Elastoplastic Damage Constitutive Model Research Articles

Study on Elastoplastic Damage Constitutive Model and Permeability Evolution Law of Gas-Bearing Coal

Study on Elastoplastic Damage Constitutive Model and Permeability Evolution Law of Gas-Bearing Coal

Investigation of soil damping for offshore wind turbine monopile-soil system in stiff clay on elastoplastic-damage model

Damping plays a crucial role in the design of offshore wind turbine (OWT) monopile foundations. The soil damping of the monopile-soil system (MSS) represents the energy dissipation mechanism arising from the interaction between the pile and the soil. It is typically derived by back-calculating from the overall damping measured in the entire OWT structure. However, few studies have independently examined the soil damping in MSS, and the impact of key parameters such as pile diameter, pile embedded depth, cyclic load amplitude, and load eccentricity on the variation of soil damping in MSS remains unclear. This paper introduces an elastoplastic-damage constitutive model for the numerical simulation of the damping ratio variation in seabed soil and MSS. The model is implemented in ABAQUS software and validated against cyclic triaxial tests on stiff clay soil. On this basis, a three-dimensional finite element sensitivity study was conducted to elucidate the effect of these key parameters on the MSS damping ratio. The results of the study reveal that the MSS damping ratio exhibits a nonlinear and asymmetric trend as the loading cycles increase. The MSS damping ratio decreases with increasing pile diameter and embedded depth but increases with increasing lateral cyclic load amplitude and load eccentricity from the mudline.

Uniaxial behavior of UHPC under cyclic compression: Experimental investigation and constitutive model

The compressive behavior of ultra-high performance concrete (UHPC) is experimentally investigated in this paper for three different micro steel fiber volume fractions (Vf= 1.0%, 1.5% and 2.0%) under uniaxial monotonic and cyclic compression. The cube specimens are loaded and fully unloaded twice per displacement increment to track the evolution of damage. Cycles are included till the peak load and after attaining the peak load, all the way till the load carrying capacity becomes marginal. A one dimensional (1D) elastoplastic damage constitutive model is proposed to simulate the damage of UHPC under uniaxial cyclic compression, incorporating the damage parameters within a damage function deduced from the tests. Damage is incorporated as a nonlinear function and thus the hysteresis behavior (distinguishable unloading and reloading paths) is adequately captured in the model. The experimental results from this study and the accompanying model demonstrate that the strength and stiffness degradation in UHPC due to low cycle fatigue stabilize at higher fiber dosage levels.

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.

Enhancing the elastoplastic damage constitutive model for clayey rocks: Incorporating anisotropy, saturation, time-dependent, and debonding effects

Enhancing the elastoplastic damage constitutive model for clayey rocks: Incorporating anisotropy, saturation, time-dependent, and debonding effects

Development of a hygrothermal constitutive model for epoxy resin considering the glass transition temperature and its applications

Epoxy resin, as a crucial constituent of aerospace-grade composites, is an important consideration in designing composites for severing service conditions in terms of the hygrothermal environment (i.e. contains both temperature and moisture). In this work, a state-of-art elastoplastic-damage constitutive model is expanded to include the hygrothermal effects which are characterized by employing a glass transition temperature Tg as a bridge. The formulation of yield and fracture strengths with respect to hygrothermal effects demonstrates a high level of mathematical consistency. The model correctly captures the plastic flow and fracture initiation behavior with hygrothermal effects, as validated through quasi-static experiments. Subsequently, the application of this hygrothermal constitutive model for an epoxy resin on micro-mechanical analysis of carbon polymer composite materials is implemented. A representative volume element (RVE) is established with a random placement of fibers. Based on the commercial software ABAQUS, different loading scenarios are applied to evaluate the mechanical response and damage evolution of the composite in different hygrothermal conditions, enabling an initial understanding of the hygrothermal effects of epoxy resins on the mechanical performance of composite materials.

