviors of rock against freeze–thaw and uniaxial loadings. Based on the parametric analysis results, it is found that UCS, Young’s modulus, and total strain energy at peak stress decrease with the increase of porosity and clay content, which emphasizes the contributions of porosity and mineral components on the mechanical properties of rock samples. It is proved that the water-contained grain-based model developed in this study can capture the damage caused by FTCs on the mechanical performance of rock from a microscopic perspective, which provides novel perspectives on the phenomenon of rock degradation in response to fluctuations in temperature.

Fault slip and seismic source response characteristics under induced stress wave

As coal mining depth and structural complexity increase, the failure severity of mining-induced fault activation leading to rock bursts escalates. Fault fracture zones, consisting of various secondary structures, are essential for understanding tectonic evolution and seismic wave propagation. The interaction between mining-induced stress waves and in-situ stress complicates the dynamics and activation markers of fault fracture zones. This paper aims to clarify the patterns of stick–slip instability and stress evolution in these zones under coal mining-induced stress waves. Using theoretical models and continuous-discrete coupling simulations, the study explores the dynamic response of fault fracture zones in the meta-instability stage, the micro-scale fracture force chain structure, and the distribution and synergistic instability of fault plane seismic sources. The research shows that fault fracture zones changes stress wave propagation path and energy redistribution due to its heterogeneity leads to multiple times decomposition of wave field. Minor delamination between the hanging wall and footwall can trigger unstable slip. Tensional seismic sources with extensive failure drive fault slip. Dynamic stress waves disrupt force chains near seismic sources, increasing hazard levels. Static in-situ stress affects shear seismic sources by influencing porosity and crack angles. Seismic sources along the fault strike transition from divergent to concentrated, trending horizontally. In the meta-instability stage, the initial fracture area locks, with strong structures causing cohesive fractures in the middle of the fault zone, releasing strain energy and forming a sudden increase in slip intensity. These findings provide crucial insights into fault fracture-development-activation markers, fault region stress deformation evolution mechanisms, and risk control of fault-induced rock bursts.

Nonlinear dynamics of wing-like structures using a momentum subspace-based Koiter-Newton reduction

Cantilevers find a wide range of applications in the design of scientific equipment and large-scale engineering structures such as aircraft wings. Analysis techniques based on linearization approximations are unable to capture the large amplitude oscillation behaviour of such structures and thus, necessitates development of dedicated nonlinear methods. In this work, the recent developments in the Koiter-Newton model reduction method are utilized to obtain nonlinear reduced order models (ROMs) from full finite element structural models in order to simulate large amplitude dynamics of cantilevers. The method describes a nonlinear system of governing equations comprising quadratic and cubic terms which are obtained as higher order derivatives of the in-plane strain energy. To ensure that the large rotations in cantilevers and the resultant foreshortening effect is also accounted for, a ROM updating algorithm is adopted where the ROM parameters are varied with the structural deflections. Linear eigenmodes of the structure are utilized to form the reduction subspace. To validate the methodology, the ROM solution is compared against experimental results and a convergence study is conducted to identify the number of modes needed to replicate the nonlinear response. Finally, a composite wingbox structure is considered for which time domain simulations are conducted and frequency response curves, obtained through a frequency sweep, are presented.

Fatigue life predictions for welded boiler water walls

Boiler water walls experience in-phase thermo-mechanical loading during start-ups and shut-downs, leading to low cycle fatigue (LCF) failure. This study aims at establishing an FEA-based failure prediction method for estimating the fatigue performance and service life of the welded water walls. The developed model is validated for predicting failure in the defect-free uniaxial fatigue specimens. Stress-mechanical strain hysteresis loops and accumulated inelastic strain energy density per cycle parameters are extracted from fatigue tests at 0.4%, 0.6%, and 0.7% strains. A combination of cyclic plasticity and continuous damage mechanics (CDM) theory is utilized to predict fatigue crack initiation sites and estimate the specimen fatigue life. Accumulated damage has been calculated for the life cycle of each specimen. FEA model predicted failure and service life agrees well with the experimental results. The established failure analysis parameters are then transferred from the specimen level to the water wall component level, thereby estimating the service life of defect-free water walls at 750 cycles.

Molecular Chain Rearrangement-Induced In Situ Formation of Nanofibers for Improving the Strength and Toughness of Hydrogels.

Although poly(vinyl alcohol) (PVA) hydrogel has high elasticity and is suitable for cartilage tissue engineering, it is difficult to have both high strength and toughness. In this study, a simple and universal strategy is proposed to prepare strong and tough PVA hydrogels by in situ forming nanofibers on the original network structure induced by a molecular chain rearrangement. Quenching-tempering alteratively in ethanol and water several times is carried out to strengthen PVA hydrogels (PVA-Etn hydrogels) due to the advantages of noncovalent bonds in adjustability and reversibility. The results show that, after three quenching-tempering cycles, PVA-Et3 hydrogel with water content up to 79 wt % shows comprehensive improved mechanical properties. The compression modulus, tensile modulus, fracture strength, tensile strain, and tear energy of the PVA-Et3 hydrogel are 270, 250, 260, 130, and 180% of the initial PVA hydrogel, respectively. The improved mechanical properties of the PVA-Et3 hydrogel are attributed to the strong cross-linked PVA chains and hydrogen bond-reinforced nanofibers. This study not only provides a simple and efficient solution for the preparation of strong and tough polymer scaffolds in tissue engineering but also provides new insights for understanding the mechanism of improving the mechanical properties of polymer hydrogels by adjusting the molecular structure.