Calculated Strain Energy Research Articles

The water vapor corrosion behavior and failure mechanism of Si with different structure at 1300 ℃

Pure silicon served as bond coat was widely used in environmental barrier coatings (EBCs) due to the excellent oxidation resistance and interfacial bonding. The formation of thermally grown oxide (SiO2-TGO) frequently caused the formation of horizontal crack in the Si surface and even caused the coating failure. However, the water vapor corrosion behavior and failure mechanism of Si have not been fully studied. The water vapor corrosion behavior of deposited Si coating, polycrystalline and monocrystalline Si was investigated at 1300 ℃ in 90%H2O-10%O2 environment. The disappearance of isolated splashed particles and coarse surface on the Si coating indicated the volatilization of Si and SiO2 during water vapor corrosion test. The characterization results indicated that the presence of defect provide the diffusion paths for oxygen and water vapor, leading to the increase of TGO formation rate. The growth of SiO2 thickness with the increase in corrosion time implied that the SiO2 formation reaction rate higher than its volatilization rate. It was important to find that the thermal mismatch between Si and α-cristobalite was contributed to the formation of mud-cracks in TGO layer by the calculation of elastic strain energy.

Numerical Simulation of GFRP-reinforced Rectangular Concrete Beams and Proposed Design Expressions

Rebar corrosion, which has emerged as a primary detrimental factor, significantly impacts the structural performance, durability, and overall serviceability of reinforced concrete (RC) structures. In response to this issue, the growing use of GFRP, which offers superior corrosion resistance compared to steel, highlights the need to compare its performance with traditional steel-reinforced beams. To address this need, this study aims to evaluate the flexural behavior of beams reinforced solely with GFRP rebar and assess their structural performance relative to steel-reinforced beams. To achieve this, finite element models of both steel-reinforced and GFRP-reinforced beams were developed using ANSYS software. The analysis focused on load-bearing capacities, displacement characteristics, and crack patterns, and included the calculation of strain energies corresponding to collapse prevention performance limits. Overall, the study concludes that these modifications enhance design guidelines for GFRP-reinforced beams, offering improved practical applications in structural design. Significant findings include the proposed modification to the minimum reinforcement ratio equation in ACI 440.1R-15 for GFRP-reinforced concrete, the introduction of a suggested strain reduction factor for GFRP rebar, and the revision of the effective moment of inertia equation with coefficients of 0.05 and 0.95. These revisions improved the general performance indicator to 1.17, yielding better results compared to other equations in the literature. The study concludes that these modifications enhance design guidelines for GFRP-reinforced beams, offering improved practical applications in structural design.

Highly Strained, Fully π‐Conjugated Porphyrin Cyclophanes: Template‐free Synthesis and Global Aromaticity

AbstractPorphyrin‐based nanohoops, nanorings, and cages with fully π‐conjugated structures are highly sought after, but their synthesis remains challenging. Herein, we report the template‐free synthesis of a highly strained, bithiophene‐bridged porphyrin cyclophane (1) from a porphyrin quinone via a stereoselective nucleophilic addition followed by intermolecular Yamamoto coupling strategy. X‐ray crystallographic analyses of 1 and its dication 12+ reveal significantly distorted cyclophane‐like geometries, with calculated strain energies of 51.2 and 80.7 kcal/mol, respectively. While the neutral compound 1 exhibits localized aromaticity, the dication 12+ is globally aromatic, with the porphyrin unit displaying weak antiaromaticity. Additionally, the dication 12+ undergoes nucleophilic addition with chloride, relieving strain. This work presents a novel synthetic strategy for highly strained, fully π‐conjugated systems with intriguing electronic properties and chemical reactivity.

Highly Strained, Fully π-Conjugated Porphyrin Cyclophanes: Template-free Synthesis and Global Aromaticity.

Porphyrin-based nanohoops, nanorings, and cages with fully π-conjugated structures are highly sought after, but their synthesis remains challenging. Herein, we report the template-free synthesis of a highly strained, bithiophene-bridged porphyrin cyclophane (1) from a porphyrin quinone via a stereoselective nucleophilic addition followed by intermolecular Yamamoto coupling strategy. X-ray crystallographic analyses of 1 and its dication 12+ reveal significantly distorted cyclophane-like geometries, with calculated strain energies of 51.2 and 80.7 kcal/mol, respectively. While the neutral compound 1 exhibits localized aromaticity, the dication 12+ is globally aromatic, with the porphyrin unit displaying weak antiaromaticity. Additionally, the dication 12+ undergoes nucleophilic addition with chloride, relieving strain. This work presents a novel synthetic strategy for highly strained, fully π-conjugated systems with intriguing electronic properties and chemical reactivity.

