Explore the vast range of titles available.

Strain energy density functions are used in CAE analysis of hyperelastic materials such as rubber and elastomers. This function can originally be obtained only by experiments using biaxial deformation, but the difficulty of such experiments has made it almost impossible to put the function to practical use. Furthermore, it has been unclear how to introduce the strain energy density function necessary for CAE analysis from the results of biaxial deformation experiments on rubber. In this study, parameters of the Ogden and Mooney–Rivlin approximations of the strain energy density function were derived from the results of biaxial deformation experiments on silicone rubber, and their validity was verified. These results showed that it is best to determine the coefficients of the approximate equations for the strain energy density function after 10 cycles of repeated elongation of rubber in an equal biaxial deformation state, followed by equal biaxial elongation, uniaxial constrained biaxial elongation, and uniaxial elongation to obtain these three stress–strain curves.

Brittleness index is a significant mechanical parameter of rocks, widely applied in various geotechnical engineering. However, existing methods for evaluating brittleness indices have their limitations. In this study, we analyzed the energy evolution characteristics before and after peak stress in both radial and axial directions and proposed a new brittleness index considering radial strain energy evolution. The proposed method was validated through experiments. The results indicate that as confining pressure increases, rock brittleness gradually decreases. The widely used rock strength-based, elastic parameter-based, and modulus-based brittleness indices fail to reflect this trend. Only energy-based brittleness indices and the new brittleness index proposed in this paper align with this trend. However, existing energy-based indices do not consider radial energy evolution. For rocks with similar axial energy evolution characteristics but significant radial energy evolution differences, the energy-based brittle index will give the same brittleness index, which fails to evaluate brittleness characteristics accurately. The brittleness index proposed in this paper can provide accurate value for brittleness index and objective evaluations. Therefore, this new method in this study is more precise and exhibits significant advantages, compared with other mentioned brittleness index evaluation methods. Highlight Considering the energy evolution characteristics before and after peak stress in both radial and axial directions, a new brittleness index was proposed. Compared with the existing brittleness index, this paper's method can better respond to the effect of confining pressure on the brittleness of the rock, which conforms to the rock property. Due to the consideration of radial energy evolution, this paper's method can more accurately characterize the brittleness of rocks with large differences in radial damage characteristics.

Ore extraction at great depths creates high stresses around mine openings which can result in violent rock failure in one of various forms of strainburst. This is especially true with strong and brittle rocks which can store a large amount of strain energy that is suddenly released at failure. The strength and brittleness of rocks have been extensively investigated in the past. The most widely accepted method for the determination of rock burstability is the strain energy storage index obtained from a non-destructive uniaxial load–unload test. However, the results of this method are not always conclusive showing less repeatability when the target test load is changed. This study concerns itself with the introduction of microscopic analysis as a tool to help validate the strain energy index results when burstability cannot be warranted based on mechanical property tests alone. In this study, two types of rocks, namely, basaltic komatiite (BK) and felsic norite (FNOR) obtained from Canadian underground mines are examined. The selection is based on the premise that felsic norite is known to be burstable from the mine experience, whereas basaltic komatiite is not necessarily burstable. A total of 60 mechanical properties tests were conducted including uniaxial compressive strength, Brazilian tensile strength, and load–unload tests. Laboratory tests on FNOR consistently exhibit high burstability; however, the results for the BK tests are not conclusive. To seek explanations for the mechanical rock behavior, 18 thin sections were examined with optical microscopy and image analysis. The findings show the tested BK specimens are dominated by alteration products, and all primary igneous minerals are lost. There is minor quartz, garnet, carbonate minerals, talc, and serpentine, which give the rock its ductile properties. The FNOR specimens are found to be relatively fresh and supported by a strong network of plagioclase with minor pyroxene, biotite, and secondary micas, explaining the higher stiffness. This study demonstrates how optical microscopy can complement mechanical property tests to evaluate burstability of rocks. Highlights Microscopic analysis was introduced to complement rock mechanical tests for the determination of rock burstability. Two types of rocks, namely, basaltic komatiite and felsic norite, were tested using rock mechanical testing and optical microscopy. The basaltic komatiite specimens are dominated by alteration products that are attributed to the rock’s ductile properties. The felsic norite specimens were discovered to be unaltered and characterized by a strong mineral network explaining the high stiffness.

