Critical Loading Rate Research Articles

Influence of loading rate on the mode II fracture characteristics of SCC samples: Experiments and numerical simulations

This paper explores the influence of loading rate on mode II fracture failure in rock. Impact experiments were performed on samples of SCC at five different impact pressures via an SHPB system. This study reveals the correlations among the peak load, fracture toughness, and dynamic elastic modulus of rock mode II fractures under diverse loading rates, as well as the alterations in fracture trajectories. Simultaneously, PFC3D discrete element software has been adopted to numerically simulate the experiments and analysis of the fracture process of rocks and the variations in crack quantity and energy from a microscopic perspective. The results suggest that dynamic mode II fracture tends to increase as the loading rate increases and that the loading rate affects the fracture failure trajectory of a sample. Concurrently, as loading increased, the percentage of shear cracks in the samples gradually decreased, whereas the proportion of tensile cracks gradually increased, indicating that the samples experienced compressive stress after mode II fracture occurred at high loading rates. The proportion of energy absorbed by the samples for crack initiation and development, as well as the kinetic energy of the particles, initially tends to decrease but then increases with increasing loading rate, which is related to whether the loading rate generates secondary cracks. It is hypothesized that there exists a critical loading rate that triggers secondary cracks in SCC samples.

Removal Characteristics of Gas-Phase D-Limonene in Biotrickling Filter and Stoichiometric Analysis of Biological Reaction using Carbon Mass Balance

Volatile organic compounds (VOCs) pose significant risks to human health and environmental quality, prompting stringent regulations on their emissions from various industrial processes. Among VOCs, d-limonene stands out due to its low threshold and contribution to malodorous emissions. While biofiltration presents a promising approach for VOC removal, including d-limonene, a comprehensive understanding of its performance and kinetics is lacking. This study aims to comprehensively assess the performance of a lab-scale biotrickling filter in treating gas-phase d-limonene. The experimental results indicate that the biotrickling filter efficiently removed d-limonene, achieving a critical loading rate of 19.4 g m−3 h−1 and a maximum elimination capacity of 31.8 g m−3 h−1 (correspondingly, up to 85% removal) at the condition of 94.2 s of EBRT. Microbial activity played a significant role in biotrickling filter performance, with a strong linear correlation being observed between CO2 production and substrate consumption. The Michaelis–Menten model was employed to represent enzyme-catalyzed reactions, suggesting no inhibition during biotrickling filter operation.

Study on strength damage model considering resistivity and failure characteristics of the frozen soil–rock mixture under different loading rates

The strength damage and deformation failure of frozen soil–rock mixture (FSRM) often restrict the safety of the major engineering construction in cold areas or the spatial development of urban underground water-rich rock and soil masses. To investigate the uniaxial strength damage evolution and failure characteristics of FSRM under different loading rates (0.3, 0.6, 3, 6, 30, and 60 mm·min−1) in the quasi-static range, resistivity monitoring and image recognition technology were used to study the time-stress-volumetric strain-resistivity changes. The results indicate that the peak stress, peak strain, initial yield modulus, and tangential modulus of FSRM increase rapidly before increasing slowly as the loading rate increases, and there are critical loading rates and post-peak failure phenomenon. Three distinct types of failure modes, bulge failure, oblique shear failure, and fragmentation failure were observed at low (0.3–0.6 mm·min−1), medium (3–6 mm·min−1), and high loading rates (30–60 mm·min−1), respectively. The macroscopic failure of the FSRM at different loading rates arises from a combination of strain rate hardening of the strength and damage softening of the structure. To predict the stress-strain characteristics at various loading rates, a damage prediction model with a damage variable correction factor considering residual strength was employed based on the improved Duncan–Chang model and damage theory of electrical resistivity, and the predicted results were in good agreement with the experimental data.

