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Assessing multiaxial fatigue theories requires experimental verification of a failure criterion, posing a significant challenge. This study aims to investigate the validity of a multiaxial fatigue method based on the Lagoda‐Macha‐Sakane (LMS) theory. The LMS theory links the critical strain energy density to the fatigue crack initiation cycles through a non‐linear equation defined by a set of empirical parameters calibrated by a strain‐controlled uniaxial fatigue test. This work adopts the LMS formulation, numerically calibrating the fatigue curve based on strain energy density from uniaxial fatigue experimental data and considering only the LMS theory for the critical strain energy density computation. This method avoids compatibility condition uncertainties and previous identification of material parameters. The study uses bi‐axial bending tests on AISI 316 L steel plate specimens with 3D finite element analyses to support computational assessment. The predictive capability of the model and the effectiveness of the testing method are presented and discussed. [ABSTRACT FROM AUTHOR]

The roof anchor cable in deep high stress roadway under the combined action of tension, shear, torsion and so on, could release accumulated strain energy instantaneously, causing the ejection accident due to anchor cable breaking, which seriously affects the safe production of coal mines. Based on the engineering background of the 1421 (3) anchor cable supporting roadway in the Zhangji Mine, the research methods of theoretical analysis, numerical simulation and laboratory test are used to reveal the energy evolution mechanism of anchor cable-surrounding rock and the energy absorption protection mechanism of anchor cable protection device. The results show that the fracture strain energy density of anchor wire is 55 MJ/m3 obtained by uniaxial tensile test and full constitutive model of anchor wire. The ejection energy released by anchor wire is positively correlated with the fracture length, axial force and diameter of anchor wire. According to the numerical simulation, the shear stress is concentrated at 0.6 m from the roof of the anchor cable, and the anchor cable is easy to break and eject. The initial velocity of the anchor cable with a length of 0.8 m is 102 m/s. Through simulation and strength theoretical analysis, the impact load limit of the original anchor cable energy absorption protection device is obtained as 20 m/s, and the impact load limit is increased to 200 m/s by increasing the base wall of the anchor cable protection device, which effectively solves the deflection failure problem of the anchor cable impact protection device. Based on the static tensile test and free fall impact test of the anchor cable protection device, the reliability of the numerical simulation results is verified, and the maximum energy absorption threshold of the protection device is 1189 J. Under the action of impact force, the spring base without protection device has a lateral offset and a shear failure at the bottom of the spring. Increasing the wall protection of the spring base can effectively restrain the base offset, give full play to the tensile energy absorption characteristics of the spring, and prevent the failure of the spring after shear damage. The test results are consistent with the numerical simulation results. The research results provide a reference for the roadway support design of the same specification parameter anchor cable, the ejection and protection of the anchor cable wire drawing breaking.

Abstract Deep rock are often in a true triaxial stress state. Studying the impacts of varying unloading speeds on their strain energy (SE) density is highly significant for predicting rock stability. Through true triaxial unloading principal stress experiments and true triaxial stress equilibrium unloading experiments on sandstone, this paper proposes a method to compute the SE density in a true triaxial compressive unloading principal stress test. This method aims to analyze the SE variation in rocks under the action of true triaxial unloading principal stresses. Acoustic emission is used to verify the correctness of the SE density calculation method in this paper. This study found that: (1) Unloading in one principal stress direction causes the SE density to rise in the other principal stress directions. This rise in SE, depending on its reversibility, can be categorized into elastic and dissipated SE. (2)When unloading principal stresses, the released elastic SE density in the unloading direction is influence by the stress path and rate. (3) The higher the unloading speed will leads to greater increases in the input SE density, elastic SE density, and dissipative SE density in the other principal stress directions. (4) The dissipated SE generated under true triaxial compression by unloading the principal stress is positively correlated with the damage to the rock; with an increase in unloading rate, there is a corresponding increase in the formation of cracks after unloading. (5) Utilizing the stress balance unloading test, we propose a calculation method for SE density in true triaxial unloading principal stress tests.

Deep rock are often in a true triaxial stress state. Studying the impacts of varying unloading speeds on their strain energy (SE) density is highly significant for predicting rock stability. Through true triaxial unloading principal stress experiments and true triaxial stress equilibrium unloading experiments on sandstone, this paper proposes a method to compute the SE density in a true triaxial compressive unloading principal stress test. This method aims to analyze the SE variation in rocks under the action of true triaxial unloading principal stresses. Acoustic emission is used to verify the correctness of the SE density calculation method in this paper. This study found that: (1) Unloading in one principal stress direction causes the SE density to rise in the other principal stress directions. This rise in SE, depending on its reversibility, can be categorized into elastic and dissipated SE. (2)When unloading principal stresses, the released elastic SE density in the unloading direction is influence by the stress path and rate. (3) The higher the unloading speed will leads to greater increases in the input SE density, elastic SE density, and dissipative SE density in the other principal stress directions. (4) The dissipated SE generated under true triaxial compression by unloading the principal stress is positively correlated with the damage to the rock; with an increase in unloading rate, there is a corresponding increase in the formation of cracks after unloading. (5) Utilizing the stress balance unloading test, we propose a calculation method for SE density in true triaxial unloading principal stress tests. [ABSTRACT FROM AUTHOR]

