Dynamic Damage Constitutive Model Research Articles

Dynamic statistical damage constitutive model based on the Hoek–Brown criterion at high strain rates

Dynamic statistical damage constitutive model based on the Hoek–Brown criterion at high strain rates

Impact response and constitutive model of basalt-polypropylene fiber-reinforced coral aggregate concrete

Basalt-polypropylene fiber-reinforced coral concrete (BPFRCAC) is a popular choice for engineering materials in the reef environment, but the dynamic behavior of BPFRCAC under extreme dynamic loads remains unclear. This study explores the impact response of BPFRCAC at strain rates ranging from 31 to 141 s−1 using split Hopkinson pressure bar (SHPB). It examines the effects of strain rate on the dynamic mechanical properties of BPFRCAC, and establishes quantitative models of the relationship between the strain rate and key mechanical parameters, including dynamic compressive strength, critical strain, dynamic elastic modulus, and toughness index. The results showed that these properties of BPFRCAC are significantly influenced by the strain rate, showing increases that correlate with the strain rate. The addition of basalt fibers (BF) and polypropylene fibers (PF) not only mitigates the failure extent of BPFRCAC but also enhances the strain rate's impact on its dynamic compressive strength and dynamic modulus of elasticity, particularly when both fibers are mixed. The failure modes of BF and PF depend on the strain rate; at lower strain rates, the probability of fiber pull-out is higher than at higher strain rates, where BF and PF are more likely to snap. A viscoelastic dynamic damage constitutive model suitable for BPFRCAC is proposed, which accurately describes the dynamic mechanical behavior of BPFRCAC. These findings provide important design insights into the use of BPFRCAC under impact conditions, and promote its wide application in reef construction projects.

A Dynamic Damage Constitutive Model of Rock-like Materials Based on Elastic Tensile Strain

To accurately characterize the damage of rock-like materials under simultaneous or alternating tensile and compressive loading, a dynamic damage constitutive model for rock-like materials based on elastic tensile strain is developed by integrating the classical compressive plastic damage model and the tensile elastic damage model. The model is based on the Holmquist–Johnson–Cook (HJC) and Kuszmaul (KUS) models, categorizing the element stress state into tensile and compressive states through positive and negative elastic volumetric strain. It utilizes elastic tensile strain to enhance the calculation method for tensile cracks, determining the tensile strength of the principal direction based on the contribution rate of tensile principal stress for uniaxial/multiaxial loading. Additionally, it establishes a maximum elastic tensile strain rate function to rectify the model’s effect on the tensile strain rate. Through the LS-DYNA subroutine development, the model proficiently delineates the distribution of ring-shaped cracks on the frontal side and strip-shaped cracks on the rear side of the reinforced concrete slab subjected to impact loading. Numerical simulations demonstrate that the model provides more accurate damage prediction results for stress conditions involving simultaneous or alternating compression and tension, offering valuable insights for damage analysis in engineering blasting or impact penetration.

Dynamic tensile mechanical properties of red sandstone under different pulse widths and amplitudes: Brazilian disk experiment and macroscopic and microscopic analysis

To investigate the dynamic tensile mechanical properties of red sandstone under varying impact pulse widths and amplitudes, we employed the response surface methodology to examine the dynamic response characteristics of sandstone under different bullet lengths and impact velocities. Subsequently, a dynamic damage constitutive model for sandstone was developed. Macroscopic and microscopic features of sandstone were analyzed through digital image correlation (DIC) and scanning electron microscopy (SEM) experiments. Additionally, ANSYS software was utilized to analyze stress wave characteristics under controlled shock waves and the impact of geological factors on rock fracturing effects. The findings revealed the following. First, the length and impact velocity of bullets exhibit an interactive effect on the tensile response characteristics of sandstone. Peak load, energy consumption rate, and energy density display a positive correlation with bullet velocity. Second, according to the DIC results, the fractal dimension of the crack is negatively correlated with the length of the bullet during equal energy impacts. Third, microscopic failure modes included fractures along particle cementation and through particles, with section roughness decreasing as bullet length increased under equivalent energy impacts. Fourth, a dynamic damage constitutive model (R2 ≥ 0.84) was established based on the Zhu-Wang-Tang (Z-W-T) model and Drucker-Prager (D-P) criterion, clarifying model parameters and influence rules. Fifth, under controlled shock waves, the pulse width facilitates crack propagation, while the pulse amplitude initiates crack formation. Optimal rock breaking efficiency is achieved when stress waves exhibit a large pulse width and low radiation values, meeting specific threshold conditions.