Energy balance survey for the design and auto-thermal thermophilic aerobic digestion of algal-based membrane bioreactor for Landfill Leachate Treatment(under organic loading rates): Experimental and simulation-based ANN and NSGA-II

Although algal-based membrane bioreactors (AMBRs) have been demonstrated to be effective in treating wastewater (landfill leachate), there needs to be more research into the effectiveness of these systems. This study aims to determine whether AMBR is effective in treating landfill leachate with hydraulic retention times (HRTs) of 8, 12, 14, 16, 21, and 24 h to maximize AMBR's energy efficiency, microalgal biomass production, and removal efficiency using artificial neural network (ANN) models. Experimental results and simulations indicate that biomass production in bioreactors depends heavily on HRT. A decrease in HRT increases algal (Chlorella vulgaris) biomass productivity. Results also showed that 80% of chemical oxygen demand (COD) was removed from algal biomass by bioreactors. To determine the most efficient way to process the features as mentioned above, nondominated sorting genetic algorithm II (NSGA-II) techniques were applied. A mesophilic, suspended-thermophilic, and attached-thermophilic organic loading rate (OLR) of 1.28, 1.06, and 2 kg/m3/day was obtained for each method. Compared to suspended-thermophilic growth (3.43 kg/m3.day) and mesophilic growth (1.28 kg/m3.day), attached-thermophilic growth has a critical loading rate of 10.5 kg/m3.day. An energy audit and an assessment of the system's auto-thermality were performed at the end of the calculation using the Monod equation for biomass production rate (Y) and bacteria death constant (Kd). According to the results, a high removal level of COD (at least 4000 mg COD/liter) leads to auto-thermality.

Loading rate effect on the strength of granular material considering particle rotation

A variety of factors have significant influences on the strength of a granular system, such as the loading rate. However, the effect of loading rate on the strength of granular material systems has not attracted extensive investigations. In this study, based on the rate-state shear strength theory of granular materials, the general frictional coefficient for the granular material system in 2D space is obtained by introducing the loading rate and considering the particle rotation. A 2D discrete element simulation of spherical glass beads system with different combinations of confining pressures and loading rates is carried out by PFC2D. The results show that the mechanical behavior of the granular material system is more affected by the high loading rate and the critical loading rate is confirmed. The response of rotation ratio and other key parameters appearing in the proposed theory are further obtained. The theoretical predictions are also compared with the numerical simulations and good agreements have been observed. It is believed that the theoretical model proposed in this work can provide a helpful path in investigating the strength of granular materials and offer a method to determine the strength of granular materials for practical engineering projects.

Experimental study on fracture damage and seismic performance of loose through-tenon joints in ancient timber structures

A looseness is typical damage of mortise-tenon joints in ancient timber structures. Brittle fractures of loose joints are likely to occur, leading to joint failure during earthquakes. This study conducts pseudo-static tests on three groups of full-scaled through-tenon joints to examine the fracture damage and seismic behavior of the loose mortise-tenon joints and determines fracture damage modes of through-tenon joints with different looseness. It uses the acoustic emission method to measure the ring count on the tenon surface, along with each joint's critical load and critical energy release rate and then analyzes the fracture damage performance of different tenon joints. In addition, this research investigates the hysteretic and skeleton curve, stiffness degradation curve, and tenon pulling quantity of the joint under various fracture damage states. The results showed that the fracture failure mode of the through-tenon joint is a fracture in the variable cross-section and along the local tenon neck. During the loading process, the critical energy release rate initially increases and then decreases as the looseness grows. In addition, with the increase of crack mouth opening displacement (CMOD) and crack length, the bending moment of the joint firstly increases and then decreases. When the variable cross-section breaks and the tenon neck partially cracks, the joints' bending moment and stiffness reduce with increasing looseness. With the increase in local embedment compression in the lower side of the beam end and the mortise, the amount of tenon pull-out of loose joints decreases under positive and negative loading.

