Damage Constitutive Model Research Articles

Compression Mechanical Properties and Constitutive Model for Soft–Hard Interlayered Rock Mass

The properties of soft–hard interbedded rock masses are significantly impacted by the strength of rock layers and the characteristics of interface surfaces. This study investigates the mechanical properties of soft–hard interlayered rock masses by preparing rock-like specimens with different interface angles. Uniaxial and triaxial compression tests were conducted to examine the compression mechanical characteristics of the specimens. Experimental results demonstrated that in the uniaxial compression tests, the peak strength of the two-layer rock-like specimen exhibits an initial decrease followed by an increase as the interface angle increases. Similarly, the peak strength of the three-layer rock-like specimen also follows a “U-shaped” pattern. The failure of both specimens shifts from tensile failure to shear failure. In the triaxial tests, the strength of the two-layer rock-like specimen initially increases and subsequently decreases as the interface angle increases. In contrast, the intensity of the three-layer rock-like specimen exhibits a decreasing trend, transitioning from shear dilation or tensile failure to shear failure. By utilizing the damage constitutive model to compute the compressive strength of the composite specimen, it was observed that the deviation from the experimental value did not exceed 2.5%, and the overall shape of the curves was in good agreement. Consequently, it is affirmed that the damage constitutive model developed in this study can accurately capture the pre-peak phase of the stress–strain relationship in soft–hard interlayered rock-like specimens, thus providing a valid representation of their mechanical behavior.

Experimental and damage model study of layered shale under different moisture contents

To investigate the mechanical properties and damage evolution law of layered shale under varying moisture contents, we conducted triaxial compression experiments on rock samples with different bedding angles and moisture levels. This study analyzed the variations in mechanical properties of layered shale under different conditions, and established a predicted model for elastic modulus based on different bedding angles and moisture content. Additionally, the damage constitutive model of layered shale was improved. The study revealed that shale’s mechanical properties display anisotropy, which is influenced by the bedding angles and moisture contents. The elastic modulus of the rock increases with the rise of bedding angle, exhibiting a ‘U’-shaped change. Conversely, the mechanical properties of rocks deteriorate, and their brittleness weakens with the increase in moisture content. When the confining pressure increased, the overall mechanical properties of shale were enhanced, and the influence of bedding on shale was weakened, but the deteriorating effect of water on rocks was hardly affected. Based on the above experiments, a predicted model of equivalent elastic modulus of shale considering the coupling effect of bedding and different moisture contents was proposed, which could effectively predict the elastic modulus of layered shale with different moisture content under different confining pressures. Furthermore, based on the predicted model of elastic modulus, an improved damage constitutive model of layered shale under triaxial loading was established, and the damage accumulation trend of layered shale was obtained, which showed an “S”-shaped change with strain. Under the coupling effect of bedding and different moisture contents, the damage of shale was advanced, but the accumulation rate of damage slowed down. With the increase of confining pressure, the influence of bedding and moisture content on the damage characteristics of shale decreased, and the damage curves under different conditions gradually tended to isotropy. The developed damage constitutive model for layered shale under different moisture contents provides theoretical support for the study of reservoir fracturing and wellbore stability.

Versatile coupling of MPM and FEM: A case study of the stability of vegetated slope

Evaluating root reinforcement in the root–soil composite is challenging due to the complex interactions among its components and the variable configurations of the roots. A proposed FEM-MPM coupled model is dedicated to examining the influence of roots on slope stability. The FEM component employed the Truss structural element type to model the dynamics and physics of the root, coupled with a damaged constitutive model, which sheds light on the effects of orientation, cohesion, and friction on the brittle or progressive failure modes of the root. The MPM counterpart provided the capability for large deformation simulation in the post-failure phase of the slope. The framework’s integration was achieved through a penalty method, correcting the dynamics of its members (translation and orientation) and linking the decay of the root with the plastic behavior of the soil through updated geometrical and mechanical properties. Several geotechnical tests and examples, such as pull-out tests, direct shear tests, and vegetated slope collapse simulations, were conducted to validate and verify the robustness of the proposed approach. The results demonstrate the methodology’s capability to capture the mechanism of root reinforcement in vegetated slope stability.