Brazing of nickel-based alloys plays a major role in the assembly of turbine components, e.g., abradable sealing systems. In a brazed joint of nickel-based alloys a composition of brittle and ductile phases can be formed if the brazing conditions are not ideal. This heterogeneous microstructure is a crucial challenge for predicting the damage behavior of a brazed joint. The initiation and evolution of microdamage inside of the brittle phase of a virtual dual-phase microstructure representing the material in a brazed joint is studied by means of numerical simulations. A phase field approach for brittle damage is employed on the microscale. The simulation approach is capable of depicting phenomena of microcracking like kinking and branching due to heterogeneous stress and strain fields on the microscale. No information regarding the initiation sites and pathways of microcracks is needed a priori. The reliability of calculating the effective critical energy quantities as a microstructure-based criterion for macroscopic damage is assessed. The effective critical strain energy density and the effective critical energy release rate are evaluated for single-phase microstructures, and the approach is transferred to dual-phase microstructures. The local critical strain energy density turns out to be better suited as a model input parameter on the microscale as well as for a microstructure-based prediction of macroscopic damage compared to a model employing the energy release rate. Regarding the uncertainty of the model prediction, using the effective critical energy release rate leads to a standard deviation which is five times larger than the standard deviation in the predicted effective critical strain energy density. [ABSTRACT FROM AUTHOR]

This study aims to enhance the mechanical properties of polylactic acid by incorporating black tea waste as an economical and sustainable additive capable of being recycled. The black tea waste, after the hot water color removal process, is milled to a fine and uniform powder size. The combination of these particles with polylactic acid is carried out using a twin-screw extruder. Specimens of pure polylactic acid and biocomposites containing 3 and 5 wt% black tea waste are manufactured using a hot press machine at a temperature of 200 °C. The filaments are also successfully extruded for three-dimensional printing purposes. Scanning electron microscopy images reveal that in the polylactic acid–3% tea biocomposite, the tea particles are appropriately dispersed within the polylactic acid matrix. The tensile test results indicate that biocomposite polylactic acid-3% tea has the highest mechanical properties, with a tensile strength of 67 MPa, demonstrating a 34% increase compared to polylactic acid. Furthermore, the biocomposite of polylactic acid–3% tea waste exhibits the best performance with a fracture energy of 2.5 kJ/m2 in the impact test. Hence, polylactic acid–3% tea biocomposite can be recommended as a suitable sustainable substitute. Finally, numerical simulations are performed on biocomposites containing double keyhole notches. This analysis is conducted to observe the behavior of biocomposite models with double keyhole notch under mixed-mode loading. The critical fracture load of the models is calculated using the strain energy density criterion. It is observed that an increase in the notch inclination angle and notch radius leads to a decrease in the fracture load in the models. [ABSTRACT FROM AUTHOR]

To accurately evaluate the probabilistic characteristics of the fatigue properties of materials with small sample data under different stress ratios, a data fusion method for torsional fatigue life under different stress ratios is proposed based on the energy method. A finite element numerical modeling method is used to calculate the fatigue strain energy density during fatigue damage. Torsional fatigue tests under different stresses and stress ratios are carried out to obtain a database for research. Based on the test data, the W t - N f curves under a single stress ratio and different stress ratios are calculated. The reliability of the models is illustrated by the scatter band diagram. More than 85% of points are within ±2 scatter bands, indicating that the fatigue life under different stress ratios can be represented by the same W t - N f curve. Furthermore, P- W t - N f prediction models are established to consider the probability characteristics. According to the homogeneity of the W t - N f model under different stress ratios, we can fuse the fatigue life data under different stress ratios and different strain energy densities. This data fusion method can expand the small sample test data and reduce the dispersion of the test data between different stress ratios. Compared with the pre-fusion data, the standard deviations of the post-fusion data are reduced by a maximum of 21.5% for the smooth specimens and 38.5% for the notched specimens. And more accurate P- W t - N f curves can be obtained to respond to the probabilistic properties of the data. [ABSTRACT FROM AUTHOR]

Both cell migration and osteogenic differentiation are critical for successful bone regeneration. Therefore, understanding the mechanobiological aspects that govern these two processes is essential in designing effective scaffolds that promote faster bone regeneration. Studying these two factors at different locations is necessary to manage bone regeneration in various sections of a scaffold. Hence, a multiscale computational model was used to observe the mechanical responses of osteoblasts placed in different positions of the trabecular bone and gyroid scaffold. Fluid shear stresses in scaffolds at cell seeded locations (representing osteogenic differentiation) and strain energy densities in cells at cell substrate interface (representing cell migration) were observed as mechanical response parameters in this study. Comparison of these responses, as two critical factors for bone regeneration, between the trabecular bone and gyroid scaffold at different locations, is the overall goal of the study. This study reveals that the gyroid scaffold exhibits higher osteogenic differentiation and cell migration potential compared to the trabecular bone. However, the responses in the gyroid only mimic the trabecular bone in two out of nine positions. These findings can guide us in predicting the ideal cell seeded sites within a scaffold for better bone regeneration and in replicating a replaced bone condition by altering the physical parameters of a scaffold. [ABSTRACT FROM AUTHOR]