Understanding the static rate dependence of early fracture behavior of cemented paste backfill using digital image correlation and acoustic emission techniques

In mining engineering practice, cemented paste backfill (CPB) are subjected to loads at different static rates, so it is crucial to clarify the mechanical evolution mechanism of CPBs at different static rates. This work aims to understand the early fracture evolution mechanism of the CPB at static rates. First, the CPB with different static rates were monitored in real-time using acoustic emission (AE) and digital image correlation (DIC) techniques, and the effects of static rates on the CPB compressive strength as well as failure characteristics were analyzed; then, the intrinsic relationship between AE rise time/amplitude (RA) and average frequency (AF) was used to classify the crack types, and AE b-values and RA fractal dimensions were discussed for the crack evolution of the scale; finally, the strain field, displacement field, and dilation characteristics of the CPB were investigated. The results show that the increase in static rate increases the compressive strength of the CPB increase first and then decreases, and there is a critical loading rate effect. The final failure form of the specimen is transformed from tensile failure to tensile-shear composite failure with the increase of static rate. In addition, the growth of the loading rate will inhibit the formation of tensile cracks and promote the development and expansion of shear cracks. The trend of the AE b-value and the RA fractal dimension have a synergistic feature, which can be used as a sudden drop before and after the peak intensity as the failure precursor information of the CPB. The increased static rate will make the CPB reach the dilatancy state in advance, and the changing pattern of dilatancy stress synergizes with the peak strength. The study results provide a theoretical basis for evaluating the structural safety of the CPB.

Study on the Macro-Micro Mechanical Properties of Grout Consolidated Coal under Different Loading Rates.

The bore hole is sealed from a sealing hole: the surrounding coal fracture permeability and grout cementation form a new consolidated body and coal material. In this paper, the characteristics of the macroscopic compressive strength, microscopic interface bending, porosity, and fractal dimension of the consolidated body were studied, and the structure strength relationship between loading rates, porosity, fractal dimension, and uniaxial compressive strength (UCS) was established. The results show that the loading rates had a great and consistent effect on the macro- and micro-mechanical properties of the consolidated body. Macroscopically, in the range of 0.1~0.4 mm/min, the UCS and elastic modulus of the solidified body increased with the increase in the loading rate, and there was a critical loading rate (η = 0.4 mm/min). At the microscale, with the increase in loading rates, the interface bending phenomenon, porosity, fractal dimension, and UCS of the grout and coal were consistent, showing a trend of increasing first and then decreasing. The fractal dimension was linearly correlated with the UCS and porosity. The loading rates, porosity, fractal dimension, and UCS had a multivariate nonlinear regression distribution.

Numerical Investigation of Asphalt Concrete Fracture Based on Heterogeneous Structure and Cohesive Zone Model

The fracture behavior of asphalt concrete is closely related to its internal structure. A deep understanding of the relationship between the internal structure and fracture behavior of asphalt concrete is very important for sustainable and durable pavement design. In this paper, a CZM-based FE model was developed to investigate the fracture behavior of asphalt concrete. An image-aided approach was used to generate the 3-D internal heterogeneous structure of asphalt concrete. A series of 2-D cross sections were extracted from the 3-D structure for finite element modeling. Then numerical simulations of SCB tests were conducted and validated with experimental results. With the validated CZM-based FE model, the effects of some critical factors, including temperature, loading rate, aggregate geometry, fracture strength, and fracture energy, on the fracture behavior of asphalt concrete were investigated. The analysis results showed that the average damage of the adhesive elements was higher than that of the cohesive elements at the peak load. At lower temperatures, asphalt concrete tends to crack earlier, and the cracking path tends to be marginally closer to the aggregates. A higher loading rate may induce more, but minor, element damage since the CZM elements in asphalt mortar cannot bear much more stress through deformation. Angular aggregates may induce a higher percentage of damaged elements, especially adhesive-damaged elements. On average, each 10% increase in fracture energy allows the specimen to bear 2.31% more load and 2.82% more displacement. Sufficient fracture energy could improve the ability of asphalt concrete to resist fracture.