A Systematic Hierarchical Virtual Screening Model for RhlR Inhibitors Based on PCA, Pharmacophore, Docking, and Molecular Dynamics.

RhlR plays a key role in the quorum sensing of Pseudomonas aeruginosa. The current structure-activity relationship (SAR) studies of RhlR inhibitors mainly focus on elucidating the functional groups. Based on a systematic review of previous research on RhlR inhibitors, this study aims to establish a systematic, hierarchical screening model for RhlR inhibitors. We initially established a database and utilized principal component analysis (PCA) to categorize the inhibitors into two classes. Based on the training set, pharmacophore models were established to elucidate the structural characteristics of ligands. Subsequently, molecular docking, molecular dynamics simulations, and the calculation of binding free energy and strain energy were performed to validate the crucial interactions between ligands and receptors. Then, the screening criteria for RhlR inhibitors were established hierarchically based on ligand structure characteristics, ligand-receptor interaction, and receptor affinity. Test sets were finally employed to validate the hierarchical virtual screening model by comparing it with the current SAR studies of RhlR inhibitors. The hierarchical screening model was confirmed to possess higher accuracy and a true positive rate, which holds promise for subsequent screening and the discovery of active RhlR inhibitors.

A real space convolution‐based approximate algorithm for phase field model involving elastic strain energy

AbstractPhase field models have been employed extensively in the study of microstructure evolution in materials. Elasticity plays an important role in solid‐state phase transformation processes, and it is usually introduced into phase field models in terms of the elastic strain energy by applying Khachaturyan–Shatalov microelasticity theory. Conventionally, this energy is derived in the reciprocal space and results in full‐space Fourier transformation in practice, which becomes bottle‐neck in large‐scale and massively‐parallel applications. In this article, we propose an error‐controlled approximation algorithm for scalable and efficient calculation of the elastic strain energy in phase field models. We first derive a real‐space convolutional representation of the elastic strain energy by representing the equilibrium displacements in the Khachaturyan–Shatalov microelasticity theory using Green's function. Then we propose an error‐controlled truncation criterion to approximate the corresponding terms in the phase field model. Finally, a carefully designed parallel algorithm is presented to carry out large‐scale simulations. The accuracy and efficiency of the proposed algorithm are demonstrated by real‐world large‐scale phase field simulations.

Исследование кинетики формообразования деталей сферического подшипника скольжения из коррозионно-стойких сталей, полученных объемной штамповкой пористых заготовок

Introduction. Spherical powder sliding bearings are widely used in various branches of mechanical engineering. Therefore, the development of a promising method of production of spherical sliding bearing parts from powders of corrosion-resistant steels with specified properties is an urgent task. Purpose of work: is to study the kinetics of forming during cold die forging of spherical sliding bearing parts from stainless steel powder blanks, and to assess the effect of the chemical composition of lubricants and the design of the pressing tool on the structure and properties of the bearing outer ring. Materials from sprayed powders of stainless chromium-nickel steels obtained by cold die forging of sintered blanks coated with lubricants are studied in the work. The following research methods were used: mechanical tensile testing, metallographic studies and cold die forging process simulation. Results and its discussion. It is revealed that the resistance and work of deformation, as well as the kinetics of forming of the outer ring of the spherical sliding bearing are influenced by chemical composition of powders and lubricants, microstructure and mechanical properties of the blank material, configurations of the end surfaces of punches. The top and bottom edges of the outer bearing are most intensively sealed when the punch faces are made with a chamfer angle of 30–40 degrees. With an increase in the relative strain degree by height up to 0.30–0.35 its residual porosity amounted to 0.5–2.0 %. The features of definition of strain state and calculation of strain energy in the implementation of the offered method and the choice of technological parameters of the cold die forging process of sliding bearings parts are shown. A simple method for calculating and experimentally determining the coefficient of contact friction in the process of cold die forging of porous stainless steel blanks is developed, which allows to establish the effect of lubricant composition on the strain resistance at different values of the degree of radial deformation and to develop optimal methods of cold die forging of porous blanks in the production of parts of different complexity.

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.