In this paper, the SWT model was improved by incorporating the Walker equation into the strain–life curve. The established model takes into account the material's sensitivity to mean stress by introducing the Walker exponent, w. Under uniaxial loading condition, the proposed model can reduce to the SWT model, Manson‐Coffin equation, and Walker model for w values of 0.5, 1, and 0, respectively. Under multiaxial symmetric loading, when w = 0.5, the proposed model can be simplified as another SWT correction model (CXH) proposed by Chen et al. The prediction accuracy of the established model was validated using about 200 data points collected from literature. These data points were obtained from tests conducted on eight different kinds of metals under various multiaxial loading paths. The verification results indicate that 96.8% and 97.9% of the data points fall within the factor‐of‐three boundary for the loading paths without and with mean stresses, respectively. Highlights: Shear terms have significant influence on fatigue damage under non‐proportional loading.An improved SWT model is proposed by incorporating Walker equation into strain–life curve.Procedures for determining the critical plane and damage parameters were presented.Good predictions are obtained for loadings with/without mean stress. [ABSTRACT FROM AUTHOR]

The objective of this paper was to study low temperature crack resistance mechanism of steel slag asphalt mixture(SAM). Thermal stress restrained specimen test (TSRST) and three-point bending test were carried out to evaluate the low-temperature crack resistance of SAM and basalt asphalt mixture (BAM). Based on the digital image correlation technique (DIC), the strain field distribution and crack propagation of SAM were analyzed from the microscopic point of view, and a new index, crack length factor (C), was proposed to evaluate the crack resistance of the asphalt mixture. The crystal phase composition and microstructure of steel slag aggregate (SA) and basalt aggregate (BA) were studied by X-ray diffraction (XRD) and scanning electron microscopy (SEM) to explore the low-temperature crack resistance mechanism of SAM. Results show that the low-temperature crack resistance of SAM is better than that of BAM; SAM has good integrity and persistent elastic deformation, and its bending failure mode is a hysteretic quasi-brittle failure; The SA surface is evenly distributed with pores and has surface roughness. SA has the composition phase of alkaline aggregate-calcite (CaCO3), so it has good adhesion to asphalt, which reveals the mechanism of excellent low-temperature crack resistance of SAM. [ABSTRACT FROM AUTHOR]

Fatigue cracks were found at the diaphragm cutouts in the orthotropic steel deck (OSD) of a self-anchored suspension bridge while the in-service time of the bridge was less than 10 years. The causes of fatigue cracks of the diaphragm cutout are investigated in this study. The fatigue cracks initiated from the intersections of the arc curves and the straight lines, which form the geometrical discontinuity to the cutout edge. The in situ monitoring and finite element analysis under fatigue load model indicate that the cracking region in the cutout is in bidirectional compression. However, the thermal-structural analysis and tests show that the rib-to-diaphragm welding process produces high tension residual stress at the cracking points of the cutouts. The cutouts are under tension-compression cyclic loading because of the coupled stress, which is derived from the vehicle-induced stress and the welding residual stress. The results show that the strain energy method can present a reasonable fatigue life estimation for the diaphragm cutouts with full consideration of the residual stress. [ABSTRACT FROM AUTHOR]

In laminated composite materials design, optimization mainly targets the stacking sequence configuration, which is defined by the lamina thickness and fiber orientations within each layer. Recent studies emphasize the increasing role of Machine Learning in promoting innovative composite designs by facilitating the accurate modeling of essential properties such as strength and stiffness. This study introduces two metamodels that utilize feed-forward artificial neural networks, taking laminate thickness and fiber steering angles as input parameters. The output variables, including strain energy density and the Tsai-Wu failure index, enable the prediction of stacking sequence configurations for laminated materials, a capability confirmed in a case study. The results showcase neural network models with the ability to predict these variables, achieving coefficients of determination above 0.90 for testing data. Consequently, this modeling approach has the potential to be a tool for designers, aiding in decision-making processes for the subsequent optimization of stiffness and strength in structural components made of laminated composite materials. [ABSTRACT FROM AUTHOR]

Filaments used in textile products have many design parameters such as length, diameter, tip shape, material properties, etc. In order to design and develop the products efficiently that satisfy the desired functions, it is important to estimate the mechanical properties of filaments with various design parameters and to quantify the effects of design parameters on the mechanical behavior. In this study, we focused on as one of the design parameters of textile products, and evaluated the effects of this parameter on the mechanical properties of filaments under the sliding behavior based on the numerical and experimental approach. The results had shown that the difference in the tip shape of filaments affects the load value applied to the contacting body. It was also shown that the difference in the tip shape affected the deformation behavior. The difference of the tip shape was caused by the strain energy density of filaments during sliding movement. We believed that the results obtained in this study would be useful for the design and development of textile products efficiently. [ABSTRACT FROM AUTHOR]