Simultaneous removal of H2S and NH3 from raw biogas in hollow fibre membrane bioreactors

H 2 S and NH 3 are toxic, corrosive and odorous gases that often co-exist in gas streams emitted from industrial processes, including biogas produced in anaerobic digestion plants. A hollow fibre membrane bioreactor (HFMB) was tested for simultaneous biological removal of H 2 S and NH 3 from raw biogas. The HFMB achieved a removal efficiency (RE) > 99% for treating up to 1850, 915 and 1200 ppm v of H 2 S at an empty bed residence time (EBRT) of 187, 92 and 46 s, respectively. The RE of NH 3 was > 99% when the inlet NH 3 concentrations were up to 460, 355 and 750 ppm v at an EBRT of 187, 92 and 46 s, respectively. At an EBRT of 46 s, the RE of H 2 S and NH 3 was in the range of 85–97 and 73–95%, respectively, for inlet biogas laden with 1200–1700 ppm v of H 2 S and 750–1050 ppm v of NH 3 . The critical loading rates of H 2 S and NH 3 were about 150 and 40 g m −3 h −1 , respectively. S 0 (52%), SO 4 2 − (48%) and N 2 (92%) were the end products of the H 2 S and NH 3 bioconversion. Different sulfide oxidizers including aerobic (e.g. Smithella sp., Sulfuricurvum sp. and Thiomonas sp.) and anoxic (e.g. Rhodanobacter sp., Sulfuritalea sp. and Thiobacillus sp.) chemolithotrophs contributed to the H 2 S bioconversion. Aerobic (e.g. Pseudomonas sp., Stenotrophomonas sp. and Nitrosospira sp.) and Fe(III) dependent anaerobic (e.g. Clostridium_sensu_stricto_12 sp., Rhodoferax sp. and Dechloromonas sp.) ammonium oxidizers contributed to the NH 3 bioconversion. Denitrifiers including denitrifying phosphorus accumulating organisms (e.g Candidatus_Contendobacter sp.) contributed to the denitrification process. • Hydrophilic polyethersulfone HFMB simultaneously treated H 2 S and NH 3 from raw biogas. • Maximum H 2 S and NH 3 flux through membrane module was 1.94 and 0.55 g m -2 day -1 , respectively. • The critical loading rate of H 2 S and NH 3 was close to 150 and 40 g m -3 h -1 , respectively, at an EBRT of 46 s. • Outlet/inlet CH 4 ratio ( ∼ 0.99) confirmed low ( < 1%) biogas dilution in the HFMB. • Both aerobic and anoxic processes contributed to H 2 S and NH 3 bioconversion in the HFMB.

Biomechanical State of the Operated Thoracolumbar Junction in Lateroflexion

Summary. The zone of the thoracolumbar junction is the most susceptible to traumatic injuries due to anatomical and physiological features. Accordingly, the stabilization of this section of the spine requires high reliability.&#x0D; Objective: to study the stress-strain state of the model of the thoracolumbar spine after resection of Th12-L1 vertebrae with different types of transpedicular fixation under lateroflexion.&#x0D; Materials and Methods. Mathematical finite element model of a fragment of the human thoracolumbar spine (Тh9-L5) was developed. We modeled the result of decompressive-stabilizing surgery with total removal of Th12-L1 vertebrae including installation of vertebral body replacing implant and fixation with a transpedicular system using 4 pairs of screws. Lateroflexion was modeled by applying a load of 350 N.&#x0D; Results. When evaluating the model without crosslinks and using monocortical pedicle screws, it was found that the maximum loading values in Th10, Th11, L2, and L3 vertebral bodies were 3.4, 2.0, 3.5, and 8.6 MPa, respectively; loading on pedicle screws installed in the indicated vertebrae was 48.4, 48.3, 23.3 and 43.5 MPa. When using bicortical screws without crosslinks in the vertebral bodies, the values were 3.1, 2.5, 3.8, 9.6 MPa and 49.9, 51.9, 25.8, 44.8 MPa, respectively; when using a combination of short screws and crosslinks in the vertebral bodies, the values were 3.2, 2.0, 2.6, 7.5 MPa and 47.6, 47.5, 22.6, 41.2 MPa, respectively; when using crosslinks and bicortical screws, the values were 3.0, 2.2, 2.7, 8.8 MPa and 48.3, 49.6, 24.3, 42.5 MPa, respectively.&#x0D; Conclusions. In lateroflexion, monocortical pedicle screws cause lower critical loading rates compared to long screws at all control points of the model. Crosslinks help to reduce stress levels. The use of monocortical pedicle screws in combination with transverse ties seems to be the most biomechanically effective in lateroflexion.