Experimental study on dynamic impact of hydrothermal treated coal in different coal ranks

The new supercritical hydrothermal fracturing technology possesses promising applications in the field of coal and coalbed methane extraction. The research designed hydrothermal processing and true triaxial Hopkinson bar impact fracturing experiments on coals of different coal rank, measured the damage using acoustic waves and scanning electron microscopy. The results of the study showed that: 1. Hydrothermal treatment caused initial damage to coals in different coal ranks, resulted in the reduction of coal acoustic wave speed and dynamic strength. 2. As the coal rank advanced, the metamorphic degree of coal increased and its dynamic strength increased, and the dynamic strength of anthracite reached 149.79 MPa. 3. A pore expansion model of hydrothermally treated coal was established, which indicated that the porosity of hydrothermally fractured coal increased as a whole but the distribution of pore size was more concentrated in the process of hydrothermal fracturing in conjunction with adsorption resolution curves. 4. A dynamic damage constitutive model of coal after hydrothermal treatment under true triaxial circumferential pressure was proposed, which had great significance for evaluating the dynamic disaster safety after hydrothermal fracturing in coal mines.

Dynamic uniaxial compression mechanical properties of self-compacting rubber concrete subjected to different strain rates

Rubber concrete is a kind of light green building material, which is prepared by mixing rubber powder or rubber crumb into ordinary concrete in a certain proportion and then introducing rubber concrete through vibration-free technology to prepare self-compacting rubber concrete. Uniaxial compression tests were carried out on self-compacting rubber concrete with two particle sizes at different strain rates, and the effects of strain rate and rubber content on the dynamic mechanical properties of self-compacting rubber concrete were studied. The microstructure of self-compacting rubber concrete before and after damage was analyzed. Compared with ordinary concrete, the self-compacting rubber concrete is capable of maintaining good integrity during damage, when the rubber powder content exceeds 10% and the rubber crumb content exceeds 15%. The results indicate that as the strain rate increases, both the peak stress and the elastic modulus increase, indicating the strain rate enhancement effect, while the strain rate effect of the peak strain is not evident. Moreover, the model equations of peak stress and elastic modulus strain rate effect were established, the dynamic damage constitutive model was proposed, the damage evolution was analyzed, and the stress intervals were assigned to the various stages of damage evolution.

A dynamic damage constitutive model and three-dimensional internal crack propagation of rock-like materials in bond-based peridynamic

The original bond-based peridynamic model addresses brittle fracture rather than progressive fracture. It also does not account for the impact of strain rate on bond strength and fails to incorporate the impact of internal length on non-local long-range forces. As a result, it is inadequate for simulating the dynamic failure of rock-like materials under impact loading. To address these limitations, a new approach involves a sextic polynomial attenuation function. This function captures the impact of internal length on non-local long-range forces and leads to the derivation of a corresponding micro-modulus expression. A damage function and a new failure criterion are integrated to describe the nonlinear mechanical behavior and progressive failure of rock-like materials. The influence of strain rate on bond dynamic strength is considered to reflect the strain rate effect in rock materials. The outcome is a newly proposed dynamic damage constitutive model that overcomes the three shortcomings of the original bond-based peridynamic model when simulating the dynamic failure of rock-like materials. Numerical examples are simulated based on this model, and their results are compared with the experimental data. This comparison allows further exploration of the volumetric fracturing behavior and mechanical properties of rock specimens with internal flaws in three dimensions when subjected to impact loading. The findings demonstrate the effectiveness of the proposed model in accurately simulating crack propagation and mechanical properties across varying strain rates in rock-like materials. Notably, the internal flaw's depth significantly influences the specimen's mechanical properties and energy utilization efficiency at a specific flaw angle α=90°. Complex three-dimensional cracks, consisting of shell-like, wing, anti-wing, and shear cracks, emerge due to the interconnection of various crack types. The shape of these cracks is intricately linked to the flaw angle and depth. Ultimately, this model solves the challenge of capturing internal crack growth during dynamic impact processes that are often difficult to observe in experimental tests.

