Strain Energy Distribution 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.

Experimental and theoretical analysis of strain hardening behavior of friction-stir-welded Al-4.2Zn-3.1Mg aluminium alloy

The strain hardening behavior of friction stir welded AA7039 (Al-4.2Zn-3.1 Mg) alloy was explored in terms of dislocation density, crystallite size, hardening capacity, hardening exponent, and strain hardening rate. Strain hardening behavior was analyzed for base metal and friction stir welded specimens. Four different models were used to calculate the dislocation density viz., Scherrer model, uniform strain model (USM), uniform stress distribution model (USDM), and uniform strain energy distribution model (USDEM). Maximum dislocation density was obtained in base metal for all models (maximum for USM, 3.9 × 10 15 m − 2 ) with a minimum crystallite size of 15.81 nm. The low dislocation density in FSW samples is due to the higher heat input in the FSW process. Strain hardening stages were shown by Kocks–Mecking type plots. Lower strain hardening capacity was obtained for BM, i.e. 0.427 as compared to FSW samples, due to the higher dislocation density of BM. It was determined that there is an inverse relationship between the strain hardening capacity and the strain hardening exponent. Strain hardening rate was higher for BM than FSW specimens, and similar results were obtained from mathematical relations that indicate the adequacy of the results. The ultimate tensile strength was 2.5% higher than the BM at a rotational speed of 1325 rpm, 35 mm/min of welding speed and 1.65° tilt angle. The maximum strength friction stir-welded specimen showed a more ductile fracture surface than the BM because the grain boundary phase disappeared or broke up in the thermomechanical affected zone.

Prediction method for re-damage behavior of the repaired CFRP bolted joint

Composite materials are widely used in various aircraft due to their high specific strength, stiffness, corrosion resistance, and robust design flexibility. However, when subjected to complex loading conditions, composite structures are susceptible to damage, necessitating prompt repair upon aircraft return. Analyzing the re-damage process of repaired structures is crucial for assessing aircraft structural reliability, lifespan, and determining whether a repeat flight is warranted. In this study, a prediction method was proposed for re-damage behavior through meso-modeling and energy analysis of the repaired composite bolted joint. First, this article established a meso-mechanical model for composite laminates, analyzed force transfer characteristics at the fiber − matrix interface, and derived equations for stress field. Additionally, a strain energy distribution model was developed for composite bolted repaired joint near fibers and repaired area, proposing a damage prediction method based on the strain energy criterion. This method could anticipate the location, type, sequence, and magnitude of damage. Finally, simulation calculations yielded mechanical characteristics of the repaired area under typical load conditions, while loading tests verified the feasibility of the prediction method. This study offered an effective means of predicting performance degradation in composite structures and provided a vital direction for optimal spacecraft structure repairing methods and parameters.

Computational comparison study of virtual compression and shear test for estimation of apparent elastic moduli under various boundary conditions.

Virtual compression tests based on finite element analysis are representative noninvasive methods to evaluate bone strength. However, owing to the characteristic porous structure of bones, the material obtained from micro-computed tomography images in the finite-element model is not uniformly distributed. These characteristics cause differences in the apparent elastic moduli depending on the boundary conditions and affect the accuracy of bone-strength evaluation. Therefore, this study aimed to evaluate and compare the apparent elastic moduli under various, virtual-compression and shear-test boundary conditions. Four, nonuniform models were constructed with increasing model complexity. For representative boundary conditions, two, different, testing directions, and constrained surfaces were applied. As a result, the apparent elastic moduli of the nonuniform model varied up to 55.2% based on where the constrained surface was located in the single-end-cemented condition. Additionally, when connectivity in the test direction was lost, the accuracy of the apparent elastic moduli was low. A graphical comparison showed that the equivalent-stress distribution was more advantageous for analyzing load transferability and physical behavior than the strain-energy distribution. These results clearly show that the prediction accuracy of the apparent elastic moduli can be guaranteed if the boundary condition on the constraint and loading surfaces of the nonuniform model are applied symmetrically and the connectivity of the elements in the testing direction is well maintained. This study will aid in precision improvement of bone-strength-indicator determination for osteoporosis prevention.