Resilience of hollow fibre membrane bioreactors for treating H2S under steady state and transient conditions

H2S removal performance by hollow fibre membrane bioreactors (HFMBs) was investigated for 271 days at ambient (20 ± 2 °C) temperature employing an inlet H2S concentrations up to 3600 ppmv and empty bed residence time (EBRT) of 187, 92 and 62 s. Different operating conditions including pH control (with or without), famine period, shock loads (4–72 h) and different biomass types (presence or absence of suspended biomass) were investigated. The H2S flux and mass-transfer coefficient were significantly higher for the biotic HFMBs (R1 and R2) compared to the abiotic control (R3) at all employed EBRTs. Significant differences in H2S removal efficiency (RE) and elimination capacity (EC) were noted for different inlet H2S concentrations, EBRTs, pH and biomass type. The HFMB achieved >99% RE at steady-state for biotic operation with an EC of 33.8, 30.0 and 30.9 g m−3 h−1 at an EBRT of 187, 92 and 62 s, respectively. Sulfate (92–93%) was the main sulfur species in the H2S bioconversion process. The HFMB showed a good resilience to shock loads and showed quick recovery (<24 h) after withdrawal of the shock loads. The HFMB had a critical loading rate of H2S about 135 g m−3 h−1 under transient-state.

Effect of Loading Rate and Confining Pressure on Strength and Energy Characteristics of Mudstone under Pre-Cracking Damage

In order to explore the deformation and failure law of deep surrounding rock roadway disturbed by strong dynamic pressure, the triaxial mechanical properties of mudstone samples under pre-cracking damage conditions were tested to study the deformation and failure characteristics and energy evolution mechanism in the damage process, under different loading rates and confining pressures. In the mechanical experiment, the specimen is pre-cracked to simulate the damage and failure of surrounding rock during roadway excavation, and the damage degree model of rock specimen is established. The results show that the loading rate and confining pressure have significant effects on the peak strength and energy characteristics of mudstone at the average damage degree of 0.12, and the peak strength increases with the increase in confining pressure and loading rate. Under the same confining pressure, the energy increases first, and then decreases with the increase in loading rate, and the loading rate at the turning point is called the critical loading rate. Under the same confining pressure, the closed stress of mudstone gradually increases with the increase in loading rate, and the closed stress and loading rate show a good linear relationship. Through the fitting relationship, it is found that the fitting correlation coefficient between the closed stress of mudstone and the loading rate is as high as 0.99. The elastic strain energy ratio presents a composite function of exponential function with natural constant e, which is a nonlinear process.

Bone fixation implants with in-situ controllable stiffness: Modifying the R-curve behavior by 3D printing

The difference in bone stiffness with the metallic bone fixation implants increases the risk of re-fracture due to osteoporosis in the implant area. In this study, a PLA-based bio-composite bone fixation implant with controllable stiffness capability was fabricated with a 3D printer, and crack growth in samples has been studied. The stiffness controllability was made possible by controlling the fiber and polymers fractions in the 3D printing process. A logical relationship was observed between Vf, critical load, and strain energy release rate. Therefore, it can be expected that the fracture toughness can be estimated in thermoplastic bio-composites bone fixation based on the Vf.