A damage constitutive model of layered slate under the action of triaxial compression and water environment erosion

Based on the macroscopic structure control theory, The slate with a significant bedding plane is a composite rock mass composed of rock blocks containing microscopic defects, joint surface closure elements, and shear deformation elements. Considering the coupling damage effect of water erosion and triaxial compressive load on bedding structure plane, the transversely isotropic damage constitutive model of slate under triaxial compressive load is derived with the dip angle of bedding and confining pressure as the variable. Firstly, based on the statistical theory of continuous damage mechanics and the maximum tensile strain criterion, the transversely isotropic deformation constitutive model of rock block with micro-defects is given; Secondly, based on the phenomenological theory of closed deformation and shear-slip deformation mechanism of layered structural plane under the coupling action of water erosion and triaxial compression load, the calculation formula of axial deformation of layered structural plane under the coupling action is given; Finally, to verify the accuracy of the established constitutive model, triaxial compression tests are carried out to study the influence of dip angle and confining pressure on the macroscopic mechanical properties and mechanism of slate. The results show that: the established triaxial compression damage constitutive model of bedding slate can accurately describe the stress–strain relationship of bedding slate after water environment erosion. With the increase of bedding dip angle, the strength and deformation capacity of the bedding slate first decreases and then increases, showing a U-shaped distribution as a whole. There are three main types of failure: tension shear composite failure, shear slip failure, and splitting tension failure.

Biaxial compressive failure criteria and constitutive model of high-strength geopolymer concrete after high temperature

This paper studies the effect of high temperatures (20℃, 200℃, 400℃, and 600℃) and stress ratios (σ2/σ3) (0.15, 0.3, 0.45, and 0.60) on biaxial compressive strength and strain development patterns of high-strength geopolymer concrete (HGPC). Experimental observations indicate that HGPC exhibits laminar damage similar to ordinary Portland concrete (OPC) before and after exposure to high temperatures, under biaxial compression. Unlike OPC, damage in HGPC initially passes through coarse aggregates at room temperature but shifts predominantly to the aggregate-mortar interface at 600℃. The biaxial compressive strength envelope of HGPC expands with rising temperatures. The increased multiple of biaxial compressive strength (σ3/fm) for HGPC at room temperature rises and then falls with increasing stress ratios, peaking at a stress ratio of 0.45 and surpassing the values for OPC and high-strength concrete (HSC). Before high temperature, the modulus of elasticity of HGPC is higher than that of OPC and decreases with increasing temperature, decreasing by about 45–60% for every 200°C increase, and the reduction is greater than that of OPC. The existing failure criterion is not suitable for HGPC after high temperature, this paper develops a new biaxial compression failure criterion for HGPC before and after high temperature based on Kupfer's criterion, taking into account the effect of temperature. The proposed failure criterion calculation results are well in agreement with the experimental data. A damage constitutive model for HGPC considering the effect of temperature and lateral pressure is also proposed, combining the Weibull distribution model for the ascending branch and a modified empirical model for the descending branch. This combined model effectively predicts the stress-strain relationship of HGPC under various temperature 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.

Residual mechanical properties of high strength concrete BBR9 subjected to dynamic uniaxial compressive loading

In recent years, enormous efforts have been devoted to accurately quantifying the residual load-bearing capacity of concrete at the material level when exposed to elevated temperatures. However, relatively less attention has been given to investigating the effects of dynamic events such as terrorist attacks, earthquakes, and hurricanes, which can cause complete collapse of concrete structures and have significant public and economic consequences. Hence, in the present study, a modified Kolsky compression bar system integrated with a momentum trapping technique was implemented to develop precisely controlled pre-/post peak high strain-rate loading to introduce distinctive states of damage inside the high strength concrete HSC-BBR9 specimens and to measure the corresponding plastic strain. Thereafter, the partially damaged specimens were tested to quantify the residual mechanical properties (e.g., residual stiffness and residual strength) at different plastic strain levels. Furthermore, a high-resolution laboratory micro-CT scanner was used to visualize the 3D crack network morphology in the partially damaged specimens. The findings demonstrated a remarkable decrease in the residual capacity with increasing levels of damage-induced plastic deformation. Additionally, the results showed a fundamental difference in the influence of internal damage on residual stiffness and strength to be acknowledged in the formulations of future constitutive damage models for concrete materials.

A Statistical Damage Constitutive Model for Graded Gravels Incorporating the Degree of Compaction and the Damage-Softening Index

A Statistical Damage Constitutive Model for Graded Gravels Incorporating the Degree of Compaction and the Damage-Softening Index

The effect of recycled fibers on shear properties of concrete at different ages and damage constitutive model based on 3-dimensional morphology analysis

To study the shear properties and damage constitutive model of plain concrete (PC) and nylon fiber recycled from waste reinforced concrete (RNFRC), the direct shear test under different normal stresses (σn, from 1 to 5 MPa) with a continuous horizontal rate of 0.5 mm/min is conducted on the cube specimens at different ages. The 3D roughness parameters of shear surface and the evolution of shear strength components are studied. Results show that the peak shear strength of RNFRC at 3, 7 and 28 d ranges from 6.65 to 12.09, 8.07–13.94 and 8.93–15.27 MPa under different σn, exhibiting varying degrees of enhancement compared to those of PC. The values of the 3D roughness parameter C gradually increase while Rs and the joint roughness coefficient (JRC) decrease with increasing σn. The evolution of shear strength components is affected clearly by σn. The calculation results of shear damage constitutive model match well with the experimental results.