Under environmental exposure, the mechanical properties of elastomers change due to ageing, all while enduring mechanical service loading conditions. The influence of ageing on the multiaxial mechanical response of elastomers remains an understudied question, lacking exploration in both experimental evidence and modelling proposals. The present study describes an experimental/numerical approach to characterize the multiaxial behaviour of elastomers with consideration of ageing. This technique associates complex experimental tests conducted with a hexapod device, with a Data-Driven Identification (DDI) algorithm. Practically, heterogeneous strain fields are measured by Digital Image Correlation (DIC), and the corresponding stress and energy fields are calculated by DDI. These fields are visualized through three-dimensional maps, encompassing kinematical quantities and strain energy density. These maps convincingly capture the stiffening induced by ageing, in different deformation modes. Finally, the coupling between ageing and multiaxiality is foregathered in a material database that can be fitted for further modelling purposes.

Cork composites are byproducts from wine stopper production, resulting from the agglomeration of cork granules with a thermoset resin. The resulting compound is a versatile and durable material with numerous industrial applications. Due to its unique properties, such as low-density, high-strength, excellent energy absorption, and good thermal and acoustic insulators, cork composites find room for application in demanding industries such as automotive, construction, and aerospace. However, agglomerated cork typically has a polyurethane matrix derived from petrochemical sources. This study focuses on developing eco-friendly porous polyurethane biocomposites manufactured with the used cooking oil polyol modified with cork. Since cork and polyurethane foam are typically used for impact shock absorption, the manufactured samples were subjected to impact loading. The assessment of crashworthiness is performed through 100 J impact tests. A finite element numerical model was developed to simulate the compression of these new composites under impact, and the model validation was performed. The highest specific absorbed energy was obtained for petrochemical polyol composites with the 3% addition of natural or modified cork. The research conducted in this study showcased the feasibility of substituting certain petrochemical components used for the synthesis of the polyurethane matrix with ecological waste vegetable oil components. [ABSTRACT FROM AUTHOR]

Α fatigue crack growth analysis to simulate the effect of plastic pre‐straining on fatigue crack growth by taking into account the cyclic material properties is presented. A critical energy concept is implemented, which correlates the critical energy for failure under low cycle fatigue with the critical energy at the crack tip from the SED criterion, using an appropriate scaling factor. The fatigue damage process area controlling the crack increment is defined by the cyclic plastic zone. Analytical fatigue crack growth rates in plastically pre‐strained steels are verified and compared with experimental data in the S355MC and S460MC HSLA steels showing good agreement. Highlights: FCG model takes effectively into account the Morrow energy method and the SED criterion.FCG simulation is based exclusively on the cyclic properties of pre‐strained material.The cyclic properties used reflect the cyclic hardening change after plastic deformation.Analytical FCG rates agree well with experimental FCG rates of S355MC and S460MC steels. [ABSTRACT FROM AUTHOR]

The fracture behavior of specimens made of polylactic acid and weakened by inclined double keyhole notches is investigated by both experimental and numerical methods. The test specimens are fabricated by two different methods; fused deposition modeling and traditional methods. The mechanical behavior of specimens was investigated under mixed‐mode loading with different notch inclination angles, various notch tip radius, and multiple raster angles. An experimental program was performed, and 72 new experimental data were provided. A fracture criterion based on the strain energy density is used to assess the critical fracture loads of the tested specimens. Good agreement is found between experimental and numerical data. The results showed that increasing the notch inclination angle and notch tip radius led to a decrease in the fracture load of the specimens. Also, fracture loads of the classical specimens are higher than the 3D‐printed specimens. In the 3D‐printed specimens, fracture loads for the samples with raster angles of 0°, 45°, and 90° have the highest value, respectively. Highlights: Fracture assessment of polylactic acid specimensSpecimens were weakened by using an eccentric inclined double keyhole notchSpecimens manufactured by fused deposition modeling and traditional methodInvestigation of different notch inclination angles and notch tip radiusEvaluation of specimens using experimental and numerical analysis methods [ABSTRACT FROM AUTHOR]

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In order to improve the problem of insufficient measurement scale and accuracy in the process of fracture toughness testing by indentation method, a method for assessing the fracture toughness of steel based on Berkovich indentation strain energy density (SED) is proposed based on the critical indentation energy (CIE) method. The fracture toughness of nine steels is evaluated by considering both elastic and plastic energies and correcting the critical total pressure depth. The results show that the relative error of the toughness measured by considering only the plastic energy is found to be in the range of 5% to 20%, whereas the relative error of the toughness measured by considering both the elastic and plastic energies is found to be within 5%. At the same time, determining the fitting range for the critical total indentation depth requires avoiding the region where the elastic modulus of the material rises near the surface. These improve the accuracy of evaluating the fracture toughness of steel based on the CIE method using the Berkovich indenter. [ABSTRACT FROM AUTHOR]

