Strain Energy Research Articles

Molecular dynamics study on nanodust removal strategies from nanotrench structures

The process of removing nanodust adhering to nanostructured surfaces is important for improving yield and sustainability in manufacturing fields that utilize the structural characteristics of patterns. In this study, we computationally proposed a method to remove nanodust from a trench-shaped Si substrate using an atomic force microscopy tip. A molecular system is thus constructed in which a Si substrate with a trench structure, a cylindrical C tip, and a spherical Cu nanoparticle coexist. By moving the C tip in a specific direction and pushing it into direct contact with the Cu nanoparticle, the interaction force between the Cu and the sidewall of the Si substrate can be substantially reduced. In particular, moving the C tip in a direction parallel to the pattern can effectively push nanodust away while minimizing damage to the Si substrate. The damage experienced by the substrate during the process was comprehensively evaluated using the von Mises stress, adhesion energy, contact area, and strain energy density developed by the axial stress components. The suitability of this method was systematically evaluated based on the diameter of the Cu nanoparticle and its position relative to the C tip. For each case, the maximum strain energy experienced at the edge of the trench structure was quantified, which suggests appropriate nanoparticle removal process conditions from a structural perspective. The strategy can be potentially used as a repair method for semiconductor production components, such as pellicles and hard masks.

Hardness and microstructural evolution of CoCrFeNi high-entropy alloys during severe plastic deformation

In this study, the evolution of hardness and microstructure in a CoCrFeNi high-entropy alloy processed by high-pressure torsion was investigated. An initial increase in hardness was attributed to the rapid increase in low-angle grain boundaries (LAGBs), accompanied by a high density of dislocations. With continuous straining, some LAGBs evolved into high-angle grain boundaries and completed the grain boundary strengthening. A remarkable increase in hardness was achieved in the final stage of hardness enhancement, primarily due to the formation of numerous twins within nanograins, which were mainly formed by the emission of Shockley partial dislocations emerging from grain boundaries. Furthermore, a twin trailing the stacking fault was found in the nanograin, and a critical stress for twin nucleation was estimated to be about 2.16 GPa. Defects with low-energy configurations are closely correlated with the thermal stability of nanocrystalline CoCrFeNi alloys. The defects within nanograins yielded an average strain of about 1.1 % and the corresponding strain energy was identified to about 17 J g−1.

Induced Seismicity Controlled by Injected Hydraulic Energy: The Case Study of the EGS Soultz‐Sous‐Forêts Site

AbstractHow induced seismicity in deep geothermal project (enhanced geothermal systems, EGS) is controlled by fluid injection is of central importance for monitoring the related seismic risk. Here we analyze the relationship between the radiated seismic energy and the hydraulic energy related to the fluid injection during several hydraulic stimulations and circulation tests at Soultz‐sous‐Forêts geothermal site. Based on a harmonized database, we show that the ratio between these energies is at first order constant during stimulations and of the same magnitude independently of the stimulation protocol and injection depth. Re‐stimulations are characterized by a sharp evolution of this ratio during injection which ultimately converges to the characteristic value of the reservoir. This supports that the seismicity is caused by the relaxation of the pre‐existing strain energy in the stimulated volume, rather than by the deformation generated from fluid injection. The ratio appears as an intrinsic large‐scale property of the reservoir that can be assessed at the very beginning of the first stimulation. Based on this property, we suggest a way to predict the largest magnitude of the induced seismic events knowing the maximum targeted hydraulic energy of the injection.

End-to-End Bent Perylene Bisimide Cyclophanes by Double Sulfur Extrusion.