Damage Evolution Characteristics and Constitutive Model for Coal and Rock under Asymmetric Loading.

Tunnels and shaft mining roadways are often subjected to varying degrees of asymmetric loading due to terrain relief or project excavation. In order to analyze the influence of the asymmetric degree of loading on the mechanical properties and damage rupture law of coal rock, uniaxial compression tests of coal rock under four asymmetric loading modes were carried out, the influence of the asymmetric coefficients of loading on macro- and micromechanical properties of coal and rock was analyzed, and a statistical damage constitutive model of coal and rock was established to reflect the asymmetric loading degree. The results of the study show that the peak stress of the coal rock decreases gradually with the increase in the asymmetric coefficient of loading, and the two are linear functions of each other. The distribution of the acoustic emission ringing count peak value is concentrated under uniform loading, while the acoustic emission ringing count rate presents a multipeak phenomenon under asymmetric loading, and the peak value points are scattered. In the case of asymmetric loading, the stress concentration on the edge of the upper loading plate leads to shear failure, and the microscopic cracks are concentrated near the interface between the loading zone and the nonloading zone. According to the established damage constitutive model, when the damage degree is the same, the larger the asymmetric coefficient, the smaller the strain value, which indicates that the asymmetric loading promotes the damage of coal and rock.

Investigation of the Hydro-mechanical Response and Entropy-based Probabilistic Damage Constitutive Model of Basalt under Compression

Investigation of the Hydro-mechanical Response and Entropy-based Probabilistic Damage Constitutive Model of Basalt under Compression

Evolution and prediction of static and seismic properties in diatomite-incorporated concrete members exposed to freeze-thaw cycles

Freeze-thaw cycles induce substantial durability concerns for concrete infrastructures in cold regions. Traditional approaches to assess freeze-thaw degradation in concrete necessitate extensive environmental and mechanical testing, which are both resource-intensive and time-consuming. This paper introduces a concrete freeze-thaw damage constitutive model, designed for the accurate and efficient quantitative evaluation and prediction of the evolution in concrete's mechanical properties post freeze-thaw cycles. This model specifically considers the impact of supplementary cementitious materials, like diatomite. A numerical program was then developed to simulate the stress-strain responses of both diatomite-enhanced and ordinary concrete under freeze-thaw conditions. Based on these insights, the model was extended to structural members, creating a seismic and static finite element simulation methodology. The findings demonstrate the improvements in the mechanical performance of diatomite- incorporated concrete subjected to both static and seismic loads. This model offers theoretical support for predicting the mechanical behavior evolution of concrete materials and structures in cold climate regions.

Damage evolution and failure mechanism of masonry walls under in-plane cyclic loading

Masonry structures often exhibit poor seismic performance during earthquakes owing to their low material strength, structural integrity, and ductility. To address the mechanism of in-plane damage and collapse of masonry walls subjected to earthquake ground motion, three full-size brick walls, one with structural columns and two without structural columns, were designed and constructed in this experimental study to quantitatively investigate the effect of structural columns on the seismic performance of masonry walls. Quasi-static tests of masonry walls subjected to cyclic lateral loading were conducted using electrohydraulic servo actuators. The in-plane damage evolution and failure mode of the masonry walls under lateral loading were investigated. A numerical model with a novel plastic damage constitutive model of masonry was established. The accuracy of this model and the calculation results were verified by comparing them with the crack development and mechanical property curves obtained from the experiments. Based on the numerical model, a parametric analysis was conducted to investigate the influence of critical factors, such as mortar strength, vertical load, and height-to-width ratio, on the seismic performance of masonry structures. The test results showed that structural columns can effectively improve the performance of masonry structures. Properly installed structural columns can improve the peak load-bearing capacity, ductility, and energy dissipation of masonry structures. The masonry damage constitutive model used in this study could simulate the damage to masonry wall specimens well and reflect the hysteretic curves of the specimens within an acceptable range of accuracy. Thus, it provides a valuable reference for physical experiments. An appropriate mortar strength and vertical compressive stress can effectively enhance the load-bearing capacity of masonry structures within a certain range. For structural column walls. Walls with mortar strengths (average compressive strength) of 12.5 MPa, 10 MPa, 7.5 MPa, and 5 MPa showed an increase in peak bearing capacity of 26.2 %, 23.9 %, 18.5 %, and 9.4 %, respectively, compared to walls with mortar strengths (average compressive strength) of 2.5 Mpa. The aspect ratio had a significant impact on the shear load-bearing capacity of the masonry walls. An increase in the aspect ratio led to a transition from shear failure to flexural failure and a subsequent decrease in shear load-bearing capacity. For masonry walls with structural columns, increasing the diameter of the longitudinal steel in the structural columns can enhance the load-bearing capacity of the masonry wall, resulting in a significant improvement in its overall performance.