This study aims to tackle the problem of frequent coal-rock dynamic events caused by local stress concentration in deep mining working face under high static stress environment. Specifically, by taking the deep working face of Hongqinghe Mine located in Xinjie Mining Area as an example for analysisthis paper investigates the geological conditions of No. 3-1coal seam that are affected by the mining method and the coal rock dynamic disaster events occurred during mining; utilizes numerical simulation to simulate the mining stress field and energy field of the stope; analyzes the potential coal burst instability area and mechanism of coal burst gestation and catastrophe in the stope during the mining of the No. 3-1103 working face; probes into the sources of catastrophic stress and influencing factors of coal-rock disasters in dangerous areas, puts forward targeted prevention and control measures. Results show that: ① the roof strata structure, goaf and coal pillar are the key factors influencing coal burst in the stope during the mining of the No. 3-1103 working face; ② the simulation results indicatethe location and characteristics of the coal burst instability area in the stope of the No. 3-1103 working faces, as well as the simulation outlines 5 strong coal burst areas and 11 medium coal burst areas presented in the stope; ③ Measures are proposed for coal burst during mining from the perspective of cutting off the dynamic load source, reducing static load stress concentration, and blocking the transmission of high concentration stress. Detailed measures include implementing multi-source prevention and control in areas with high static or high static+dynamic loads, implement pre-pressure off-load measures prior to mining, and local risk relief and coal burst prevention and reduction treatments during mining.

Rock bursts are aggressive dynamic failure processes that involve the rapid release of strain energy stored in a rock under unloading conditions. The dynamic fracture and strain energy transformation characteristics of rock unloading failure must be investigated to predict and control rock bursts. This study adopts the discretized virtual internal bond (DVIB) method to investigate this problem. The element partition method is performed in the DVIB method to investigate the effect of cracks on rock unloading failure. Three indicators, i.e., fracture area, the fractal dimension of the failure pattern, and energy release ratio (kinetic energy over strain energy), are adopted to evaluate the failure intensity. Simulation results show that a critical strain energy density (SED) for rock unloading failure exists. The unloading failure occurs only when the SED exceeds the critical value. Subsequently, under the same SED conditions, the effect of the lateral pressure coefficient (LPC), heterogeneity, and size on rock unloading failure is investigated. As the LPC increases, the failure intensity increases slowly and then decreases significantly. The critical LPC is approximately 0.5, indicating that the unloading failure is the most severe. The simulation results suggest that the crack can reduce the energy release capacity of the rock and then restrain rock unloading failure. When the precrack angle is 0° or 90°, the precrack barely affects the rock unloading failure, and the failure intensity is similar to that of the intact rock. When the precrack length or the density of random precracks is larger, the rock unloading failure is weaker. [ABSTRACT FROM AUTHOR]

Non-crystalline solids have important applications in engineering and science. To predict the stress-strain behaviour of these materials, this work constructs an efficient strain energy density function using the concepts of molecular interactions. Considering hard contact between molecules, strain energy density of materials is defined in terms of packing fraction (volume occupied by the molecules per unit volume of the material) in deformed configurations. The packing fraction is represented in terms of strain invariants of right Cauchy-Green deformation tensor. Constitutive model obtained from the present strain energy density function is applied for predicting finite deformations of the materials like uniaxial extension, equibiaxial extension, and pure dilation. We observe that increasing reference packing fraction increases the Cauchy stress components. Results obtained from the present theoretical model is compared with experimental results of flexible polyurethane foam materials. We obtain good agreement with the experimental results. The present strain energy density function can be applied for predicting deformation as well as stress-strain behaviour of any other micro/nano components used in engineering systems. [ABSTRACT FROM AUTHOR]

An experimental study that allows for thermal-structural analysis of steel structures subject to non-spreading cryogenic spills is described. A local, non-spreading cryogenic spill was replicated by building a liquid nitrogen pool in the middle of six EH36 steel plates with a central crack of different length. The results of the temperature measurement and the thermal analysis are reported in the first and second part of this three-part companion paper. The computational study reported herein comprises stress analysis based on temperature-dependent von Mises plasticity combined with the SED failure criterion. Comparison of experimental and numerical results for stresses, fracture initiation and crack path shows satisfactory agreement. The numerical study indicates that the SED failure criterion is a useful concept for practical design of ship and offshore structures subjected to sub-zero temperatures and thus exposed to the risk of brittle failure when exposed to cryogenic spills. [ABSTRACT FROM AUTHOR]

To accurately evaluate the probabilistic characteristics of the fatigue properties of materials with small sample data under different stress ratios, a data fusion method for torsional fatigue life under different stress ratios is proposed based on the energy method. A finite element numerical modeling method is used to calculate the fatigue strain energy density during fatigue damage. Torsional fatigue tests under different stresses and stress ratios are carried out to obtain a database for research. Based on the test data, the Wt-Nf curves under a single stress ratio and different stress ratios are calculated. The reliability of the models is illustrated by the scatter band diagram. More than 85% of points are within ±2 scatter bands, indicating that the fatigue life under different stress ratios can be represented by the same Wt-Nf curve. Furthermore, P-Wt-Nf prediction models are established to consider the probability characteristics. According to the homogeneity of the Wt-Nf model under different stress ratios, we can fuse the fatigue life data under different stress ratios and different strain energy densities. This data fusion method can expand the small sample test data and reduce the dispersion of the test data between different stress ratios. Compared with the pre-fusion data, the standard deviations of the post-fusion data are reduced by a maximum of 21.5% for the smooth specimens and 38.5% for the notched specimens. And more accurate P-Wt-Nf curves can be obtained to respond to the probabilistic properties of the data.