True triaxial energy evolution characteristics and failure mechanism of deep rock subjected to mining-induced stress

In deep rock engineering, complex stress conditions are encountered, which leads to difficulties in engineering disaster prevention and control. To investigate the failure behaviors and mechanisms of deep rock mining, a series of tests was designed for mining-induced failure at different simulated depths using a multifunctional true triaxial geophysical (TTG) apparatus. The results showed that both the simulated depth and mining disturbance affected the deformation characteristics of the sandstone specimens. With increasing depth, the strength gradually increased. The peak strength increased fastest in the single-sided unloading failure test (SUFT) and slowest in the stress loading and unloading failure test (SLUFT). The failure mode also changed significantly. In the displacement loading failure test (DLFT), the failure mode gradually changed from tensile failure to shear failure. In the SLUFTs, the failure mode of the specimens changed from layer cracking to shear failure. In the SUFTs, the failure mode of the specimen transitioned from layer cracking to tensile shear failure and then to shear failure. Scholars have previously proposed an elastic strain energy calculation method for true triaxial stress conditions. An elastic strain energy calculation method applicable to different mining disturbance was proposed under true triaxial stress conditions, and the evolution characteristics of the work done, elastic strain energy, and dissipated energy were analyzed. Additionally, a method to quantitatively characterize the relationship between macroscopic cracks and dissipated energy was proposed, and microscopic fracture analysis was performed using scanning electron microscopy (SEM). Different depths and various types of mining-induced failure were fully considered, and the specimen deformation, failure type, energy evolution (including dissipation), and failure mechanisms were analyzed. The results can provide guidance for deep underground engineering projects.

Kaji Teoritis Pengaruh Variasi Letak Retak Terhadap Perambatan Retak Dengan Pendekatan Double Cantilever Beam (DCB)

One of the causes of structural failure is the presence of defects in the form of cracks that appear during the manufacturing or usage process of the structure. The propagation of cracks in the structure greatly depends on the value of the energy released rate possessed by the defective structure. Therefore, it is necessary to calculate the energy released rate of a structure that has a crack. One simple approach is the double cantilever beam (DCB) method. The DCB approach is derived from the change in strain energy with respect to the change in crack length. In this study, variations in crack length and crack location will be analyzed using the DCB approach and compared with the Finite Element Method (FEM) approach. It can be concluded that the calculation of strain energy can be performed using the cantilever beam approach, where the results do not significantly differ from the FEM calculations. Additionally, the strain energy is heavily influenced by the length of the beam, as longer beams result in a significant increase in strain energy (cubic relationship). The value of Energy Released Rate (ERR) is highly influenced by the crack length; a longer initial crack length leads to a quadratic increase in the Energy Released Rate (ERR). Furthermore, the value of Energy Released Rate (ERR) is also affected by the crack location; the closer the crack is to the surface of the beam, the higher the Energy Released Rate (ERR) will be.

A comprehensive analysis of in-plane functionally graded plates using improved first-order mixed finite element model

In this study, the mechanical behaviors of the in-plane functionally graded plate (IFG) are comprehensively explored via a finite element (FE) model. The current FE model is developed base on improved first-order shear deformation theory (FSDT) in conjunction with the mixed FE formulation. The volume fraction as well as the material properties change smoothly along the width and length of the plates for six different patterns. A simple improved transverse shear stress is applied to modify its distribution across the thickness of the IFG plates. Hence, the transverse shear stress equals zeros on the lower and upper surfaces of the IFG plates. Besides, no shear correction factor is needed for calculation of shear strain energy. A four-node mixed plate element, IMQ4, is established via mixed FE formulation for mechanical analysis of the IFG plates. The accuracy and fast convergence rate are validated via some examples. A comprehensive parametric analysis is provided to demonstrate the roles of several parameters including the material gradient index, the side-to-thickness ratio, aspect ratio, and boundary conditions on the mechanical behaviors of the IFG plates.

Tuning structural and electronic properties of single wall AlN nanotubes

The electronic and structural characteristics of the armchair and zigzag single-walled AlN nanotubes (SWAlNNTs) have been considered by using density functional theory (DFT). The effects of tube diameter on the Al–N bond length, the buckling separation, tube lengths, valence band maximum (VBM), conduction band minimum (CBM), Fermi energy, strain energy, and bandgap have been studied. The strain energy calculation revealed that higher-diameter nanotubes are more stable than those with smaller diameters consequently at the same chirality armchair AlNNTs are more stable than zigzag types. It revealed a correlation between the bandgap and buckling: the smaller the bandgap, the higher the buckling, and the buckling separation increases by decreasing tube diameter. The 2p-orbitals of Al and N atoms have the most contribution to CBM and VBM, respectively. All zigzag and armchair AlNNTs are semiconductors having direct and indirect bandgap, respectively. It is also found that for both zigzag and armchair AlNNTs, with increasing nanotube diameter, the bandgap increased. The conclusions of this study can definitely be useful in future experimental works on optoelectronic devices.