Damage constitutive model and meso-failure characteristics of freeze–thaw rock under triaxial compression

Damage constitutive model and meso-failure characteristics of freeze–thaw rock under triaxial compression

Creep behavior and damage constitutive model of sandstone: an experimental study on seepage-load coupling

Creep behavior and damage constitutive model of sandstone: an experimental study on seepage-load coupling

Compaction elastoplastic damage constitutive model of rock under hydro-mechanical coupling: A heuristic modeling method based on internal state variables theory

Based on the internal state variables (ISV) theory, this paper employs a heuristic modeling approach to investigate the compaction elastoplastic damage constitutive model of rocks under hydro-mechanical coupling. The heuristic modeling method demonstrated herein can seamlessly integrate with existing constitutive theories, facilitating a broader spectrum of research on hydro-mechanical coupling constitutive models. Furthermore, a numerical solution was conducted in the principal axes via stress spectrum decomposition, which can well reflect the distinct characteristics of compaction deformation and the influence of water pressure on rock stress distribution. Utilizing the classic Drucker-Prager (D-P) criterion, the modeling method and numerical algorithm were implemented to derive a hydro-mechanical coupling compaction elastic–plastic damage constitutive model. This contribution expands the application domain of the classic D-P criterion within the context of hydro-mechanical coupling environments. The rationality of the model was confirmed through compression test data under various water pressures and confining pressures. Water pressure increases nonlinear compaction deformation by changing the opening degree of microcracks under low confining pressure, which has not been paid enough attention in existing research. This study thoroughly considers the influence of water pressure on compaction deformation. The developed process of “heuristic modeling method-numerical method-model application” is helpful for enriching the constitutive theory of rock under hydro-mechanical coupling.

Numerical simulation and multi-objective optimization of thin-walled aluminum/carbon fiber reinforced plastic hybrid tubes under axial crushing

Crushing behavior analysis and energy absorption optimization are crucial for lightweight structures in automotive applications. The present paper aims to investigate the crushing behavior of thin-walled aluminum/CFRP hybrid tubes under axial loading using an explicit finite element (FE) simulation. The damage constitutive models of aluminum and CFRP are implemented by coding the user-defined subroutine VUMAT in ABAQUS/Explicit, which includes the damage initiation and evolution laws and element deletion scheme. Parametric studies are conducted to assess the effects of radius and aluminum layer thickness on the crushing performance of hybrid tubes. Additionally, a multi-objective optimization is performed on the Isight platform using a non-dominant sorting genetic algorithm (NSGA-II) and technique for order preference by similarity to ideal solution (TOPSIS) with entropy weight method. The optimization aims to maximize crashworthiness and increase energy absorption capacity, enabling designers to select an optimum size ratio.

Mechanical-permeability characteristics of composite coal rock under different gas pressures and damage prediction model

Determining the influence of gas pressure on the mechanics, permeability, and energy evolution of gas-bearing composite coal is helpful to better understand the formation process and prevention measures of gasdynamic disasters. In this paper, true triaxial mechanical-permeability tests are carried out on the gas-bearing composite coal rock under different gas pressures, focusing on the influence of gas pressure on the mechanics, permeability, and energy response characteristics of the composite coal rock, and a damage constitutive model based on energy dissipation is established. The results show that increasing the gas pressure decreases the load bearing capacity, strain, pre-peak relative permeability, and deformation capacity of the sample. The greater the gas pressure is, the greater the relative permeability decreases and the greater the post-peak relative permeability increases. The gas pressure has a great influence on the energy of the sample. The elastic strain energy ratio (Ue/U) increases with the increase in gas pressure, and the dissipative energy ratio (Ud/U) decreases with the increase in gas pressure. The coal-rock composite constitutive model based on energy dissipation is in good agreement with the experimental curves.

Damage Research of the Cut-and-Cover Tunnel under Static and Seismic Load

This article uses the finite element software ABAQUS to establish an damage constitutive model for cut-and-cover tunnels, which studies the damage parameters for different filling heights under static load and damage evolution under seismic load. It is found that high filling has a significant impact on the damage of cut-and-cover tunnels, and earthquake waves affect the degree and distribution of lining damage. By studying the model of setting the LRL, it was found that it can effectively reduce the degree of damage. Therefore, it is necessary to set a LRL for high backfill cut-and-cover tunnels. And the damage parameters of different parts of the cut-and-cover tunnel are analyzed, and it was found that the arch crown and arch shoulder of the cut-and-cover tunnel were the most prone to damage. Therefore, reinforcement measures should be taken in the structural design.

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.