It has not been solved that the fruits and vegetables such as strawberries, cells, blood and a bottle of sake are damaged, broken during transportation. It is the greatest factor in this situation that there is a dangerous vibration frequency range where these are easy to scratch and are prone to death. If there are eigen frequencies within this dangerous frequency range，it is good to be redesigned such that the eigen frequencies within this dangerous frequency range are moved out of the range. But it is difficult to apply the existing topology optimization methods using homogenization method or density method or thickness distribution method. As fundamental research, it is demonstrated the effectiveness of the proposed method based on the strain and kinetic energy density distributions of the targeted eigen modes for a flat plate compared to the conventional topology optimization method using thickness distribution as follows. (1) It is possible to control plural eigen frequencies by deciding interactively how the topology should be changed from the observation of kinetic and strain energy density distributions of the targeted eigen modes in a very short time compared to the conventional topology optimization method. (2) In the case of the proposed method, it is not necessary to get a new topology from the thickness or density distribution after the optimization results. (3) It can be checked the validity of the task set for the conventional topology optimization method by observing the strain and kinetic energy density distributions of the targeted eigen modes which are actively used in the proposed method.

We study the crack-tip fields in a three-dimensional (3D) plate with a V-shaped crack employing Rajagopal's theory of elasticity with the strain-limiting effect. The classical linear elastic fracture mechanics (LEFM) theory bears a well-documented inconsistency, i.e., for a static crack problem under the traction-free boundary condition, the LEFM theory predicts singular crack-tip strains. Such results are inconsistent with the constitutive relation derived using the assumption of uniform bound for the strain values. Instead, Rajagopal's recent theory of elasticity provides implicit constitutive relations between the linearized strain and Cauchy stress in which one can impose an a-priori upper bound for strains. We formulate the strain-limiting theory comprehensively in this article. The linearized strain is expressed as a nonlinear function of the Cauchy stress. The equation for the equilibrium of the linear momentum under a special type of nonlinear constitutive relation reduces to a second-order quasilinear elliptic boundary value problem (BVP). Using a Picard-type linearization and a continuous Galerkin-type finite element technique, we solve several BVPs with tensile and shear displacement loading. The numerical results for the strains, the stresses, the stress intensity factor (SIF), and strain energy density (SED) are obtained for different Poisson values, strain-limiting parametric values, and the V-shaped angles. The growth of the near-tip strains is far less than that of stresses, and the results for both the SIF and SED are also consistent with the results from LEFM. Our work demonstrates that the framework of Rajagopal's theory of elasticity can provide a basis for developing physically meaningful and mathematically well-posed BVPs to study evolution of cracks, damage, nucleation, or failure in elastic bodies. [ABSTRACT FROM AUTHOR]

This study conducted a series of biaxial stretching tests on the spinal dura mater. To investigate the specific effects of different loading patterns on mechanical responses of the dura mater, load-controlled asymmetric (longitudinal vs. circumferential loading at 1:0.5 and 0.5:1 ratios) and equi-load (longitudinal vs. circumferential at a 1:1 ratio) biaxial stretching tests were performed. The dural meninge was found to be most compliant when a circumferentially dominant loading pattern (longitudinal vs. circumferential at a 0.5:1 ratio or physiological biaxial stretch) was used. Additionally, physiological biaxial stretch resulted in the lowest strain energy density in the toe region of stress–strain curves, i.e., physiological deformation ranges, whereas mechanical loading caused abruptly stiffening of the linear region of stress–strain curves even under circumferentially dominant loading. On the other hand, stress relaxation and elastin content of the dural tissue had no effect on stored strain energy density within the range of biaxial stretch tested in this study. These results indicate that physiological biaxial stretching contributes to structural protection of the spinal cord and the spinal dura, which may be attributable to changes in the arrangement of embedded collagen fibers and concomitant mechanical interactions with surrounding tissues. [ABSTRACT FROM AUTHOR]