The Dynamic Mechanical Properties and Damage Constitutive Model of Ultra-High-Performance Steel-Fiber-Reinforced Concrete (UHPSFRC) at High Strain Rates.

A high strain rate occurs when the strain rate exceeds 100 s-1. The mechanical behavior of materials at a high strain rate is different from that at middle and low strain rates. In order to study the dynamic compressive mechanical properties of ultra-high-performance steel-fiber-reinforced concrete (UHPSFRC) at high strain rates, an electro-hydraulic servo universal testing machine and a separate Hopkinson pressure bar (SHPB) with a diameter of 120 mm were used, respectively. A quasi-static compression test (strain rate 0.001 s-1) and impact compression test with a strain rate range of 90~200 s-1 were carried out to study the failure process, failure mode, and stress-strain curve characteristics of UHPSFRC at different strain rates and quantify the strain rate strengthening effect and fiber toughening effect. Based on the statistical damage theory and energy conversion principle, a dynamic damage constitutive model considering the effects of strain rate and fiber content was constructed. The results showed that the rate correlation of UHPSFRC and the fiber toughening properties showed a certain coupling competition mechanism. When the fiber content was less than 1.5%, with an increase in the steel fiber content, the crack initiation and propagation time of the specimen was extended, and the strain rate sensitivity gradually decreased. When the fiber content was 2%, the impact compressive strength of the specimen was optimal. Compared with UHPC, the dynamic increase factor (DIF) of UHPSFRC was significantly lower. The dynamic damage constitutive model established in this paper, considering the influence of strain rate and fiber content, has a good applicability and can describe the mechanical behavior of UHPSFRC at a high strain rate.

Thermal-mechanical coupling in drilling high-performance CFRP: Scale-span modeling and experimental validation

The focus of this study is to explore a scale-span thermal–mechanical coupling method for predicting the dynamic mechanical progressive failure behaviors and predicting thermal damage during the drilling process of Carbon Fiber Reinforced Plastic (CFRP). Initially, a thermal conduction constitutive model of drilling CFRP was developed based on the proposed thermal distribution ratio calculation method. Meanwhile, a dynamic span-scale progressive damage constitutive model for CFRP, incorporating modified micromechanics failure criterion with bilinear damage evolution laws, was proposed, and a bilinear cohesive model, including three damage modes, is employed to simulate interlaminar delamination. Subsequently, a user-defined material subroutine VUMAT was implemented on the ABAQUS/Explicit platform to simulate the thermal–mechanical coupling behaviors of drilling T700S-12K/YPH-23 CFRP using a twist drill bit. Finally, a comprehensive information monitoring platform for CFRP drilling experiments was established to validate the accuracy of the simulation results by considering drilling temperature, thrust force, and hole-wall morphology. The results demonstrate excellent agreement between the established thermal–mechanical coupling span-scale model and the experimental data. Furthermore, the simulation effectively captures the various damage behaviors and thermal conduction phenomenon, that occur during the intact drilling process.

Dynamic mechanical response and damage constitutive model of end-jointed rock bridge with different water content states under impact load

In rock slope engineering, the dynamic mechanical behavior of rocks is significantly influenced by the length of rock bridges and their moisture content. This study explored the dynamic characteristics of defective rocks under impact loads through dynamic impact tests on specimens varying in rock bridge lengths and moisture states, conducted using a Split Hopkinson Pressure Bar (SHPB). The experimental results revealed that both moisture state and rock bridge length markedly affect the dynamic compressive strength and elastic modulus. Additionally, there is a significant correlation between the energy dissipation density and the specimen's moisture state and rock bridge length. The failure process, captured via a high-speed camera, exhibited a transition in fracture mode from predominantly tensile to tensile-shear failure with increasing rock bridge length. Moreover, an enhanced ZWT model was developed and validated for the dynamic damage constitutive model of defective rocks. This model, incorporating four parameters, precisely characterizes the stress–strain relationship of defective rocks under high strain rates and effectively demonstrates the dynamic response of rocks with varying rock bridge lengths and moisture states. The findings of this study are vital for advancing the understanding of rock dynamics in varying conditions and offer significant insights for geological and civil engineering applications, particularly in the design and assessment of rock structure stability in slopes.