A numerical study to discriminate between the hydrostatic and deviatoric strain energies impact on cells activity during bone remodelling

Bone remodelling is regulated by specific cellular activities. In particular, the osteocytes are able to transform a mechanical signal into a chemical one and transmit it to the osteoclasts and osteoblasts cells. Additionally, osteocytes are more sensitive to fluid shear than pressure stress. Thus, the mechanical environment, especially the type of external loads applied to the bone structure, may highly influence its evolution over time. In this paper we propose a strain energy based model in which we distinguish between the deviatoric and hydrostatic energy contributions. We study here simple loads and geometries for which the strain energy distribution is homogeneous. From these two cases, we are able to show that when considering more complex structures such as the bone microstructure where the energy distribution is heterogeneous, it is necessary to discriminate between the deviatoric and hydrostatic energy parts.

Novel Cardiovascular Stent Based on Hibiscus-Aestivation-Inspired Auxetic Unit Cell

Conventional stents have some limitations, such as dogboning and foreshortening, that can lead to issues like in-stent restenosis and thrombosis. Negative Poisson's ratio stents, called auxetic stents, are known as a solution to overcome these challenges due to their unique deformation mechanism. Auxetic stents are scale-independent, and their behavior depends solely on their geometry. In this study, a novel auxetic unit cell inspired by aestivation mechanism of the Hibiscus flower is designed, developed, and implemented in plane, and a tube to achieve a novel NPR cardiovascular stent. The stent structure is fabricated using two methods, including a novel 7-axis laser cut method capable of producing stents the same size as human blood vessels from an SS 316 L tube, and fused deposition modelling 3D printing at a scale 20 times larger than the metallic sample using PLA filaments. Novel laser cut effectively overcame some challenges in laser cutting stents, including HAZ and thermal shocks. SEM images are taken from the laser cut sample, and the manufacturing method's accuracy and surface quality are investigated. Fabricated metallic and polymeric stent samples proposed negative Poisson's ratio equal to 0.89 with an average of 4.38 and 14.8% errors, respectively, compared with finite element analysis. Finally, the structure's stress, strain energy distribution pattern, and unit cell distribution have been examined. Furthermore, the stent thickness parameter, drug release patch application, and stent implementation process are also investigated using FEM method. Proposed geometry in stent application showed solutions to conventional positive Poisson's ratio stent challenges.

Design of railway transition zones: A novel energy-based criterion

Railway transition zones (RTZs) experience higher rates of degradation compared to open tracks, which leads to increased maintenance costs and reduced availability. Despite existing literature on railway track assessment and maintenance, effective design solutions for RTZs are still limited. Therefore, a robust design criterion is required to develop effective solutions. This paper presents a two-step approach for the formulation of a preliminary-design criterion to delay the onset of processes leading to uneven track geometry in RTZs. Firstly, a systematic analysis of each track component in a RTZ is performed by examining spatial and temporal variations in kinematic responses, stresses and energies using a finite element model of an embankment-bridge transition. Secondly, the study proposes an energy-based criterion to be assessed using a model with linear elastic material behavior and states that an amplification in the total train energy in the proximity of the transition interface is an indicator of increased (and thus non-uniform) degradation in RTZs compared to the open tracks. The correlation between the total strain energy (assessed in the model with linear material behaviour) and the permanent irreversible deformations is demonstrated using a model with non-linear elastoplastic material behavior of the ballast layer. In the end, it is claimed that minimising the magnitude of total strain energy will lead to reduced degradation and a uniform distribution of total strain energy in each trackbed layer along the longitudinal direction of the track will ensure uniformity in the track geometry.

