Elastic Damage Research Articles

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.

Research on the widths of protective coal pillars in main roadway based on the damaged foundation beam model

Long-term stability of the protective coal pillars in coal mines can ensure normal and safe use of roadways; in turn, the integrity of the roadway plays an important role in safe and efficient mining in coal mines. The initial damage and rheological damage caused by coal-seam excavation disturbance have important influences on the selection of reasonable widths of the protective coal pillars. Based on damage mechanics and the theory of elastic foundation beams, a coupled damage constitutive relationship of rock-like materials is proposed in this work by considering the influence of threshold and residual strength to establish the mechanical model of the elastic damage foundation beam. By theoretical analysis and numerical calculation, the differential equation of the deflection curve of the beam is solved, the influence range of the advance abutment pressure under the condition of coupling damage is obtained, and the width of the protective coal pillar is determined. The results show that compared with the elastic foundation beam model, after considering the coupling damage of coal, the influence range of the advance abutment pressure increases with time over a certain duration. At the end of this duration, the influence range of the advance abutment pressure remains almost unchanged. For the case considered in this paper, the long-term stability of the roadway is guaranteed when the width of the coal pillar is 120 m. The potential interference or change related to the specific situation of the site can be studied by changing the relevant parameters in the model to study different working conditions, or the damage of the roof rock beam during the mining process of the working face can be considered, which will be the subject of further research in the future.

On the sensitivity of sea ice deformation statistics to plastic damage

Abstract. We implement a plastic damage parametrization, distinct from the elastic damage in the elasto-brittle framework, in the standard viscous–plastic (VP) sea ice model to disentangle its effect from resolved model physics (visco-plastic with and without damage) on its ability to reproduce observed scaling laws of deformation. To this end, we compare scaling properties and multifractality of simulated divergence and shear strain rate, as proposed in the Sea Ice Rheology Experiment (SIREx) studies, with those derived from the RADARSAT Geophysical Processor System (RGPS). Results show that including a plastic damage parametrization in the standard viscous–plastic model increases the spatial but decreases the temporal localization of simulated linear kinematic features (LKFs) and brings all spatial deformation rate statistics in line with observations from RGPS without the need to increase the mechanical shear strength of sea ice as recently proposed for lower-resolution viscous–plastic sea ice models. In fact, including damage with a healing timescale of th=30 d and an increased mechanical strength unveils multifractal behavior that does not fit the theory. Therefore, a plastic damage parametrization is a powerful tuning knob affecting the deformation statistics of viscous–plastic sea ice.

Anisotropic Damage Mechanism of Coal Seam Water Injection with Multiphase Coupling.

After coal seam water injection, coal mechanical properties will change with brittleness weakening and plasticity enhancement. Aiming at the problem of coal damage caused by the coal seam water injection process, based on nonlinear pore elasticity theory and continuum damage theory, a nonlinear pore elastic damage model considering anisotropic characteristics is proposed to calculate and analyze the gas-liquid-solid multiphase coupling effect with the fully coupled finite element method during the coal seam water injection process. The research results indicate that the wetting radius of calculated results by the model agrees well with the in situ test results, and the relative errors are less than 10%. Water saturation and induced damage of the coal body in the parallel bedding direction are greater than that in the vertical bedding direction during the coal seam water injection process, which exhibits significant anisotropic characteristics. With the increasing water injection time, the induced damage of the coal body also increases near the water injection hole. Considering the inherent permeability arising with damage, it has a significant impact on both water saturation and induced damage, which also indicates that there is a strong interaction between water saturation and induced damage. The theoretical model reveals the coal damage mechanism of gas-liquid-solid multiphase coupling after coal seam water injection and provides a theoretical prediction of coal containing water characteristics in engineering practice.

Elastic Damage Healing Model Coupling Secondary Damage Variable for Self Healing Materials

A one-dimensional constitutive model, based on the principles of continuum damage mechanics, is developed for capturing healing in certain materials during unloading and rest periods. A secondary damage variable is defined to address the drawback of existing models for damage and healing in capturing the complete material failure. An energy-based damage evolution function is adopted for primary and secondary damage variables, and phenomenological healing evolution is defined. The proposed implicit elastic damage-healing model is implemented by the return-mapping technique, and the model response is demonstrated for different loading histories.