An elastoplastic damage constitutive model for capturing dynamic enhancement effect of rock and concrete through equivalent stress history

The strength enhancement effect of rock and concrete under dynamic loading is one of the significant response characteristics differing from quasi-static loading. Typically, current dynamic constitutive models describe this phenomenon by adopting strain/stress rate dependent functions. In this study, a novel elastoplastic damage constitutive model that captures the dynamic strength increase through the equivalent stress history is developed by coupling the incubation characteristic time (ICT) criterion and the unified strength theory (UST). Specifically, the ICT criterion substitutes the stress history for the strain/stress rate to predict dynamic yield strength of rock and concrete. And the equivalent stress expressed by the UST provide an appropriate selection of the stress history in the ICT criterion under complex stress states. Furthermore, based on the non-associated plastic flow rule and the plastic-damage evolution law, combined with the equation of state, the proposed constitutive model is established and implemented numerically. The dynamic stress-strain curves of granite were reconstructed by a series of numerical tests on a single element, which verified the accuracy of the proposed constitutive model and the reliability of the numerical algorithm by comparing the experimental data. The proposed model was applied to the numerical simulation of dynamic compression-shear tests on inclined sandstone specimens loading by the split Hopkinson pressure bar (SHPB) and fragmentation experiments of single borehole granite specimens under blast loading, respectively. And the experimental dynamic crack patterns on the specimen surface captured by high-speed cameras match the simulated damage distribution well. In addition, several common concrete constitutive models and the proposed model were employed to simulate the dynamic response of reinforced concrete beams under near-field blast loading. The damage patterns and the mid-span residual displacement calculated numerically by the proposed model are more consistent with the experiments than other concrete models. As a conclusion, the proposed model, coupled the ICT criterion and the UST, provides a new perspective and paradigm for characterizing the responses of rock and concrete subjected to intense dynamic loads.

Mechanical behaviors and elastoplastic damage constitutive model for heterogeneous frozen soil

The significant feature that distinguishes frozen soil from unfrozen soil is the existence of ice structures within it. To investigate the effect of ice lenses on the mechanical properties of frozen soil. A series of tests were conducted on three types of heterogeneous frozen soil under different temperatures and normal stresses. The test results showed that the strength and ductility of frozen soil decrease as the number of ice lenses increase under the same temperature and normal stress. The ice lenses within frozen soil intensify its strength attenuation under loading, the damage variable considering the cutting effect of ice lenses were established based on the fracture mechanics, and an elastoplastic damage constitutive model for heterogeneous frozen soil was proposed. The method was redeveloped in COMSOL Multiphysics, and the rationality was verified based the test results. The variation of damage variable and plastic strains of heterogeneous frozen soil under shear loading were analyzed.​ Finally, a digital model of undisturbed frozen soil was established using X-ray CT, and the failure mechanisms of the undisturbed frozen soil were investigated by the proposed model.

A thermodynamic damage model for 3D stress-induced mechanical characteristics and brittle–ductile transition of rock

Due to the existence of true three-dimensional high-geostress in deep underground engineering, rock shows different mechanical properties and brittle–ductile behaviours from conventional triaxial stress states, however, the different characteristics of rock are not clear. Therefore, a series of true triaxial tests were performed on deeply buried marble to investigate the effects of σ2 and σ3 on the characteristic strength (peak strength, yield strength and residual strength), post-peak deformation and brittle–ductile behaviour. Based on test results, a three-dimensional elastoplastic damage constitutive model that describes plastic hardening and damage softening of rock was established within the framework of irreversible thermodynamics, and a sensitivity analysis of key parameters ( η and ζ) was performed. A method that controls the brittle–ductile behaviour of rock through key parameters η and ζ was studied, and functions of these two parameters with σ2 and σ3 were proposed. The proposed model was implemented numerically with the cutting-plane algorithm in a finite element program. A series of numerical simulation experiments were performed, and numerical simulation and experimental results are consistent. In addition, brittle–ductile transition of marble under untested true triaxial stress levels were reasonably predicted.