Mechanical Properties of Rock Specimens Containing Pre-Existing Cracks with Different Dip Angles Based on Energy Theory and Cohesive Element Method

To investigate the influence of the crack dip angle on the strength of rock specimens, uniaxial compression tests were conducted on granite specimens containing pre-existing cracks. The strain energy evolution during the loading process was analyzed, and the loading-induced cracking process was simulated using the cohesive element method. Both the experimental and numerical results indicate that cracks significantly impact the plastic-yielding stage of the stress–strain curve more than the initial and elastic deformation stages. When the crack dip angle is less than 45°, the stress concentration near the crack is significant, which is an important factor affecting the strength and elastic strain energy distribution of rock specimens. When the crack dip angle is greater than 45°, the degree of stress concentration decreases, and the uniformity of the elastic strain energy distribution and the possibility of crack bifurcation increase. Combining the energy theory with the cohesive element method helps comprehensively understand the initiation, propagation, and coalescence of microcracks near pre-existing crack tips. These research results can provide a reference for geotechnical engineering design and structural stability assessment.

Development of a non-uniform cellular automata framework for sizing, topology and layout optimization of truss structures

This article presents a bi-level non-uniform cellular automata (CA) algorithm for the solution of sizing, topology and layout optimization of truss structures. The non-uniform CA was successfully used in a previous study to solve the weight optimization problem of truss structures for topology and sizing (El Bouzouiki, Sedaghati, and Stiharu 2021. Computers & Structures 242: 106394). In this article, an extended version of the non-uniform CA algorithm is proposed, based on the fully stressed design approach and the distribution of strain energy within the structure, to find the optimal position of the cell’s (joint’s) coordinates. The proposed non-uniform CA algorithm can solve the minimum weight optimization problem of truss structures subjected to both stress and displacement constraints. Several benchmark problems are presented to demonstrate the efficiency and accuracy of the proposed methodology.

Quasi-Static Model Test of Pile-Supported Wharf under Cyclic Lateral Loading

The pile-supported wharf (PSW) is one of the most common structures in harbor engineering. To investigate the dynamic response characteristics of the PSW, a quasi-static model test of a PSW–ground system under cyclic lateral loading is conducted. The deformation and damage processes of piles and the sand stratum are observed and obtained. The hysteresis characteristics of the PSW–ground system and the response characteristics of piles are systematically explored. The strain energy of the pile group on the sloping ground is calculated and analyzed. The results show that there are two peak bending moments on the pile, and the maximum one occurs at the pile top. The pile embedded depth and the loading direction strongly affect the strain energy distribution of the pile group. Under downslope direction loading, the center piles have the largest strain energy percentage. The strain energy extends from the center piles to the outside piles with the increase in loading displacement amplitude. The test results indicate that the landside pile and center pile should be strengthened during seismic design.

Mechanics of woven roving/ mat laminate failure in a quasi-static tensile test

Based on tensile tests of non-standard specimens with large dimensions, an attempt was made to explain the mechanics of failure of woven roving/mat laminates with different numbers of layers. The need to use non-standard specimens in tests resulted from the impossibility of interpreting the processes taking place in tensile specimens in specimens with standard dimensions, the results of which are published in the scientific literature. In the tensile tests, four loading phases were observed, in which in the last two the structure of matrix was failed by micro- and macro-cracks, and finally by delamination through the laminates. To describe the fracture mechanics of the discussed laminates, the principle of energy equivalence was used in the transformation of elastic strain energy into binding energy. Although the processes of laminate destruction occur in the matrix, depending on the number of layers, it was found that two different processes of destruction of the internal structure with three variants of elastic strain energy distribution lead to the final delamination of the laminates. The use of energy to describe the failure of laminates in the third phase of specimen loading leads to the definition of such concepts as the dominance of failure stresses and the dominance of failure strains in the process of cracking the laminate structure. Experimental studies indicate a gradient distribution of binding energy towards the center of unloaded specimens, assumed on the basis of a literature review.