Unveiling deformation behavior and damage mechanism of irradiated high entropy alloys

The oxide dispersion strengthening (ODS) high entropy alloy (HEA) exhibits the high elevated temperature performance and radiation resistance due to severe atomic lattice distortion and oxide particles dispersed in matrix, which is expected to become the most promising structural material in the next generation of nuclear energy systems. However, microstructure and damage evolution of irradiated ODS HEA under loading remain elusive at submicron scale using the existing simulations owing to a lack of atomic-lattice-distortion information from a micromechanics description. Here, the random field theory informed discrete dislocation dynamics simulations based on the results of high-resolution transmission electron microscopy are developed to study the dislocation behavior and damage evolution in ODS HEA considering the influence of severe lattice distortion and nanoscale oxide particle. Noteworthy, the damage behavior shows an unusual trend of the decreasing-to-increasing transition with the continuous loading process. There are two main types of damage micromechanics generated in irradiated ODS HEA: the dislocation loop damage in which the damage is controlled by irradiation-induced dislocation loops and their evolution, the strain localization damage in which the damage comes from the dislocation multiplication in the local plastic region. The oxide particle hinders the dislocation movement in the main slip plane, and the lattice distortion induces the dislocation sliding to the secondary slip plane, which promotes the dislocation cross-slip and dislocation loop annihilation, and thus reduces the material damage in the elastic damage stage. These findings can deeply understand atomic-scale damage mechanism and guide the design of ODS HEA with high radiation resistance.

Determination of nonlocal kernels in nonlocal models for solving strain localization problems

ABSTRACT The strain localization during the damage and failure of materials can be accurately predicted by nonlocal continuum theories. Yet, the results of theoretical predictions are directly affected by the nonlocal kernel formulation. In this study, the correlation between the nonlocal kernel formulation and the strain localization simulation results is revealed. First, based on the nonlocal damage theory, a novel free energy functional was proposed with strain and damage parameters as independent variables, and a constitutive relation considering nonlocality and elastic damage was derived within the framework of continuum thermodynamics. Then, one-dimensional governing equations were obtained through the dual-linearization method. Finally, strain localization predictions obtained with several nonlocal kernel formulations were presented, and the relationship between the nonlocal kernels and the solution was analyzed, thereby determining an appropriate nonlocal kernel function for the strain localization problem.

Widely Employed Constitutive Material Models in Abaqus FEA Software Suite for Simulations of Structures and Their Materials: A Brief Review

The structural response of masonry/concrete structures depends upon the load-carrying mechanism and subsequently deformations produced by loads carried. In masonry/concrete structures, identification of the stress/strain imposing stress conditions and strain hardening/softening makes the structural response more complicated. Elastic damage models or elastic-plastic constitutive laws are inadequate to simulate masonry/concrete response under high strain-rate loadings. Further, irreversible or plastic strain cannot be realized using the elastic damage model. Several constitutive damage models are available in the literature. In this article, a concise explanation of the functioning of different material models in the Abaqus software package has been provided. These models include concrete damage plasticity for concrete and masonry, traction separation constitutive laws for brick-mortar interface, Hashin's criteria for CFRP, Johnson-Cook plasticity for steel, and crushable foam plasticity hardening for metallic foams. Researchers frequently utilize these models for numerical simulations and modeling of infrastructural elements and their respective materials when subjected to various structural loads. Besides, this paper presents a discourse on problem-solving methods and a comparison between explicit and implicit analysis. The research provides valuable input to researchers and practitioners in the field of structural engineering for an in-depth understanding of the functioning of Abaqus' pre-existing material models.

Elastoplastic damage behavior of quasi-brittle rocks considering crack closure evolution

Crack closure evolution in compaction stage of quasi-brittle rocks is a very common phenomenon. A distinct feature of quasi-brittle rocks is that, under compression, presence of microcracks can increase nonlinear mechanical response of rock under low confining pressure, while gradually decrease nonlinear behavior of rock under high confining pressure. Previous studies have mainly focused on modelling the damage evolution caused by plastic strain, with few attempts to describe nonlinear behavior of compaction stage and reveal elastic damage dissipation mechanism triggered by the crack closure evolution. This paper presents a coupled elastoplastic damage model, which incorporates crack closure to describe the distinct behavior of rock based on the framework of continuum thermodynamics. Comparison between the model predictions and test results of three rock specimens shows that the model can capture whole process mechanical behavior of quasi-brittle rocks over a wide range of confining pressure using a set of model parameters. Parametric studies are carried out to quantify the effects of crack closure evolution and dissipation mechanism of elastic damage and plastic flow of the rock. The proposed model based on an implicit return mapping algorithm has been used to simulate the plastic damage response of rock specimen under displacement control.