To evaluate rock brittleness more accurately, a new rock brittleness index based on the peak elastic strain energy consumption ratio (PEECR) was proposed in this study. Considering the relationship between rock brittleness and energy evolution characteristics of rock materials under confining pressure, the PEECR was defined as the dissipated proportion of peak elastic strain energy relative to failure energy and residual elastic strain energy (the maximum value of PEECR is 1.0, which indicates the corresponding rock will fail immediately after reaching the peak strength). The evaluation accuracy of the PEECR was verified based on the conventional triaxial compression tests on shale under six confining pressures, and the universality of the PEECR was also analyzed according to test data of six types of rocks from previous studies. The results show that the PEECR continuously decreases with the increasing of confining pressures, and is suitable for various types of rocks and a wider range of brittleness degrees. Finally, the evaluation accuracies of the PEECR and 11 existing rock brittleness energy indexes were compared and analyzed, and the results indicate that PEECR can evaluate rock brittleness more accurately.HighlightsA new rock brittleness index based on peak elastic strain energy consumption ratio (PEECR) was proposed considering the relationship between the rock brittleness and energy evolution characteristics of rock materials under confining pressures.It is verified based on conventional triaxial compression tests that PEECR can accurately evaluate rock brittleness, and is suitable for various types of rocks and a wider range of brittleness degrees.The evaluation accuracy for rock brittleness of PEECR is higher than other existing indexes by comparison based on test results, and PEECR can be popularized in practical application.

Strain energy change plays a pivotal role in the occurrence of earthquakes and rockbursts during deep mining operations. This study is dedicated to elucidating strain energy changes within the context of longwall mining at the Yuejin Coal Mine, a crucial step for optimizing design and mitigating rockbursts and seismic events. We introduce innovative analytical models to quantify strain energy changes resulting from fault coseismic slip, accounting for both mining-induced additional stress and background stress. Our analysis identifies fault types as critical parameters influencing strain energy variations. Calculations conducted across various scenarios reveal substantial spatial heterogeneity in strain energy distribution, contingent upon fault coseismic slip. Notably, fault slip in close proximity to the working face leads to localized strain energy concentration. To validate our findings, we compare them with monitoring data from the vicinity of the F16 fault at the Yuejin Coal Mine, further allowing us to propose that mining-induced fault coseismic slip constitutes an additional triggering factor for rockbursts or coal bursts, complementing the existing known factors. This underscores the significance of incorporating fault coseismic slip considerations into mining safety protocols, as it has the potential to trigger coal or rockbursts. Highlights Uncovered how fault coseismic slip impacts strain energy changes in deep longwall mining. Developed innovative models to calculate strain energy changes from fault slip, considering mining and background stresses. Observed significant spatial differences in strain energy distribution, linked to total energy release and fault- slip behavior. Correlated findings with F16 fault data, identifying mining-induced fault slip as a new cause for rock (coal) bursts.

Despite significant progress in developing mixed-mode I/II fracture criteria for orthotropic materials, many existing criteria still fail to fully consider the complexities of the fracture process zone (FPZ) and the arbitrary crack-fiber angles. This research addresses these limitations by developing generalized mixed-mode I/II fracture criteria for orthotropic materials. The proposed criteria are based on the concepts of minimum strain energy density and maximum strain energy release rate, which are combined with the reinforcement isotropic solid model. Including the non-singular term (T-stress) in the calculations improves the accuracy of crack growth predictions. Furthermore, based on these proposed criteria, an expression for the equivalent mode I fracture toughness is developed, which can be used to calculate the fracture toughness for any given crack orientation in orthotropic materials. The validity of the proposed criteria is evaluated through comparisons with available experimental data for wood species and composite materials. The results show that the newly proposed criteria offer more accurate predictions of material fracture behavior compared to classical criteria. The new approach, which includes the FPZ effects together with T-stress, provides a more realistic representation of crack growth in orthotropic materials under mixed-mode I/II loading conditions.