Dynamic damage constitutive model for UHPC with nanofillers at high strain rates based on viscoelastic dynamic constitutive model and damage evolution equation

This study established a dynamic damage constitutive model for ultra-high performance concrete (UHPC) with nanofillers, based on a viscoelastic dynamic constitutive model and a damage evolution equation. Ten types of nanofillers, including particle, tube and flake nanofillers, were incorporated to modify UHPC. The split Hopkinson pressure bar was used to obtain the relationship between stress and strain of UHPC specimens at a strain rate of 200/s-800/s. The experimental results indicated that the dynamic compressive strength of UHPC with nanofillers at strain rates of approximately 200/s, 500/s, and 800/s can reach 172.8 MPa, 219.6 MPa, and 275.9 MPa, respectively, reflecting an increase of 85.2 %, 76.5 %, and 53.9 % compared with the blank UHPC. The established dynamic damage constitutive model considered the damage accumulation with strains under dynamic loading. The fitting coefficients of the dynamic damage constitutive model, when compared against experimental results, range from 0.8796 to 0.9963, showing a higher accuracy compared with traditional Zhu-Wang-Tang (ZWT) viscoelastic model, especially at a strain rate of approximately 200/s.

Dynamic Mechanical Properties of Heat-Treated Shale under Different Temperatures

As a typical rock, shale’s reservoir depth is about 1500–4000 m, and the temperature of the shale reservoir at this depth is 150 °C. Therefore, in order to study the dynamic strength of shale at this temperature, it is necessary to consider the effects of temperature and strain rate on the dynamic strength of shale, and then establish the damage constitutive model of shale. This paper took black shale from the Sichuan Basin as the research object, combined it with the separated Hopkinson bar experiment and temperature control system, and conducted the Hopkinson bar experiment on shale at room temperature, 60 °C, 90 °C, 120 °C, and 150 °C, and at three groups of air pressures of 0.2 MPa, 0.3 MPa, and 0.4 MPa. The stress–strain curves of shale at the same strain rate and different temperature and at the same temperature and different strain rate were obtained. In the temperature difference range of this experiment, the dynamic strength of the sample presented two opposite trends (increasing and decreasing) with the increase in temperature, which was determined via the direction of the bedding. The peak strength linearly increased with the increase in strain rate. Based on the Weibull statistical distribution and the D–P failure criterion, a statistical damage constitutive model of shale dynamic strength considering the effects of temperature and strain rate was obtained. By modifying the parameters F0 and m, the dynamic strength statistical damage constitutive model of shale was in good agreement with the experimental results.

Elastic–Plastic Dynamic Damage Constitutive Model of Cement-Stabilized Steel Slag

Elastic–Plastic Dynamic Damage Constitutive Model of Cement-Stabilized Steel Slag

Mechanical performance study of basalt-polyethylene fiber reinforced concrete under dynamic compressive loading

In order to enhance concrete's impact resistance, this study investigates the effects of single basalt fiber and basalt-polyethylene hybrid fiber on concrete through split Hopkinson pressure bar (SHPB) tests, emphasizing their significance in engineering applications. A comparative analysis of the failure modes, dynamic compressive strength, dynamic compressive toughness, and dynamic growth factor of specimens was conducted under different strain rates and polyethylene fiber volume fractions. The study considered concrete damage, strain rate effect, and the toughening effect of fibers, introducing the damage factor, and establishing a dynamic damage constitutive model for fiber-reinforced concrete. The results showed that basalt-polyethylene fiber reinforced concrete (BPFRC) exhibited better impact resistance and deformation capability. There were improvements observed in dynamic compressive strength, dynamic compressive toughness, and dynamic growth factor. The addition of basalt fiber (BF) and polyethylene fiber (PE) played a buffering role in inhibiting crack propagation and slowing down the damage process. The optimum PE volume fraction for dynamic compressive strength was 0.1% at a strain rate of 60 s−1, 0.15% at a strain rate of 95 s−1, and 0.05% at a strain rate of 120 s−1, all with a BF volume fraction of 0.25%. The optimum fiber volume fractions for dynamic compressive toughness and dynamic peak toughness were consistent, both at 0.25% BF and 0.1% PE. The established dynamic damage constitutive model for fiber-reinforced concrete can effectively describe the impact resistance performance of BPFRC, and the experimental curves fit well with the constitutive curves. Furthermore, it was observed that BF acted as macrofibers, bridging to restrain the post-hardening cracking of concrete, while PE acted as microfibers, inhibiting the propagation of plastic cracks, reducing internal defects in concrete, and enhancing the ductility and toughness of concrete. Consequently, BPFRC holds significant potential value in engineering applications.