Damage effect and progressive failure mechanism of sandstone considering different flaw angles under dynamic loading

In many engineering applications, it is essential to have information about rocks that inherently contain pre-existing flaws under dynamic loading conditions. Dynamic impact tests are conducted on samples with varying flaw angles using the split Hopkinson pressure bar (SHPB) test system and the Digital Image Correlation system (DIC). The characteristics of the samples after dynamic loading, including dynamic strength, energy dissipation, and fractal fracture, are compared and analyzed. As the flaw angle increases, the peak stress and strain exhibit a typical V-shaped pattern, reaching the minimum value at 30°, and the initial initiation position shifts from the flaw tips to the middle of the flaw. Failure modes can be divided into three modes depending on the flaw angle. The progressive failure process, taking into account the heterogeneity of the rock, is demonstrated by developing an elastic damage constitutive model that uses dynamic compression and tensile tests to parameterize it. As the flaw angle increases, the initial damage zone also moves from the flaw tips to the middle of the flaw. Failures around the hole with redistributed stress are observed, and the failure mechanisms can be explained with the aid of strain energy density (SED). Using fracture mechanics, the analytical solution of stress around the flaw is provided, and the variation of crack initiation angle, stress distribution, and energy dissipation under different flaw angles is theoretically explained, which is in good agreement with the experimental and simulated results.

Damage constitutive model and numerical simulation of in-plane tear failure for architectural fabric membranes

Tearing failure is the key factor affecting the safety of tension fabric structures, but there is a lack of material damage models and numerical methods needed to simulate tearing failure. This paper investigates the macroscopic damage model of architectural fabrics and the numerical simulation method for its tearing failure. Firstly, based on the incremental stress update scheme, theoretical descriptions of the material model considering the nonlinear elastic damage behavior are presented. Then, the influence of stiffness softening laws and the mesh schemes are investigated, and the advantages of easy implantation and good precision of the proposed model are validated by comparison with the cohesive element model embedded in ABAQUS. Compared with the experiment results and theoretical model, the predicted results are in good agreement for various crack length cases, and the nonlinear variation mechanism of tearing residual strength is revealed. Also, the effect of the tensile strength and fracture energy are discussed, and it is found that the crack tip blunting effect causes the linear elastic fracture mechanics not applicable.

Analysis of Cement Sheath–Rock Damage Mechanism—A Case Study on Water Injection Wells

In the field of water injection wells within oilfields, comprehending the intricate mechanics of water channeling and the resulting rock damage on the external cemented surface holds paramount significance for the efficient management of reservoirs. This paper presents a comprehensive study aimed at illuminating the complex nature of rock damage on the external cemented surface of casings and deciphering the underlying mechanisms that underpin water channeling occurrences. To this end, a robust constitutive model is established and refined to capture the multifaceted interactions inherent in rock damage on the cemented surface. This model introduces a modified bonding force approach to enhance shear stress precision and thoughtfully accounts for the profound effects of elastic–plastic behavior, cracking damage, and elastic-cracking coupling damage on damage progression. Subsequently, the refined model is employed to investigate rock damage on the external cemented surface of water injection wells, encompassing variations in confining pressure, rock width on the cemented surface, and the ratio of Young’s modulus between the cement sheath and the rock. The research findings emphasize the interplay between cracking and elastic damage as the catalyst for rock damage on the cemented surface. Impressively, the accuracy of the refined constitutive model for the cemented surface has advanced by over 5% compared to prior studies. The manipulation of confining pressure and the Young’s modulus ratio enhances peak fracture water pressure, signifying substantive strides in comprehending damage propagation mechanics. Furthermore, the study discerns the negligible influence of rock width on the cemented surface regarding damage patterns. These findings have important implications for the effective management of water injection wells, providing insights for the restoration of water channeling wells and proactive measures against water channeling phenomena. They also contribute to the refinement of well cementing practices and the proficient management of water channeling and water flooding in oilfields. The research findings have profound implications for the domain of water injection wells, offering novel insights into the restoration of water channeling wells and the implementation of preemptive measures against water channeling phenomena. These findings hold the potential to guide the refinement of well cementing practices and the adept management of water channeling and water flooding wells within the studied oilfield.