Bending inherently planar π-cores consisting of only six-membered rings has traditionally been challenging because a powerful transformation is required to compensate for the significant strain energy associated with bending. Herein, we demonstrate that sulfur extrusion can achieve substantial molecular bending of a perylene structure to form a substructure of a Vögtle belt, a proposed yet hitherto elusive carbon nanotube fragment. Bent perylene bisimide (PBI) derivatives were synthesized through a double-sulfur-extrusion reaction from the corresponding sulfur-containing V-shaped precursors with an internal alkyl tether. The effect of bending the inherently planar PBI core, which is a recent topic of interest for the design of advanced organic electronic and optoelectronic materials, was investigated systematically. Increasing the curvature leads to a red shift in the absorption and emission spectra, while the fluorescence quantum yields remain high. This stands in contrast with the nonemissive features of previously reported nonplanar PBI derivatives based on conjugative tethers. Detailed photophysical measurements indicated that the increasing curvature with shorter alkyl tethers (i) slightly facilitates intersystem crossing and (ii) significantly suppresses the internal conversion in the excited state of the present bent PBI derivatives. The latter characteristics originate from the restricted dynamic motion associated with the charge-transfer (CT) character between the core chromophores and the N-aryl units.

Tensile behavior of square-twist origami inspired mechanical metamaterials with soft joints and chirality applications

The performance and behavior of origami-inspired mechanical metamaterials are closely related to their structural design and the joints sub equivalent to the crease, in addition to material selection. Current research on square-twist origami focused on the unidirectional formation between its stable states. However, the complete process of squeezing-folding and stretching-unfolding as well as the mechanical behavior under tensile loading have not been thoroughly studied. In this study, square-twist origami mechanical metamaterials (STOMMs) with soft joints are proposed and investigated. The complete process of typical STOMMs from a flat state to folded stable state by extrusion folding and then returning to a flat state by stretch unfolding is explored using the finite element method. The strain energy and deformation characteristics of STOMMs are revealed at eight special stages during the folding, stable state, and unfolding processes. Additionally, the influence of geometric parameters on strain energy, deformation, and tensile behavior is also investigated. Finally, inspired by origami chirality, combinatorial mechanical metamaterials with self-locking/non-self-locking behavior are proposed and validated for their tensile and self-locking behavior. The studies could provide new content for origami-inspired soft joint mechanical metamaterials in terms of self-locking and load-bearing.

Pseudo-static topology optimization using the evolutionary-type method for reinforced concrete shear walls

For improved ductility in seismic-design reinforced concrete shear walls, a methodology referred to as pseudo-static topology optimization is incorporated to guide the design process. This approach involves a stepwise elimination of elements from the initial structural configuration, under specified conditions such as reciprocating loads, displacement constraints and volume limitations. The primary objective of this optimization is to maximize the structural capacity for energy dissipation. This is achieved by creating a sensitivity analysis based on variations in cumulative plastic strain energy resulting from element deletions. The final optimized topologies exhibit bar structures with exceptional capacity for energy dissipation. These optimized configurations evolve with changes in height–width ratios and axial compression ratios, shifting from structures with uniform energy dissipation to those with a two-level distribution. Furthermore, the orientation of the main bars changes from folded bars on both sides to inclined straight bars, depending on the specific conditions.

Decoupling mechanical and chemical effects on energetics of coherent nanoprecipitates with interfacial segregation

Interfacial energetics for coherent interfaces are typically calculated using two key concepts: interfacial energy and coherency strain energy. Although these calculations are well-established in pristine systems, their direct application to doped systems often leads to inaccuracies. This is primarily because foreign solute atoms not only modify interfacial energetics but also introduce additional mechanical and chemical effects within the bulk phases. To address this, our study employs the PSTRESS tag in VASP to simulate equivalent lattice stresses induced by solute atoms without physically incorporating them. This novel approach allows us to isolate the doping energy caused by the solute atoms’ mechanical and chemical effects, thereby enhancing our understanding of the impacts of dopants solely on interfacial energetics. Furthermore, we extend the calculations of interfacial energy and coherency strain energy to doped interfaces, providing a precise and effective evaluation method for both bulk and interfacial energetics in doped systems.