Co-effects of bedding planes and loading condition on Mode-I fracture toughness of anisotropic rocks

The mechanical and fracture behavior of rocks are mainly determined by the discontinuous defects inside the rock and the external force state. The focus of this research is to clarify the co-effects of bedding planes and loading conditions on the fracture behavior of anisotropic rocks. Notched semi-circular bend (NSCB) tests are performed on anisotropic rocks with varied bedding angles (from 0° to 90°) and loading conditions (from static loading to impact loading). By analyzing the failure characteriacs recorded throught the experiments and fracture toughness of anisotropic rocks (shale and coal), a critical loading rate, two failure modes, three empirical relations, upper and lower envelopes are provided. In addition, bedding effects, laoding rates effects and co-effects between them are further investigated. The experimental results indicate that the bedding effects is the most obvious under static loading and becomes weaker as loading rates increase. At this time, the loading rates effects plays a dominant role. Under the co-effects of bedding plane and loading conditions, the failure modes become more complex and the fracture toughness exhibits inconsistent characteristics for anisotropic shale and coal. Due to the different internal discontinuities, the maximum loading rate that shale and coal can withstand differs greatly, which further affects their mechanical and failure behaviors. The results have sightful implications to the response of anisotropic rocks to engineering activities.

Effect of loading rate on the mode II dynamic fracture characteristics of 40Cr steel

40Cr high strength steel is often used in aerospace and national defense fields due to its excellent mechanical properties. Therefore, the research on the mode Ⅱ dynamic fracture characteristics and failure mechanism of 40Cr high strength steel under high-speed impact has important scientific significance and engineering value. Experiments and numerical simulations were carried out to study the mode Ⅱ dynamic fracture properties of 40Cr material under high loading rates. Based on the newly designed specimen and the novel test technique for mode Ⅱ dynamic fracture, the experimental-numerical method was used to determine the dynamic stress intensity factor curve of the crack tip during the loading process. The crack initiation time of the specimen was obtained by the strain gauge pasted on the specimen, and the mode Ⅱ dynamic fracture toughness of 40Cr was finally determined. The effect of loading rate and the failure mechanism of the material were also studied. The results show that within the present loading rate range of this work (1.08−5.53 TPa·m1/2/s), the mode Ⅱ dynamic fracture toughness of 40Cr presents a positive correlation with the loading rate. Through the analysis of the fracture morphology of the recovered specimen, it is found that there exists a transition from tensile failure mode to adiabatic shear failure mode with the increase of loading rate, and the critical loading rate is about 2.92 TPa·m1/2/s. When KⅡd≤1.70 TPa·m1/2/s, the 40Cr steel mainly exhibits brittle fracture; when KⅡd is in the range of 2.12−2.92 TPa·m1/2/s, the fracture mainly presents the morphological characteristics of ductile fracture; when KⅡd ≥ 3.19 TPa·m1/2/s, the material failure is mainly caused by adiabatic shear bands. Brittle fracture is dominated by strain rate hardening mechanism, ductile fracture is dominated by strain/strain rate hardening and thermal softening mechanisms, and adiabatic shear fracture is dominated by thermal softening mechanism.

Mechanical behavior of coal under different mining rates: A case study from laboratory experiments to field testing

During deep mining, the excavation disturbance stress path is the domination factor for the stability of the surrounding rock mass as well as the ground pressure. One of the important parameters of the stress path is the loading or unloading rate of the disturbed rock or coal, which depended on the mining rate. To achieve a well understanding of the mining rate and its effect on the coal behavior, a preliminary case investigation of the mechanical properties of the coal at the various mining rates in both the laboratory scale and field scale was performed. Based on the uniaxial compression test and the digital image correlation (DIC) method, the mechanical behavior of the coal samples, such as the evolution of the strength, surface deformation, crack propagation, and elastic strain energy of the coal under the various loading rates were analyzed. A threshold range of the loading rate has been observed. The uniaxial compressive strength (UCS) and releasable elastic strain energy (Ue) increase with increasing loading rate when the loading rate is below the threshold. Otherwise, the UCS and Ue may decrease with the loading rate. Under the low loading rate (≤0.05 mm/min), the tensile deformation of the original defects could result in crack coalescence, whereas failure of the coal matrix is the key contributor to the crack coalescence under the high loading rate (greater than0.05 mm/min). Afterwards, with the consideration of the bearing capacity (UCS) and energy release of the mining-disturbed coal mass (Ue), a power exponential relationship between the mining rate (MR) in the field and the critical loading rate (vc) in the laboratory was proposed. The application potential of the formulas was then validated against the field monitored data. Finally, based on the critical loading rate, the released strain energy, and the monitored pressure on the roof supports, a reasonable mining rate MR for the Ji15-31030 working face was determined to be approximately 3 m/d.