The fatigue strength of cast steel components is severely affected by manufacturing process-based bulk and surface imperfections. As these defect structures possess an arbitrary spatial shape, the utilization of local assessment methods is encouraged to design for service strength. This work applies the elastic–plastic strain energy density concept to study the fatigue strength properties of a high-strength cast steel alloy G12MnMo7-4+QT. A fatigue design limit curve is derived based on non-linear finite element analyses which merges experimental high-cycle fatigue results of unnotched and notched small-scale specimens tested at three different stress ratios into a unique narrow scatter band characterized by a scatter index of 1:TΔW¯(t)=2.43. A comparison to the linear–elastic assessment conducted in a preceding study reveals a significant improvement in prediction accuracy which is assigned to the consideration of the elastic–plastic material behaviour. In order to reduce computational effort, a novel approximation is presented which facilitates the calculation of the elastic–plastic strain energy density based on linear–elastic finite element results and Neuber’s concept. Validation of the assessment framework reveals a satisfying agreement to non-linear simulation results, showing an average root mean square deviation of only approximately eight percent in terms of total strain energy density. In order to study the effect of bulk and surface imperfections on the fatigue strength of cast steel components, defect-afflicted large-scale specimens are assessed by the presented elastic–plastic framework, yielding fatigue strength results which merge into the scatter band of the derived design limit curve. As the conducted fatigue assessment is based solely on linear–elastic two-dimensional simulations, the computational effort is substantially decreased. Within the present study, a reduction of approximately 400 times in computation time is observed. Hence, the established assessment framework presents an engineering-feasible method to evaluate the fatigue life of imperfective cast steel components based on rapid total strain energy density calculations.

Cork composites are byproducts from wine stopper production, resulting from the agglomeration of cork granules with a thermoset resin. The resulting compound is a versatile and durable material with numerous industrial applications. Due to its unique properties, such as low-density, high-strength, excellent energy absorption, and good thermal and acoustic insulators, cork composites find room for application in demanding industries such as automotive, construction, and aerospace. However, agglomerated cork typically has a polyurethane matrix derived from petrochemical sources. This study focuses on developing eco-friendly porous polyurethane biocomposites manufactured with the used cooking oil polyol modified with cork. Since cork and polyurethane foam are typically used for impact shock absorption, the manufactured samples were subjected to impact loading. The assessment of crashworthiness is performed through 100 J impact tests. A finite element numerical model was developed to simulate the compression of these new composites under impact, and the model validation was performed. The highest specific absorbed energy was obtained for petrochemical polyol composites with the 3% addition of natural or modified cork. The research conducted in this study showcased the feasibility of substituting certain petrochemical components used for the synthesis of the polyurethane matrix with ecological waste vegetable oil components.

In this paper, the strain energy density (SED) is used to study the over-examination to tire in flywheel test induced by pressure correction process. Flywheel test is the main method for evaluating tire durability, which cannot be measured on flat ground due to the variable road conditions. "Pressure Correction" is a necessary step in flywheel tests, but this process can lead to an over-examination of tire durability, which means the tire durability will be underestimated. However, it is impossible to obtain the tire durability from ideal flat ground test, so this paper utilizes the finite element method (FEM) to simulate the tire rolling condition on flat ground and differently sized flywheels, and the SED is used to evaluate the over-examination of tire durability in flywheel test. According to the results, a flywheel with too small diameter has a large amount of over-examination, and the amount caused by a large flywheel is acceptable. This methodology can be a guideline to assess the over-examination on different sized flywheel tests relative to the flat ground, and for the certain tire in this study, flywheels with 3–5 times the tire diameter appear to have an acceptable over-examination. [ABSTRACT FROM AUTHOR]

In order to improve the life expectancy of the rear axle housing in a mining dump truck, an energy-based anti-fatigue optimization design method was presented in this paper. The finite element model of rear axle housing was constructed and testified by the experimental data. The load history was obtained through multi-body dynamics analysis, and the multi-load step nonlinear finite element analysis was carried out to obtain the stress-strain response under different working conditions. The strain energy density method was used to evaluate the fatigue life of rear axle housing, and the results showed that its fatigue endurance was insufficient. Then, the lifetime of the most dangerous point was taken as the optimization objective, and the different plate thickness was considered as the design variables. The approximate model was constructed based on the response surface method, and the anti-fatigue optimization design was finally conducted on the bearing structure through the multi-island genetic algorithm. The minimum fatigue life of optimized rear axle housing was doubled. [ABSTRACT FROM AUTHOR]