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.HighlightsA 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.

Studies have shown that the deformation of Ti alloys is due to the competition between hardening and softening effects under dynamic loading. However, there are limited indicators of this behaviour throughout the complete stress–strain process. This study aims to quantify the impact of strain rate and temperature on the hardening/softening behaviour of Ti-6Al-4V using a split-Hopkinson pressure bar system over a range of 2000 to 7000 s −1 strain rates and temperatures from 25 to 800°C. Firstly, this study proposes an evaluation index of material hardening/softening behaviour based on the complete stress–strain curve and energy evolution characteristic. Further, the dynamic mechanical properties of Ti-6Al-4V are investigated through the analysis of the stress–strain relationship and fracture morphology. Finally, the hardening/softening index is calculated and analysed. The findings revealed that the fracture surface of the impact specimen displayed dimple-like and smooth features, that are significantly influenced by both temperature and strain rate. The stress–strain curves demonstrated that Ti-6Al-4V exhibits remarkable strain-rate strengthening, plastic increasing, and strain work hardening behaviour. The hardening/softening index B r decreases with an increase in strain rate. For specific strain rates of 3000, 5000 and 7000 s −1 , B r increases as the loading temperature rises from 25 to 400°C, but decreases when the loading temperature is increased to 600°C. At a strain rate of 2000 s −1 , B r increases monotonically until the loading temperature reaches ∼ 800°C. These observations are found to be related to the microstructural evolution at varying temperatures and strain rates. Graphic Abstract

The plastic behavior of strengthened haunched beams utilizing carbon fiber-reinforced polymers (CFRP) was investigated using a probabilistic design that took into account random concrete properties, CFRP properties, and complementary strain energy values, with the reliability index serving as a limiting index, as the proposed method considers a novel method that deals with probabilistic parameters for models with limited plastic behavior designed based on the reliability index. The data used in this research were gathered and evaluated in a recent study on simply supported haunched beams reinforced with carbon fiber-reinforced polymers. The purpose of this research was to use the reliability limitation index for simulated strengthened haunched beams by taking into account randomness in concrete and CFRP properties and the complementary strain energy value, which is considered a plastic behavior controller that provides an illustration of the damage amount within the reinforcement steel bars. The results indicate how randomness affects the behavior of the presented models, which are chosen to have different numbers of CFRP strips. The variable randomness affects load and deflection values where the reliability index value increases as the corresponding load value decrease, reflecting the increased probability of failure in models subjected to higher loading conditions, while tension concrete damage percentages are reflected in the damage pattern presented in the results, showing that as the produced load increases, so does the damage intensity. It is also obvious that the reliability index served as a limitation index while taking concrete characteristics and complementary strain energy as random variables.

Vibration-based damage detection is a range of methods that utilizes the dynamic response of a structure to evaluate its condition and detect damage. It is an important approach for structural health monitoring and has drawn much attention from researchers. While multiple reviews have been published focusing on different aspects of this field, there has not been a study specifically examining the recent development across the range of methods, including natural frequency, mode shape, modal curvature, modal strain energy, and modal flexibility-based damage detection methods. This paper aims to fill this gap by reviewing the recent application of these methods in civil structures, including beams, plates, trusses, frames, and composite structural members. The merits and limitations of each method are discussed, and research opportunities are presented. This broader review also provides an opportunity for critical comparison across this range of methods. While predominantly reviewing experiment-based studies, this review also considers some numerical studies that may motivate further research.