Influence of water on rockburst proneness of sandstone: Insights from relative and absolute energy storage

To fully understand the influence of water on rockburst proneness from energy storage viewpoint of rock and to check the performance of energy-related rockburst proneness indexes, several groups of uniaxial compression tests at different stress levels are performed on three types of red sandstone specimens (i.e., the saturated, natural, and oven-dried specimens). The method of combining strain energy calculations and experimental observations is used to assess the rockburst proneness. The progressive failure of the three types of specimens is recorded by a high-speed (H-S) camera, and the rockburst proneness is comprehensively assessed by considering the failure features of the rock specimens (including the fracture sound, fragment ejection, fragment distribution, and far-field ejection mass ratio). The laboratory results reveal that the rockburst proneness of the natural and oven-dried sandstone specimens is similar. However, compared with the natural and oven-dried specimens, the water-saturated specimens exhibit a visible weaker rockburst proneness. It is also evident that the linear energy storage and dissipation laws are applicable to the saturated, natural, and oven-dried specimens. Most interestingly, the energy storage and energy dissipation coefficients are nearly immune to the presence of water in the red sandstone. Based on this, the definitions of absolute energy storage capacity and relative energy storage capacity are adopted to describe the influence of water on the energy storage performance of rocks. It is found that water dramatically weakens the absolute energy storage capacity, but has little and negligible effect on the relative energy storage capacity of sandstone. Considering the direct and indirect indexes, the accuracy of several representative energy-related rockburst proneness indexes is comprehensively compared in terms of the far-field ejection mass ratio, and their performance is discussed from the relative and absolute energy storage aspects. According to their performance, it is strongly recommended to use the direct index for determination of rockburst proneness when energy-related indexes are used.

Generalization of the mixed-space cluster expansion method for arbitrary lattices

Mixed-space cluster expansion (MSCE), a first-principles method to simultaneously model the configuration-dependent short-ranged chemical and long-ranged strain interactions in alloy thermodynamics, has been successfully applied to binary FCC and BCC alloys. However, the previously reported MSCE method is limited to binary alloys with cubic crystal symmetry on a single sublattice. In the current work, MSCE is generalized to systems with multiple sublattices by formulating compatible reciprocal space interactions and combined with a crystal-symmetry-agnostic algorithm for the calculation of constituent strain energy. This generalized approach is then demonstrated in a hypothetical HCP system and Mg-Zn alloys. The current MSCE can significantly improve the accuracy of the energy parameterization and account for all the fully relaxed structures regardless of lattice distortion. The generalized MSCE method makes it possible to simultaneously analyze the short- and long-ranged configuration-dependent interactions in crystalline materials with arbitrary lattices with the accuracy of typical first-principles methods.

A consistent ordinary state-based peridynamic formulation with high accuracy

Peridynamics has shown great potential in numerical analysis of various engineering problems. However, its accuracy is still not quite satisfactory. In this paper, a consistent ordinary state-based peridynamic formulation (OSB-PD) is presented and significant improvement in computational accuracy is achieved. The starting point of the method is the investigation of the difference between the theoretical horizon and its counterpart in numerical implementation. Due to this difference, the original OSB-PD is inconsistent. The idea of modifying the theoretical horizon to eliminate such difference is proposed, based on which the consistent OSB-PD is developed. Numerical results show that the proposed method remarkably improves the accuracy of the original OSB-PD. Particularly, in calculating strain energy density, it almost achieves machine precision for constant strain field; for linear strain field, it shows orders higher accuracy than the original method. It is worth noting that such high accuracy is achieved with very small horizon and thus the proposed method is very fast. Capability of the proposed method in modeling crack propagation and fragmentation is also demonstrated.

A Distributional Model of Bound Ligand Conformational Strain: From Small Molecules up to Large Peptidic Macrocycles.

The internal conformational strain incurred by ligands upon binding a target site has a critical impact on binding affinity, and expectations about the magnitude of ligand strain guide conformational search protocols. Estimates for bound ligand strain begin with modeled ligand atomic coordinates from X-ray co-crystal structures. By deriving low-energy conformational ensembles to fit X-ray diffraction data, calculated strain energies are substantially reduced compared with prior approaches. We show that the distribution of expected global strain energy values is dependent on molecular size in a superlinear manner. The distribution of strain energy follows a rectified normal distribution whose mean and variance are related to conformational complexity. The modeled strain distribution closely matches calculated strain values from experimental data comprising over 3000 protein-ligand complexes. The distributional model has direct implications for conformational search protocols as well as for directions in molecular design.