Experimental study on influence of wetting-drying cycle on dynamic fracture and energy dissipation of red-sandstone

To study the influence of the wetting-drying cycles and loading rate on dynamic fracture toughness and energy dissipation of rocks under the dynamic loads, the split Hopkinson pressure bar (SHPB) system was used to perform the dynamic impact tests on NSCB specimens of red sandstone after different wetting-drying cycles. The loading rate response characteristics of fracture toughness of specimens after different wetting-drying cycles were analyzed, and the energy dissipation law of dynamic fracture under the impact loads was obtained. The results show that under a given number of wetting-drying cycles, with the increase of loading rate, the dynamic fracture toughness shows an overall trend of increasing. When the critical loading rate K˙IC is exceeded, the dynamic fracture toughness no longer increases. At the fixed loading rate, the dynamic fracture toughness of red sandstone decreases linearly with the increase of wetting-drying cycles, and the higher the loading rate, the more sensitive the fracture toughness to the wetting-drying cycle. With the increase of the loading rate, the dynamic fracture energy increases exponentially and becomes more sensitive to the loading rate. Under the fixed wetting-drying cycles, the dynamic fracture toughness of red sandstone has a logarithmic relationship with the increase of fracture energy.

A simple and computationally efficient stress integration scheme based on numerical approximation of the yield function gradients: Application to advanced yield criteria

In this paper, we have modified the stress integration scheme proposed by Choi and Yoon [1]; which is based on the numerical approximation of the yield function gradients, to implement in the finite element code ABAQUS three elastic isotropic, plastic anisotropic constitutive models with yielding described by Yld2004-18p [2], CPB06ex2 [3] and Yld2011-27p [4] criteria, respectively. We have developed both VUMAT and UMAT subroutines for the three constitutive models, and have carried out cylindrical cup deep drawing test simulations and calculations of dynamic necking localization under plane strain tension, using explicit and implicit analyses. An original feature of this paper is that these finite element simulations are systematically compared with additional calculations performed using (i) the numerical approximation scheme developed by Choi and Yoon [1]; and (ii) the analytical computation of the first and second order yield functions gradients. This comparison has shown that the numerical approximation of the yield function gradients proposed in this paper facilitates the implementation of the constitutive models, and in the case of the implicit analyses, it leads to a significant decrease of the computational time without impairing the accuracy of the finite element results. In addition, we have demonstrated that there is a critical loading rate below which the dynamic implicit analyses are computationally more efficient than the explicit calculations.

Study on the mechanical properties of compacted snow under uniaxial compression and analysis of influencing factors

Snow is an important natural resource and an indispensable part of winter engineering construction in cold regions, but relatively little research has been done on its mechanical properties. To better understand snow in winter in cold regions and during freezing rain and snow disasters, the mechanical properties of snow under uniaxial compression are studied. Uniaxial compression tests were carried out on compacted snow at different temperatures (−5 °C, −10 °C, −15 °C, and − 25 °C), loading rates (1 mm/min ~ 300 mm/min) and densities (0.35 g/cm3, 0.40 g/cm3, 0.45 g/cm3, 0.50 g/cm3, 0.55 g/cm3, and 0.60 g/cm3). The results showed that plastic deformation transitions to brittle failure in snow with an increase in the loading rate. The critical loading rate between the two deformation modes was within the range of 10 mm/min ~ 30 mm/min; as the loading rate increased, the uniaxial compressive strength first increased and then decreased. The loading rate corresponding to the ultimate compressive strength was between 10 mm/min and 30 mm/min. The uniaxial compressive strength increased with increasing density, and the ultimate compressive strength achieved in these tests was 1.68 MPa. Additionally, the uniaxial compressive strength of snow increased with decreasing temperature, and the relationship was especially obvious at low loading rates and high densities. The loading rate, density and temperature are the key factors affecting the uniaxial compressive strength of snow