Optimizing misfit dislocation glide kinetics for enhanced threading dislocation density reduction in Si1−xGex/Si(001) layers through dynamic growth rate control

Relaxed Si1−xGex layers on Si(001) serve as virtual substrates for strained Si or Ge layers. However, plastically relaxed layers inevitably contain misfit and threading dislocations, negatively affecting devices. Deposition of a SiGe layer on the backside of the substrate introduces a dislocation reservoir at the wafer edge that can reduce the threading dislocation density (TDD) of Si0.98Ge0.02/Si layers, as these preexisting dislocations start gliding toward the wafer center upon reaching the critical thickness. Here, we show that this low-strain system can be used effectively to study dislocation glide kinetics. In agreement with the literature, dislocation glide is a thermally activated process with an activation energy of 2.12–2.16 eV. Near the critical thickness, relaxation is sluggish and inefficient due to the linear dependence of the glide velocity on excess stress. At lower growth rates, dislocations from the edge reservoir are activated in a lower density due to the increase in the critical thickness through partial strain relaxation by already activated dislocations. Contrary to common models, here, the lowest possible growth rate is not essential for minimizing the TDD. Instead, a careful balance between low and high growth rates is beneficial. Overcoming the initial sluggish and inefficient relaxation phase is critical while also avoiding accumulation of strain energy, and, therefore, the activation of dislocation sources. Only in a later stage of buffer growth, the growth rate should be reduced to a minimum. With this method, the TDD of strain relaxed Si0.84Ge0.16 layers is reduced to 7 × 104 cm−2.

Macro‐meso damage cracking and energy dissipation of rock‐backfill composites: Effect of cyclic disturbance frequency

AbstractThis work aims to reveal the effect of cyclic disturbance frequency, i.e., 0.01, 0.1, 0.5, and 1.0 Hz, on damage cracking and energy dissipation characteristics of rock‐backfill composite structure specimens. Testing results show that fatigue volumetric strain and secant modulus increase with increasing disturbance frequency; low‐frequency disturbance leads to an earlier volume expansion. In addition, the strain energy density increases with increasing disturbance frequency. Most of the energy are dissipated for the specimen under high‐frequency disturbance. Finally, computed tomography scanning reveals the influence of disturbance frequency on failure modes; tensile‐splitting failure and shear failure are likely to occur at the surrounding rock subjected to high‐ and low‐ frequency disturbances. Low‐frequency‐disturbed stress seems easily to stimulate cracks at the rock‐backfill interfaces and the backfill; the backfill can absorb much more energy than high‐frequency circumstances. It is suggested that the role of backfill in energy absorption, contact support, and stress isolation is disturbance frequency dependent.

Twinning-dominated microstructure evolution and deformation mechanism during cold rolling in pure rhenium

The extremely high work hardening rate and the high cracking propensity were the main challenges that limit the successful deformation processing of rhenium. Rolling tests to 82% thickness reduction were conducted at room temperature, and three-stage twining evolution behavior was revealed. At 10% rolling reduction, primary {112¯1} tension twins were activated and dislocation accumulation appeared near the twin boundary. As the rolling reduction increases to 45%, twin-twin interactions prevailed and abundant GNDs accumulated around {112¯1} twin boundaries and {112¯1} twin- {112¯1} twin interactions. More importantly, A new twinning sequence behavior in rhenium, secondary {112¯1} twins within primary {112¯1} twins, was investigated. After twinning saturation, shear bands were formed due to the promoted local plastic deformation by the twin lamellar structure and submicron-scale isolated twins, which brought pronounced strengthening of rhenium. The extremely high work hardening rate of rhenium was found to mainly originate from the twin lamellar structure and twin-twin interactions. High temperature annealing released the stored strain energy, achieving a synergistic effect of high tensile strength and ductility. This study provides a systematic investigation into the deformation structure during the large reduction cold rolling in rhenium and provides insights into unique twinning evolution and shear bands.