Experimental validation study on snap through and coiling up of deployable composite shells

AbstractBistable reeled composite shells (BRCS) have been widely used in deployable space structures due to advanced properties of light weight and large volume reduction. A finite element simulation and experimental validation to study the transition of BRCS between their two stable states are performed. In this article, multiscale representative volume element (RVE) modeling is used to compute the equivalent mechanical properties of carbon/epoxy plain woven fabrics that were utilized to construct the deployable composite laminates, followed by experimental verification. The deformation characteristics and strain energy distribution of the deployable composite shell (DCS) during snap through and coiling up are investigated using finite element analysis (FEA) and verified by strain‐gauge and digital image correlation (DIC) tests. The results show that the strain energy distribution in the snap through and coiling up of the carbon/epoxy plain woven BRCS with laminate stacking sequence of [+45/−45] is approximately symmetric. Additionally, an offset phenomena is observed during the coiling up of the BRCS in the finite element modeling. A parametric analysis is complemented to investigate effects of fiber angles on the deformation characteristics and strain energy distribution of the shell structures during snap through and coiling up.Highlights Shell deformation during snap through and coiling up was investigated. DIC test was performed to capture the shell deformation. Strain energy distribution of the deployable composite shell was discussed. Offset phenomena are observed during the coiling up.

The mechanics of embedded fiber networks

Fiber networks underlie the mechanical behavior of a wide range of natural and engineered materials. Interestingly, these networks are often embedded within amorphous matrices rather than appearing in isolation. However, despite their frequent occurrence as embedded rather than isolated networks, few prior studies have focused on investigating the role of embedding on the emergent mechanical behavior of these systems. To address this, we adopt a mortar-type embedding approach within the finite element framework and perform simulations to systematically fill this knowledge gap. Within this study, we focus on soft tissues as an exemplary class of materials where embedded fiber networks are essential to mechanical function. Specifically, we investigate the role of embedding on the strain energy distribution within the networks across the bending, stretching, torsional, and shear fiber-level loading modes. Therein, we specifically focus on semi-flexible fiber networks. In addition to revealing the role of embedding on the networks themselves, we also investigate how the networks affect the mechanics of the matrix material. Together, we find that embedding fundamentally alters the mechanics of semi-flexible fiber networks and the surrounding matrices. Most importantly, we find that embedding semi-flexible fiber networks leads to strain-stiffening and negative Poynting effect of the resulting composite material. Furthermore, semi-flexible fiber networks induce stress heterogeneity in their host material and increase its resistance to compression. Overall, our work improves our fundamental understanding of an important class of materials. By making our implementation openly available, we also hope to help others learn more about embedded semi-flexible fiber networks in the context of materials other than soft tissues.

Attenuation analysis of low-frequency surface waves in the ultra-low-frequency bandgap of embedded seismic metamaterials

Seismic metamaterials (SMs) have potential applications in the protection of buildings from earthquake hazards, while research on the attenuation of low-frequency seismic waves is still limited. In this paper, an embedded seismic metamaterial with an ultra-low-frequency bandgap is proposed as a research object to analyze the attenuation of low-frequency seismic surface waves. The band structure of the proposed SM has the absence of surface wave solutions and has an ultra-low-frequency complete bandgap with a range of 0–16.3 Hz. Subsequently, the vibration modes and strain energy distribution of the SMs lattice, especially at low frequencies, are analyzed. The results show that there are vibration modes with energy concentrated in the SM and near the surface in the range of 0–1.3 Hz. According to the amplitude reduction analysis, the surface wave has no attenuation in the range of 0–1.3 Hz, and the attenuation zone is 1.3–20 Hz. Two types of actual seismic records are used as input signals to validate the attenuation zone. This indicates that some of the low-frequency surface waves in the ultra-low frequency-bandgap could not be attenuated. It is necessary to analyze the low-frequency band with large strain energy in conjunction with vibration modes and amplitude reduction when designing SMs with the ultra-low-frequency bandgap. Moreover, the effects of parameters and gradient arrangement on proposed SM attenuated low-frequency surface waves are analyzed, where the soil Young’s modulus is the key factor affecting the SM attenuated low-frequency surface waves.