Mesoscale modelling of CRTS II slab tracks subjected to thermal action and vehicle loads

Evaluation of the damage and deformation of cast-in-situ concrete joints between the precast concrete track slabs of the China Railway Track System (CRTS) II is crucial to the safe operation of high-speed railways. To investigate the damage and deformation evolution of concrete joints under thermal action (caused by the natural meteorological environment) and vehicle loads, a two-dimensional thermal–mechanical coupled numerical model of concrete joints at the mesoscale was developed. This model analyses the influence of three factors – concrete strength, maximum diameter of the joint concrete aggregate and vehicle speed. First, meteorology and heat transfer theory were used in thermal simulations. Then, the non-linear characteristics of the joint concrete were modelled as a two-phase composite material based on the random aggregate algorithm and strain-based elastic damage theory at the mesoscale. The cohesive zone model was used to simulate the interfaces between precast slabs. The reliability of the proposed model was assessed using field measurements. The results of a numerical example showed that the maximum aggregate diameter of the joint concrete significantly affected damage evolution in the joint concrete and concrete strength has a slight effect on joint uplift.

Research on Rolling Contact Fatigue Failure of the Bearing Used in High-Speed Electric Multiple Units’ Axle Box Based on a Damage-Coupled Elastic–Plastic Constitutive Model

The axle box bearing is a crucial component of high-speed electric multiple units (EMU) and is exposed to harsh working conditions, making it susceptible to subsurface-induced rolling contact fatigue (RCF) under long-term alternating stress. The objective of this paper is to develop a damage-coupled elastic–plastic constitutive model that can accurately predict the RCF life of EMU axle box bearings made from AISI 52100 bearing steel. The total damage is divided into elastic damage related to the shear stress range and plastic damage associated with plastic deformation. Material parameters are determined based on experimental data from the literature, and validation is conducted to ensure the validity of the model. Finally, the RCF behavior of the EMU axle box bearing, including crack initiation, crack propagation, and spalling, is simulated, and reasonable results are obtained. This study provides valuable insights into the RCF behavior of EMU axle box bearings and contributes to the accurate prediction of the fatigue life.

A STUDY OF MECHANICAL PROPERTIES OF REINFORCED CONCRETE BEAM USING ARDUINO MICROCONTROLLER

Thispaper presentsthe use of an open source-based technology, Arduino microcontroller, which is used for free vibration test by using accelerometer ADXL345 comparing with one of common accelerometer and data-logger. The test was carried out in 3 variations: pre-loading, elastic damage (L/240), and inelastic damage (L/120). This research used reinforced concrete beam as specimens with 3000mm length, 150mm width, and 250mm depth. Specimen was installed by 2 monitoring system, Arduino equipped with accelerometer ADXL345 andcommercial data-logger NI equipped with commercial accelerometer KISTLER. The results show that relative error between ADXL345 to KISTLER is less than 5% for mode shape 1, 2, and 3 except in case inelastic damage for mode shape 3 is almost 10%.

Mechanical behavior of the cellular concrete and numerical simulation based on meso-element equivalent method

The novel cellular concrete with millimeter-size isolated spherical pores can greatly reduce the transportation cost of concrete coarse aggregate in the construction of facilities on remote islands, which utilizes spherical saturated SAP (Super-Absorbent Polymer) presoaked in seawater in situ. The mechanical property of this cellular concrete is an important basis for its engineering application. The purpose of this paper is to present a numerical method to understand more fully and efficiently its mechanical properties. According to the characteristics of meso-component of this cellular concrete, the meso-element equivalent model is improved, in which statistical homogenization method is used to substitute Voigt equivalence method. Based on the elastic damage constitutive model, uniaxial compression numerical tests are carried out on random meso-elements, and the parameters of damage constitutive model related to the porosity are obtained. On this basis, the random specimen model is divided into meso-elements of the same size, and the equivalent mechanical properties are given to the elements according to their porosities. The effectiveness of the numerical simulation method is verified by comparing with the actual test results, and it can reflect the damage process during uniaxial compressive loading.