Robotica: decoupled elastostatic stiffness modeling of hybrid robots

Abstract A decoupling method is proposed for the elastic stiffness modeling of hybrid robots based on the rigidity principle, screw theory, strain energy, and Castigliano’s second theorem. It enables the decoupling of parallel and serial modules, as well as the individual contributions of each elastic component to the mechanism’s stiffness performance. The method is implemented as follows: (1) formulate limb constraint wrenches and corresponding limb stiffness matrix based on the screw theory and strain energy, (2) formulate the overall stiffness matrix of parallel and serial modules corresponding to end of the hybrid robots based on the rigidity principle, principle of virtual work, the wrench transfer formula, and strain energy methods, and (3) obtain and decouple the overall stiffness matrix and deflection of the robot based on the Castigliano’s second theorem. Finally, A planar hybrid structure and the 4SRRR + 6R hybrid robot are used as illustrative examples to implement the proposed method. The results indicate that selectively enhancing the stiffness performance of the mechanism is the most effective approach.

On the Comparative Analysis among Topological Indices for Rhombus Silicate and Oxide Structures

A topological index (TI) is a numeric digit that signalizes the whole chemical structure of a molecular network. TIs are helpful in predicting the bioactivity of molecular substances in investigations of quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). TIs correlate various chemical and physical attributes of chemical substances such as melting and freezing point, strain energy, stability, temperature, volume, density, and pressure. There are several distance-based descriptors available in the literature, but connection-based TIs are considered more effective than degree-based TIs in measuring the chemical characteristics of molecular compounds. The present study focuses on computing the connection-based TIs for the most significant type of chemical structures, namely, rhombus silicate and rhombus oxide networks. At the end, we compare these structures on the basis of their computed result.

Energy transfer and release during the fracture of UD fiber-reinforced thermoplastic composites

This study delves into the complex dynamics of energy transfer and release during the fracture of unidirectional (UD) fiber-reinforced thermoplastic composites. Conducted through meticulous experimental observations and rigorous energy analysis, the research presents groundbreaking conclusions on the fracture toughness and energy conversion efficiency of UD carbon fiber composites under various loading conditions. A prominent focus is on how these mechanical properties are intricately linked to the sample’s fiber orientation angles and the external conditions applied during testing.The work employed tapered double cantilever beam (TDCB) as the far-field boundary to investigate the energy changes, transfer, and conversion processes during the crack propagation of unidirectional fiber reinforced thermoplastics (UDFRTPs) structures. It was found that throughout the entire propagation process, blunt extension occurs first followed by inertial extension. This is because in the initial stage of crack propagation, the stored elastic energy in the structure is relatively small, making the crack tip prone to blunting. This continuous blunting impedes the release of internal strain energy in the structure, with blunt extension accounting for a very small proportion of the entire fracture process. When the internal strain energy in the structure continues to increase to a certain extent, the blunting of the crack tip cannot prevent the release of a large amount of elastic energy inside the structure. At the same time, the excess released strain energy converts into kinetic energy and continually impacts the blunted region at the crack tip. At this point, the propagation transitions into the inertial extension stage, which occupies a significant portion of the entire fracture process.

Dynamic Failure Characteristics of Sandstone Containing Different Angles of Pre-Existing Crack Defects

Fracture within the rock is one of the main factors leading to rock destabilization and has a significant effect on the stability of the project. In this study, sandstone is used as a research target, specimens with crack inclination angles of 0°, 30°, 45°, 60°, and 90° are prefabricated, and the split Hopkinson pressure bar (SHPB) impact test of sandstone with cracks is carried out based on digital image recognition technology to explore the dynamic damage characteristics of the specimens with five angles. The basic mechanical parameters of sandstone are tested to determine the RHT model intrinsic parameters, and the numerical computational RHT model of sandstone containing crack defects is established, which is verified in comparison with the test to analyze the validity of the model. Finally, the failure characteristics of the numerical model under initial stress were carried out. The study shows the following: with the increase in the fracture angle, the dynamic compressive strength and deformation modulus are distributed in a slanting V-shape, and the inclination angle of 45° is the smallest. The strain rate and energy dissipation rate are distributed in a slanting N-shape, and the inclination angle of 45° is the largest. The transmittance shows a decreasing trend, which is the opposite of the reflectivity pattern. The crack angle determines the location and direction of the initial crack, which affects the failure mode. In addition, the parameters of the RHT constitutive model suitable for sandstone are obtained, and the damage and strength patterns of the established RHT model are highly consistent with the laboratory test results. The damage range of numerical models for crack defects with different inclination angles is negatively correlated with confining pressure values and positively correlated with axial pressure values. The damage zones are symmetrically distributed approximately perpendicular to the direction of cracks, and the confining pressure has a contributing role in the peak of the element stresses; however, the axial compression has no contribution in the peak of the element stresses.