Molecular Dynamics Simulation of Ligands from Anredera cordifolia (Binahong) to the Main Protease (M pro) of SARS-CoV-2.

COVID-19 in Indonesia is considered to be entering the endemic phase, and the population is expected to live side by side with the SARS-CoV 2 viruses and their variants. In this study, procyanidin, oleic acid, methyl linoleic acid, and vitexin, four compounds from binahong leaves-tropical/subtropical plant, were examined for their interactions with the major protease (Mpro) of the SARS-CoV 2 virus. Molecular dynamics simulation shows that procyanidin and vitexin have the best docking scores of -9.132 and -8.433, respectively. Molecular dynamics simulation also shows that procyanidin and vitexin have the best Root Mean Square Displacement (RMSD) and Root Mean Square Fluctuation (RMSF) performance due to dominant hydrogen, hydrophobic, and water bridge interactions. However, further strain energy calculation obtained from ligand torsion analyses, procyanidin and vitexin do not conform as much as quercetin as ligand control even though these two ligands have good performance in terms of interaction with the target protein.

Free vibrations of circular and sectorial plates by using the shape functions with trigonometric and hyperbolic terms

In this paper, free vibration of different plates in the polar coordinate is studied by using the Rayleigh–Ritz method and calculating strain and kinetic energies. The investigated plates include annular sectorial and circular, sectorial and circular with fixed center, circular sectorial, and solid circular. In this work, trigonometric and hyperbolic terms are used to express the shape function of each plate so that the shape function approximately satisfies boundary conditions and also regularity conditions for the solid plates. The mentioned plates can have any different types of the boundary conditions and the presented method is versatile and has no limitations. For the solid plates, the shape function is calculated in such a way that it can be used to calculate strain energy of the plate. Some types of the plates are examined as the case studies and the results are also calculated by the ABAQUS CAE for validation of the proposed method.

Mathematical Problems in Engineering Joint Structure Stiffness Analysis of an Automotive Body in White with the Finite Element Method

The finite element model of the seven connection heads of an automotive body in white is established, and the stiffness calculation is carried out by taking the lower joint of the B pillar as an example. Nine stiffness values were obtained for each branch, which can be written as a 3 × 3 symmetric matrix. The front and back bending stiffness, torsional stiffness, and internal and external bending stiffness are obtained with the decoupling method. Based on this, the finite element model for unrigid and rigid joints is established, and the three stiffness ratio coefficients of each branch of the joint are calculated and evaluated. Finally, the effects of the thickness and stiffness of the sheet metal parts on the bending condition, torsion condition, first-order bending, and torsion frequency of the body in white are discussed using the regional sensitivity analysis and strain energy calculation.

Local atomic ordering strategy for high strength Mg alloy design by first-principle calculations

In this study, solute X (X = Li, Al, Mn, Zn, Y, Zr, Nd, and Gd) solution strengthening in Mg alloys have been screened by ab initio density functional theory calculations to quantify not only the substitutional stacking-fault configurations but also the solute ordering sequence as a function of local segregation. Interestingly, it has been found that the strengthening effects of single atom addition to a supercell made of 64 atoms can be mostly attributed to lattice distortions (Mn>Nd>Gd>Y>Zn>Al>Zr>Li), while the local ordering arrangements of Mg-X complex actually contribute most to the strengthening when the solute concentration rises. For example, Nd can induce a large local atomic ordering and significantly increase the basal critical-resolved shear stress (CRSS). A linear relationship between solute concentrations and ideal strength, and the quasi-quadratic relationship between solute atomic radii and ideal strength have been observed. Simultaneously, the higher the solute concentration, the higher degree of the solid solution strengthening, resulting in a smaller quasi-quadratic function curve opening. Based on the screening of the chemical (including stacking fault energy and atomic bonds) and strain (lattice distortion energy) energy calculations, we have discovered that the solute strengthening follows the ordering sequence of Nd> Mn> Gd> Y> Zn> Al> Zr> Li. • Local ordering of Mg-X alloys was found by thermodynamic evaluations using DFT. • Both chemical and strain energy contribute to the solute strengthening ordering. • Local ordering configuration in solid solution strengthening guide the alloy by design.