Constitutive model for steel fiber reinforced concrete under shear and tension accounting for fiber orientation effect

This paper presents a constitutive model for the behavior of steel fiber reinforced concrete (SFRC) under mixed mode cracking taking into account the fiber orientation effect by using a micromechanical approach. Firstly, the resistant mechanisms of an inclined fiber are modeled by a closed-form analytical function. The bridging force is calculated by integrating on the cracked surface, the product of the fiber extraction force by its orientation probability. A modified model of the aggregate interlock mechanism is combined with the fiber bridging stresses to obtain the cohesive stresses. This mesoscale model is then extended using an elastic damage model and a fixed smeared cracking concept to assess the structural behavior. The model is finally implemented in a Finite Element Analysis (FEA) software, its performance is tested with some experimental results collected in the literature. The model successfully integrates the fiber orientation effect and shows a good prediction of stress transmission.

Research on creep characteristics of loading and unloading of hard Flint limestone

The hard Flint limestone of Shuibuya hydropower station underground construction cavern is utilized as a research object to investigate the creep problem caused by excavation of rock masses such as caverns. In order to perform a triaxial compression grade-unloading creep test, the actual adjustment path of stress during excavation of underground cavern surrounding rock is used. Limestone under different confistiff pressures is then evaluated. Based on the Nishihara model, the elastic damage element considering time-dependent damage is introduced, and the unloading creep constitutive model of stiff Flint limestone is established and verified by experiments. The results show: 1) Deformation and creep strain appear at all stress levels. 2) As the unloading amount increased from 2 to 4 MPa, the quasi-destructive stresses of the samples were smaller from 83 to 79 MPa, indicating that the unloading amount affected the final creep damage strength of the rock samples. In other words, the higher the unloading amount, the lower the ultimate creep failure strength. 3) When entering the accelerated creep stage, the axial and lateral creep strains of the sample increase non-linearly, and the rupture duration of the sample is very short. Therefore, the creep deformation and creep rate characteristics of this stage should be paid attention to in practical engineering. 4) Different from the loading stress path, the failure mode of the Flint limestone rock sample is different. When the unloading amount is 2 and 4 MPa, the creep failure mode of the Flint limestone rock sample is shear failure, showing a significant oblique section crack. 5) The non-linear creep model curve of aging damage and the fitting effect of the unloading creep test curve are acceptable. The rationality of the established non-linear creep model is illustrated.

Microstructural modeling of moisture-thermal and mechanical behavior within concrete during drying at elevated temperatures

This article presents a numerical study for the analysis of the moisture-thermal and mechanical behavior of concrete subjected to elevated temperatures. Firstly, the moisture-thermal coupled model, is proposed to better describe the strong coupling between heat and moisture transfer. Secondly, based on the mechanics of partially saturated porous media, a nonlinear elastic damage constitutive model is formulated. The simulation results of the coupled moisture-thermal model at each time step were adopted to simulate the distributions of porous behavior, thermo-chemical damage, and moisture damage within concrete under the corresponding moisture-thermal conditions. Consequently, the evolution of the mechanical properties of concrete at elevated temperatures during the entire drying process could be simulated. Finally, an application concerning drying of concrete samples at elevated temperatures was presented. The results obtained show that the proposed moisture-thermal-mechanical model has potential capacity in numerically modeling the complex coupling process of concrete structures under elevated temperatures.

Combined electronic excitation and knock-on damage in monolayer MoS2

Electron irradiation-induced damage is often the limiting factor in imaging materials prone to ionization or electronic excitations due to inelastic electron scattering. Quantifying the related processes at the atomic scale has only become possible with the advent of aberration-corrected (scanning) transmission electron microscopes and two-dimensional materials that allow imaging each lattice atom. While it has been shown for graphene that pure knock-on damage arising from elastic scattering is sufficient to describe the observed damage, the situation is more complicated with two-dimensional semiconducting materials such as ${\mathrm{MoS}}_{2}$. Here, we measure the displacement cross section for sulfur atoms in ${\mathrm{MoS}}_{2}$ with primary beam energies between 55 and 90 keV, and correlate the results with existing measurements and theoretical models. Our experimental data suggests that the displacement process can occur from the ground state, or with single or multiple excitations, all caused by the same impinging electron. The results bring light to reports in the recent literature, and add necessary experimental data for a comprehensive description of electron irradiation damage in a two-dimensional semiconducting material. Specifically, the results agree with a combined inelastic and elastic damage mechanism at intermediate energies, in addition to a pure elastic mechanism that dominates above 80 keV. When the inelastic contribution is assumed to arise through impact ionization, the associated excitation lifetime is on the order of picoseconds, on par with expected excitation lifetimes in ${\mathrm{MoS}}_{2}$, whereas it drops to some tens of femtoseconds when direct valence excitation is considered.