Numerical simulation of fault activity in the Qilian tectonic belt and dynamic background of Menyuan earthquake series

Some faults in the Qilian tectonic belt are seismogenic areas for strong earthquakes, including the western section of the Lenglongling fault, which frequently occures moderate-strong Menyuan earthquakes. In this study, using GPS velocity data of 1991–2015 as the boundary constraints, a three-dimensional viscoelastic finite element dynamic model is constructed by comprehensively considering the regional dynamic environment, crust-mantle transverse-longitudinal inhomogeneity, and spatial spreading of a complex fault system. The objective is to investigate the long-period characteristics of fault movement and stress change in the Qilian tectonic belt caused by tectonic loading, and to discuss the seismogenic conditions of the Menyuan earthquakes. The results show that the annual change of long-period movement and stress of the major faults in the Qilian Mountain tectonic zone are characterized by significant segmentation. Due to its unique geometric bend morphology, the western section of Lenglongling fault has a low movement rate, significant slip deficit and high shear stress accumulation, which are conducive to the gestation and occurrence of earthquakes. Furthermore, the seismogenic area of the Menyuan earthquake series is jointly subjected to NE-SW compressive and NW-SE tensile stress fields, and the maximum shear stress and elastic strain energy accumulate faster than in the surrounding areas. Overall, the western section of the Lenglongling fault has a strong dynamic background and favorable conditions for the frequent occurrence of the Menyuan earthquake series.

Estimation of mode I quasi-static fracture of notched aluminum–lithium AW2099-T83 alloy using local approaches and machine learning

Aluminum–lithium (Al–Li) alloys offer superior performance under different conditions that involve mechanical loading, high temperature and corrosive environment. Therefore, Al–Li alloys are being used in the defense, aerospace, and aircraft industries, specifically in structural parts such as fuselage, empennage, and wings. By modifying the chemical composition, a third generation of Al–Li alloys has been introduced to overcome the mechanical and thermal shortcomings of previous Al–Li generations. As structural parts usually contain notches, it is of paramount importance to study the strength of the newly introduced alloys in the presence of such geometrical discontinuities to select the suitable alloy for a particular application. The aim of this work is to analyze the strength of U and V-notched specimens machined from extruded AW2099-T83 Al–Li alloys under quasi-static loading. The fracture stress of specimens with various notch radii and angles were estimated using strain energy density (SED) and the theory of critical distances (TCD) methods. A support vector machine (SVM) regression model was also implemented to assess the applicability of estimating fracture stress using machine learning approaches. The results show an average absolute discrepancy of 6.6 %, 7.8 % and 2.8 % for SED, TCD and SVM methods, respectively.

Collapse analysis and robustness assessment of dropped-story steel frame structures based on structural vulnerability theory

ABSTRACT This paper proposes an improved analysis method based on the theory of structural vulnerability, which incorporates structural redundancy and comprehensively analyzes structural vulnerability and robustness by considering the changes in structural stiffness and redundancy after damage to structural members under conventional loading. The improved method takes into account the changes in the strain energy of the structure after the damage of the structural members, which can be more in line with the actual situation of continuity collapse, and solves the complex process of traditional structural vulnerability theory that requires clustering and unclustering, greatly reducing the workload as well as solving the problem of not being able to find the critical members of the structure. The improved method is used to analyze the vulnerability of a 5-story dropped-story steel frame structure, to find the critical members of the structure based on the test data simulated by ABAQUS, to evaluate the robustness, and to propose improvement measures. The results show that the improved vulnerability assessment method is more reasonable and effective and can be applied to different steel frame structures.