Analyzing the Energy and Damage Constitutive of Cemented Backfill with Different Water Content under Dynamic Load.

The dynamic characteristics of the filling body are the key parameters for designing the filling ratio and evaluating the stability of an underground stope. The different environment (water-bearing state) of the filling body in the underground stope exerts a complex impact on the mechanical behavior of the filling body. Therefore, six groups of cemented filling body specimens with different states were formed and subjected to dynamic uniaxial impact tests. The effects of water content on the mechanical properties, fractal dimension, and deformation damage characteristics of the cemented backfill under dynamic load were analyzed in depth, and a dynamic damage constitutive model that considers water damage and the compaction stage was established. The results indicate the following: (1) Due to the change of the specimen from the dry state to the water saturation state, the dynamic compressive strength of the cemented filling body decreases from 5.03 Mpa to 1.79 Mpa; however, the ductility of the specimen generally increases, and the filling body specimens with different water contents mainly exhibit tensile failure. (2) There is a significant nonlinear relationship between the water content and the fractal dimension Db of the cemented backfill specimen, and the growth rate of the fractal dimension Db tends to slow down with the increase in the water content. (3) From the energy evolution perspective, the water content of the specimen exerts a significant effect on the elastic deformation and failure stage of the stress-strain curve, and the slope of the dissipated energy-strain curve decreases with the increase in water content. (4) Based on the Weibull distribution and damage theory, a statistical damage constitutive model of cemented backfill was established, and it was compared with the experimental curve to verify the rationality of the model. Therefore, the relationship between stress and damage and the strain curves is discussed, and it is inferred that the damage evolution curve of cemented backfill is a typical S-shaped curve that exhibits a stable development-rapid increase-tending to be gentle. This study can provide a theoretical reference for further understanding the dynamic behavior and stability of backfill under different water conditions.

Effect of water saturation on dynamic behavior of sandstone after wetting-drying cycles

Fully understanding the influence of water on the rock materials' mechanical properties is of great significance to the safety design and evaluation in rock engineering. In this study, sandstone was pretreated with different wetting-drying cycles (0-15), and its pore characteristics were characterized by low-field nuclear magnetic resonance (LF-NMR) and scanning electron microscope (SEM) methods. Then, the split Hopkinson pressure bar (SHPB) tests with the same impact velocity were carried out in its dry and saturated states, respectively. The effects of water saturation on the dynamic behavior of sandstone under different porosity conditions and their mechanisms were emphasized. The results show that with the increase of cycle numbers, the porosity of sandstone increases, the dynamic strength and the total energy dissipation decreases. Moreover, the proportion of post-peak energy dissipation rises, and the degree of fragmentation intensifies. With the increase of porosity, the effect of water saturation on dynamic strength changes from enhancement to weakening. This may be related to the competition between the the Stefan effect and the contribution of pore water pressure. Finally, a dynamic damage constitutive model considering the coupling effect of the wetting-drying cycles and dynamic loads was established, and its effectiveness was verified.

Dynamic Mechanical Response and Damage Constitutive Model of Multi-flawed Rocks Under High Strain Rates

Dynamic Mechanical Response and Damage Constitutive Model of Multi-flawed Rocks Under High Strain Rates

Dynamic response characteristics and damage rule of graphite ore rock under different strain rates