Cells mechanically interact with their environment to sense, for example, topography, elasticity and mechanical cues from other cells. Mechano-sensing has profound effects on cellular behaviour, including motility. The current study aims to develop a mathematical model of cellular mechano-sensing on planar elastic substrates and demonstrate the model's predictive capabilities for the motility of individual cells in a colony. In the model, a cell is assumed to transmit an adhesion force, derived from a dynamic focal adhesion integrin density, that locally deforms a substrate, and to sense substrate deformation originating from neighbouring cells. The substrate deformation from multiple cells is expressed as total strain energy density with a spatially varying gradient. The magnitude and direction of the gradient at the cell location define the cell motion. Cell–substrate friction, partial motion randomness, and cell death and division are included. The substrate deformation by a single cell and the motility of two cells are presented for several substrate elasticities and thicknesses. The collective motility of 25 cells on a uniform substrate mimicking the closure of a circular wound of 200 µm is predicted for deterministic and random motion. Cell motility on substrates with varying elasticity and thickness is explored for four cells and 15 cells, the latter again mimicking wound closure. Wound closure by 45 cells is used to demonstrate the simulation of cell death and division during migration. The mathematical model can adequately simulate the mechanically induced collective cell motility on planar elastic substrates. The model is suitable for extension to other cell and substrates shapes and the inclusion of chemotactic cues, offering the potential to complement in vitro and in vivo studies. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Materials Science & Engineering (1673-2812) is the property of Journal of Materials Science & Engineering Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The fatigue strength of cast steel components is severely affected by manufacturing process-based bulk and surface imperfections. As these defect structures possess an arbitrary spatial shape, the utilization of local assessment methods is encouraged to design for service strength. This work applies the elastic–plastic strain energy density concept to study the fatigue strength properties of a high-strength cast steel alloy G12MnMo7-4+QT. A fatigue design limit curve is derived based on non-linear finite element analyses which merges experimental high-cycle fatigue results of unnotched and notched small-scale specimens tested at three different stress ratios into a unique narrow scatter band characterized by a scatter index of 1 : T Δ W ¯ (t) = 2.43 . A comparison to the linear–elastic assessment conducted in a preceding study reveals a significant improvement in prediction accuracy which is assigned to the consideration of the elastic–plastic material behaviour. In order to reduce computational effort, a novel approximation is presented which facilitates the calculation of the elastic–plastic strain energy density based on linear–elastic finite element results and Neuber's concept. Validation of the assessment framework reveals a satisfying agreement to non-linear simulation results, showing an average root mean square deviation of only approximately eight percent in terms of total strain energy density. In order to study the effect of bulk and surface imperfections on the fatigue strength of cast steel components, defect-afflicted large-scale specimens are assessed by the presented elastic–plastic framework, yielding fatigue strength results which merge into the scatter band of the derived design limit curve. As the conducted fatigue assessment is based solely on linear–elastic two-dimensional simulations, the computational effort is substantially decreased. Within the present study, a reduction of approximately 400 times in computation time is observed. Hence, the established assessment framework presents an engineering-feasible method to evaluate the fatigue life of imperfective cast steel components based on rapid total strain energy density calculations. [ABSTRACT FROM AUTHOR]

Fault-slip instability due to mining is a critical factor leading to coal bursts. To better understand the impact of fault-slip release energy on a coal seam, a static and dynamic numerical calculation model was established using FLAC3D with geological conditions at a mine longwall face in contact with the fault. The change in coal seam parameters under a dynamic fault-slip load was studied, including the change in vibration velocity, displacement, abutment stress, and strain energy density. The coal seam impact hazard level was classified with the change in longwall‒fault distance. Meanwhile, the numerical simulation results were compared and analyzed with microseismic monitoring records at the mining site to verify the accuracy of the results. The results showed that the increase in vibration velocity and displacement under the dynamic fault-slip load, and the sudden increase in abutment stress and strain energy density are precursors for coal bursts. As the longwall‒fault distance decrease, the coal seam is in a high-stress state, and the internal strain energy accumulates. After the dynamic fault-slip load is transferred to the coal seam, the high static and strong dynamic loads are superimposed, leading to an increased risk of coal bursts. Additionally, the coal seam stability was analyzed under three influencing factors, including the seismic energy, the seismic source location, and the burial depth. This study contributes to a better understanding of the mechanism for dynamic fault-slip loading on coal seam disturbance and provides insight into the associated coal burst propensity assessment. Highlights: A dynamic calculation model for analyzing the stability of the coal seam under fault-slip load was established. The theory that destabilization of the coal seam with high static load and strong dynamic load was proposed and verified. With the decrease of longwall‒fault distance, the coal seam is in the low coal burst risk, high coal burst risk, and post-damage stage. The stability of the coal seam was analyzed under three influencing factors, including the seismic energy, the seismic source location, and the burial depth. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Engineering Geology / Gongcheng Dizhi Xuebao is the property of Journal of Engineering Geology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Statement of the problem: Narrow implants have been recommended in high esthetic demand regions to ensure greater buccal bone thickness (BBT) and minimize soft-tissue recession due to insufficient bone support. However, a limited area of bone-implant interface can increase the risk of peri-implant bone resorption due to occlusal forces.Purpose: This article encourages the use of evidence-based finite element analysis to optimize the aesthetic outcomes in maxillary lateral incisor single-supported implant crown by accurate biomechanical planning. This study aimed to analyze the best implant dimensions that would preserve the maximum BBT and avoid peri-implant bone resorption due to occlusal forces.Materials and methods: A maxilla segment was constructed based on anthropological measurements. Four implant diameters (Ø = 3.25; 3.50; 3.75 or 4.00 mm) and two lengths (L = 10 or 13 mm) were simulated. The occlusal force parameters were defined to simulate clinical conditions. The bone resorption risk analysis was based on Frost’s mechanostat theory altering the strain output to strain energy density (SED). The peri-implant bone resorption risk indexes (PIBRri) were calculated by dividing the average of the top ten SED elements of the cortical and trabecular buccal wall by the pathologic resorption limit for each bone.Results: For trabecular bone, only the model Ø4.00L13 exhibited a low PIBRri. For cortical bone, all models presented a low PIBRri, except for models Ø3.25.Conclusion: The selection of a 3.25 mm dental implant to preserve a 2 mm BBT should be avoided since it generates a high peri-implant bone resorption risk induced by occlusal overload.