Fiber morphology design of cellulose composites through multiscale simulation

The effects of fiber orientation control on cellulose composites, which are expected to improve mechanical properties, were systematically investigated, and a comprehensive fiber morphology design procedure was developed. A multiscale finite element simulation based on homogenization theory was employed to investigate the nonlinear properties of cellulose composites and quantitatively assess the effect of fibers on mechanical properties, with a particular emphasis on the distribution of strain energy. As the main factors in fiber morphology, we focused on two particular aspects: fiber orientation, which has a large influence, and aspect ratio, which varies with defibration, in addition to frequently-controlled fiber content ratio. Numerical simulation revealed that the elastic modulus and maximum tensile stress increase linearly with increasing the proposed parameter, fiber contribution proportion (CPf). Fiber orientation and content ratio were identified as the primary factors influencing the change rate in properties with respect to the CPf . Further, the fiber aspect ratio was found to be the secondary factor that influenced the properties according to the change rate determined by the primary parameters. Furthermore, the design procedure, constructed based on the CPf, was evaluated for three cases with different fiber morphology control strategies. The results demonstrated that the proposed fiber morphology design, across all cases evaluated, achieved the target values for both the elastic modulus and maximum tensile stress with errors ranging from 2.0 to 5.4%.

Silicon surface characteristics in vibration-assisted machining process via molecular dynamics

This study investigates the impacts of vibration amplitude, vibration frequency, and sliding velocity on the characteristics of the machined silicon substrate. The results show that increasing the vibration amplitude increases atomic strain, stress, and kinetic energy distributions while decreasing subsurface damage thickness, potential energy distribution, and especially surface roughness. The surface roughness values are 7.5 Å, 6.4 Å, 6.9 Å, and 6.0 Å corresponding to vibration amplitude of 15 Å, 20 Å, 25 Å, and 30 Å. Moreover, increasing the vibration frequency results in increased atomic strain, stress, and kinetic energy levels. The surface roughness values are 7.1 Å, 7.1 Å, 6.5 Å, 6.4 Å, and 6.0 Å corresponding to the vibration frequencies of 16.7 GHz, 33.3 GHz, 50 GHz, 66.7 GHz, 100 GHz, and 200 GHz. Furthermore, increasing the sliding velocity lowers the surface quality of the silicon sample. The surface roughness values of the silicon substrate are 6.5 Å, 6.7 Å, 6.9 Å, 6.9 Å, and 7.1 Å corresponding to 50 m/s, 100 m/s, 150 m/s, 200 m/s, and 250 m/s. Improving the vibration amplitude and frequency while decreasing the sliding velocity improves surface quality by increasing the collision between the diamond tips and the substrate. Remarkably, the vibration movement of the diamond tips could leave wave marks on the substrate surface. In general, the optimal parameters that generate a good surface are 30 Å, 200 GHz, and 50 m/s.

An investigation into the effect of cross-ply on energy storage and vibration characteristics of carbon fiber lattice sandwich structure bionic prosthetic foot

Abstract Made a pioneering attempt to use the lattice sandwich structure in prosthetic foot design and pioneered the study for the lay-up design of the prosthetic foot. An innovative carbon fiber bionic prosthetic foot was designed using a sandwich structure. The effect of cross-ply on the prosthetic foot’s energy storage properties and vibration characteristics was investigated using the lattice sandwich structure prosthetic foot. The bionic prosthetic foot’s finite element model was constructed under normal working conditions according to international standards. The results indicate that the storage of strain energy increases with an increase in cross-ply under heel-strict working conditions. Under the toe-off condition, the strain energy distribution increases with the increase in cross-ply. The cross-ply number influences the mode of displacement of the bionic foot. The natural frequencies of the bionic foot increase with the increase in the cross-ply.