In the process of mining graphite mine, rock mass is often subjected to dynamic loads such as blasting or mechanical crushing, which involves dynamic responses of different strain rates, and blasting and crushing effect are affected by the rock dynamic properties and damage specials. The dynamic response characteristics and damage rule of graphite ore rock under different strain rates are very important but rarely studied in the past. To study these issues and provide support for graphite ore rock mining, the dynamic compression tests of graphite ore rock under five kinds of impact pressures were designed and carried out by using the Split Hopkinson Pressure Bar (SHPB) test system, combining with the high-speed photography system and crushing screening tests. The dynamic characteristics, crushing process, crushing mode, crushing form and fragmentation distribution of the graphite ore rock under different strain rates were analyzed. The results show that the dynamic characteristics of the graphite ore rock have obvious strain rate effect. The hardening coefficient (DIF) is positively correlated with the cubic root of strain rate, and the softening factor (K) is negatively correlated with the cubic root of strain rate. Shear failure mainly occurs in the graphite ore rock under impact load, and the crushing process can be divided into five stages, they are compaction, crack initiation, crack expansion and penetration, fragmentation collision and fragmentation fall. In addition, the crushed blocks are mainly triangular pyramid (or cone-like) fine granular and powder. The broken fragments of the graphite ore rock are in accord with the fractal geometry characteristics. That is, the average broken particle size (dS) decreases linearly with the increase of strain rate, and the fractal dimension (Da) increases weakly with the increase of strain rate. Based on D-P fracture criterion and Weibull distribution model, the dynamic damage constitutive model of the graphite ore rock was established, and the correlation between strain rate and Weibull distribution parameters (m and F0) was used to reasonably modify the damage constitutive model. The modified damage constitutive model curve is in good agreement with the experimental curve, which can basically reflect the strain rate effect of the dynamic characteristics of the graphite ore rock and the evolution characteristics of the dynamic stress–strain curve at different stage.

Mechanical properties, damage evolution and energy dissipation of cemented tailings backfill under impact loading

In order to explore the influence of average strain rate(ASR) on mechanical properties, damage evolution and energy dissipation of cemented tailings backfill(CTB), the dynamic test of CTB was carried out in the laboratory. This study shows that dynamic peak stress and initial crack stress of CTB increase exponentially with the increase of ASR, indicating that the characteristic stress of CTB has a significant strain rate effect. The dynamic peak strain and initial crack strain of CTB also increase exponentially with the increase of ASR, and the CTB with lower cement content is more likely to produce deformation and failure. The increase of ASR can improve the energy indexes of CTB at the peak stress point, and the increase of cement content can also improve the energy parameters of CTB. The energy storage limit of CTB increases exponentially with the increase of ASR. In addition, a dynamic statistical damage constitutive model of CTB was established considering ASR, and the accuracy and reliability were verified. There are three stages for the damage failure of CTB: rapid growth stage of damage, slow growth stage of damage and stable growth stage of damage. In addition, the high strain rate has a certain retarding effect on the development of cracks inside the CTB, thus inhibiting the rapid growth of damage value. Under impact loading, the CTB samples are mainly axial macroscopic main crack tensile failure and crushing failure. When the average strain rate is higher than the critical strain rate, the failure pattern of CTB is mainly crushing failure. When the average strain rate is basically the same, the damage degree of CTB with higher cement content is smaller.

Dynamic and Damage Characteristics of Mortar Composite under Impact Load

In the process of underground construction, it is common to spray concrete on the working surface, which will form a concrete-rock composite structure, to achieve the expected reinforcement effect. Compared with pure concrete or rock structures, composite structures have different mechanical properties, energy evolution and damage characteristics. Understanding the dynamic mechanics and damage characteristics of composite structures under impact loads is important to the safety of underground engineering construction. First, dynamic compression tests on different grades of mortar-sandstone composite specimens were carried out by using a Hopkinson pressure bar system to discuss the effect of impact velocities on the mechanical properties and failure modes of composite specimens. The results show that the dynamic peak stress, strain energy density and fragmentation block of the mortar-sandstone composite have an obvious strain rate effect. With an increase in impact velocity, the internal cracks of the sample do not have sufficient time to expand, and the energy absorbed by the sample leads to the continuous initiation of new cracks in the sample, resulting in an increasing damage degree of composite specimens. The increase in mortar strength can significantly increase the peak stress, improve the load-bearing capacity of the sample, and reduce the degree of sample damage. At the same impact velocity, the fragmentation degree of the mortar sample is more severe than that of sandstone, and the mortar sample is broken into powder debris, while the sandstone is broken into fragments. In addition, according to the failure properties of the composite sample, the mortar and sandstone samples are described by different damage models, and the dynamic damage constitutive model of the mortar-sandstone composite is established based on the overlay principle. The dynamic test results were fitted. The research shows that the fitting curves of the model are well fitted with the test curves and that the model accurately reflects the changes in the mechanical parameters of the composite specimens.