A phase-field fracture model for creep-fatigue behavior

A phase-field fracture model for creep-fatigue behavior is proposed. The fatigue and creep behavior are simulated by modifying the free energy functional through a total degradation function that diminishes fracture toughness with the accumulation of the relevant history variable. Specifically, strain energy density and creep strain serve as the chosen fatigue and creep history variables, respectively. To model the creep-fatigue interaction, we propose several total degradation function formulations comprising fatigue and creep degradation functions. Numerical experiments demonstrate the capability of our model to reproduce the strain-lifetime relationship and crack growth behavior under creep-fatigue loading conditions with varying hold times. Moreover, we simulated examples of plates with holes, demonstrating the capability of our model for complex crack paths.

Multiscale simulation and experimental studies on modal damping of ultra‐thick CFRP laminates

AbstractThe vibration characterization of ultra‐thick laminates widely used in aerospace and marine industries was different from that of thin laminates. However, modal testing and simulation methods were generally limited to relatively thin laminates. To explore the vibration behavior of ultra‐thick laminates, a novel multiscale simulation technology based on the representative volume modal strain energy (RVMSE) method is presented for predicting modal damping in this paper. The adaptive Greedy‐Based Generation (GBG) algorithm is used to create a 3D random distribution of fibers for composites. Modal shape information of the structure is obtained according to the Lanczos algorithm, which is used as an input parameter for the microscopic model. This is followed by homogenization based on the volumetric analysis performed on representative volume elements (RVEs) to determine the strain energy in six directions. The calculation of modal damping is performed by using the modal strain energy (MSE) method and the damping properties of the six directions. The fast rate of convergence and high accuracy of the method are demonstrated through different examples. The vibration response predictions produced by novel RVMSE methodology are shown to closely match experimental measurements, providing scope to expand the application of this approach to more complex, ultra‐thick laminate components.Highlights The RVMSE method uses a higher level of homogenization to overcome the limitations of the traditional MSE method for calculating the damping of ultra‐thick CFRP laminates. The modal parameter error is controlled to less than 10%, and the experimental results fill the gap of the damping data of ultra‐thick CFRP structure. The proposed RVMSE model improves the accuracy of dynamic response prediction for ultra‐thick laminates.

Uncovering the progressive failure process of primary coal-rock mass specimens: Insights from energy evolution, acoustic emission crack patterns, and visual characterization

The failure and instability of deep coal-rock mass structures, which are influenced by mining disturbances, are major contributors to disasters like rock bursts. This study involved conducting indoor experiments using uniaxial loading test and acoustic emission (AE) experiments on indigenous primary coal-rock mass (PCRM). We utilize chaotic bifurcation based on strain energy to characterize the progressive damage stages of PCRM, demonstrating the chaotic characteristics of energy evolution during the gradual destruction process. The degree of damage resulting from PCRM failure was evaluated by jointly applying P-wave velocity tomography and AE event localization. Additionally, the classification of crack patterns in PCRM was conducted using the RA-AF correlation analysis method. The segmentation boundaries of crack classification patterns were then redefined using the Gaussian mixture model (GMM) algorithm. The research findings indicate that the chaotic bifurcation model of strain energy classifies stress into four stages: the stable region (Ⅰ), the metastable region (Ⅱ), the bifurcation region (Ⅲ), and the chaotic region (Ⅳ). The presence of a low-velocity zone in P-waves may indicate crack accumulation and damage within the system. Additionally, areas with abnormal P-wave velocities exhibit numerous AE events. The crack classification patterns of the four stages undergo an evolution from predominantly tensile cracks to a mixture of tensile and shear cracks, and the GMM algorithm successfully identifies the optimal separation path for crack classification boundaries. We propose an adaptive kernel density estimation (AKDE) algorithm to quantify the spatial distribution of AE events, thus offering a visual representation of the damage patterns at various stages.