On the material dependency of peri-implant morphology and stability in healing bone

The microstructural architecture of remodeled bone in the peri-implant region of screw implants plays a vital role in the distribution of strain energy and implant stability. We present a study in which screw implants made from titanium, polyetheretherketone and biodegradable magnesium-gadolinium alloys were implanted into rat tibia and subjected to a push-out test four, eight and twelve weeks after implantation. Screws were 4 mm in length and with an M2 thread. The loading experiment was accompanied by simultaneous three-dimensional imaging using synchrotron-radiation microcomputed tomography at 5 μm resolution. Bone deformation and strains were tracked by applying optical flow-based digital volume correlation to the recorded image sequences. Implant stabilities measured for screws of biodegradable alloys were comparable to pins whereas non-degradable biomaterials experienced additional mechanical stabilization. Peri-implant bone morphology and strain transfer from the loaded implant site depended heavily on the biomaterial utilized. Titanium implants stimulated rapid callus formation displaying a consistent monomodal strain profile whereas the bone volume fraction in the vicinity of magnesium-gadolinium alloys exhibited a minimum close to the interface of the implant and less ordered strain transfer. Correlations in our data suggest that implant stability benefits from disparate bone morphological properties depending on the biomaterial utilized. This leaves the choice of biomaterial as situational depending on local tissue properties.

Toward New Value-Added Products Made from Anaerobic Digestate: Part 2—Effect of Loading Level on the Densification of Solid Digestate

A comprehensive understanding of the mechanisms associated with the pelletization of an anaerobic digestate is necessary to optimize the pellet production process and achieve better and more sustainable management of the digestate. This work evaluated the digestate behavior during cyclic loading and unloading in a closed matrix. The results presented here are a continuation of those observed in previous work that evaluated the effect of moisture content on the behavior of the digestate under cyclic loading/unloading conditions in a closed matrix. The effect of moisture content on the distribution of permanent and elastic strain energy demonstrated in the previous study was verified in the present work under different loading conditions. A Zwick universal machine was used for the experiments. The samples were loaded with amplitudes of 8, 11, 14, 17, and 20 kN for 10 cycles. Two distinct moisture levels of the digestate—10% and 22%—were analyzed. The results of the present study confirmed that the elastic energy dissipated was independent of the moisture content of the digestate and remained relatively constant for a wide range of the applied loads. Higher values of elastic strain energy were observed for the digestate with higher moisture content only when higher loads were applied. In the range of the studied loads, characteristic differences were noted in loading/unloading curves regardless of the load magnitude. The increase in the applied load led to an increase in pellet strength, but only when the moisture content of the digestate was 10%. The results of the pellet strength reflect well the results of irreversible energy and the conclusions about the area enclosed between loading and unloading curves.

Experimental Study on Mechanical and Damage Evolution Characteristics of Coal during True Triaxial Cyclic Loading and Unloading

Research on the mechanical properties and damage evolution of coal during true triaxial cyclic loading and unloading is of great significance for maintaining the long-term safety and stability of underground engineering structures in coal mines. In this paper, firstly, the deformation, strength and fracturing characteristics of coal during true triaxial loading and true triaxial cyclic loading and unloading were analyzed. Then, the residual strain characteristics, energy distribution and evolution of coal were systematically studied. Additionally, the damage evolution laws of coal during cyclic loading and unloading were quantitatively analyzed from the perspectives of residual strain and energy dissipation, respectively. The damage evolution law based on residual strain showed that when the intermediate principal stress was high, the damage to coal was directional. With the increase in cyclic load, the coal damage variables in the directions of σ1 and σ3 increased exponentially, while that in the direction of σ2 increased quadratically. The damage evolution law based on energy dissipation showed that the coal damage variable increased exponentially with the increase in cyclic load. With the increase in σ2, the increasing speed of coal damage variable decreased first and then increased. The damage variables established based on residual strain and energy dissipation can both reveal the damage deterioration mechanism of coal during true triaxial cyclic loading and unloading, which is of great theoretical and engineering significance for scientifically evaluating the stability of underground coal and rock engineering and preventing the occurrence of major geological disasters.