Shear behavior of ice–frozen soil interface: Experiments and elastoplastic modeling

Ice lenses and their unique patterns formed by the amount and distribution of ice within sediments and rock within various geologic and climate environments, or cryostructures, are ubiquitous in permafrost. The mechanical characteristics and deformation properties of the individual components (i.e., ice lenses, frozen soil) and the interaction between them control the overall behavior of permafrost. Unlike ice lenses and frozen soil, the mechanical behavior of the ice lenses–frozen soil interface is less studied. This article presents the results from a series of cryogenic direct shear tests and an elastoplastic model based on the damage at the ice–frozen soil interface. The tests were conducted under different temperatures (i.e., -3, -2, and -1 °C), normal stresses (i.e., 50, 100, and 200 kPa), and initial saturations (i.e., 55, 67, 77, 96, and 100%), respectively. The test results show that under the same normal stress and initial saturation, the shear stress curves transit from strain-softening to strain-hardening as the temperature increases. The volumetric deformation initially contracts and then dilates as the shear displacement increases. Further, rheological elements are introduced to explain the various components of the interface’s mechanical behavior. An elastoplastic damage constitutive model is established to describe the overall shear behavior of the ice–frozen soil interface during the entire shearing process. The parameters in the model are clearly defined with physical meanings and are easy to determine. Finally, the proposed model is applied to predict the experimental data. Comparison of the model results with experimental data demonstrates that the proposed model can well capture the shear behavior of the ice–frozen soil interface.

Monotonic and cyclic compressive behavior of ultra-high performance concrete with coarse aggregate: Experimental investigation and constitutive model

This paper presents a systematic investigation on the compressive stress-strain behavior of ultra-high performance concrete with coarse aggregate (UHPC-CA) subjected to monotonic and cyclic loading. A total of eight groups of UHPC specimens considering different coarse aggregate (CA) and steel fiber (SF) contents were tested, with a synchronous monitoring and acquisition of acoustic emission (AE) signal releasing process. The mechanical properties and performance degradation of UHPC were analyzed. The damage mechanism of UHPC under compression and synergy of CA and SF were discussed. The results show that the inclusion of CA and SF has notable positive synergetic effect on the compressive behavior of UHPC, in spite of deformability. Moreover, obvious elastic stiffness degradation of UHPC with loading cycles is observed, which is alleviated by the incorporation of CA and SF. The failure pattern of UHPC is changed from tensile cracks to shear cracks with the increase of SF and CA contents. In addition, SEM observations demonstrate that CA in matrix acts as the ‘skeletons’ of UHPC, although the microstructures of UHPC are broken because of more pores caused among the inclusions and ‘wall effect’ of CA. Finally, a semi-empirical elastoplastic damage constitutive model is developed to generate the compressive response of UHPC -CA under monotonic and cyclic loading.

A Constitutive Model of Time-Dependent Deformation Behavior for Sandstone

Considering sandstone's heterogeneity in the mesoscale and homogeneity in the macroscale, it is very difficult to describe its time-dependent behavior under stress. The mesoscale heterogeneity can affect the initiation and propagation of cracks. Clusters of cracks have a strong influence on the formation of macroscale fractures. In order to investigate the influence of crack evolution on the formation of fractures during creep deformation, a time-dependent damage model is introduced in this paper. First, the instantaneous elastoplastic damage model of sandstone was built based on the elastoplastic theory of rock and the micro-heterogeneous characteristics of sandstone. A viscoelastic plastic creep damage model was established by combining the Nishihara model and the elastoplastic damage constitutive model. The proposed models have been validated by the results of corresponding analytical solutions. To help back up the model, some conventional constant strain rate tests and multi-step creep tests were carried out to analyze the time-dependent behavior of sandstone. The results show that the proposed damage model can not only reflect the time-dependent viscoelastic deformation characteristics of sandstone, but also provide a good fit to the viscoelastic plastic deformation characteristics of sandstone's creep behavior. The damage model can also reproduce the propagation process of mesoscopic cracks in sandstone upon the damage and failure of micro-units. This research can provide an effective tool for studying the propagation of microscopic cracks in sandstone.

Triaxial elastoplastic damage constitutive model of unreinforced clay brick masonry wall

Triaxial elastoplastic damage constitutive model of unreinforced clay brick masonry wall

The Study on the Constitutive Model of Concrete for Explicit Dynamic of ABAQUS Based on Damage Energy

In this paper, the elastoplastic damage constitutive model of concrete is established based on the damage energy release rate to analyze the failure of concrete structures. Based on the user-defined material program VUMAT interface provided by the ABAQUS, the explicit algorithm is used to secondary develop the concrete model. The model is verified from mechanical behavior, mesh-dependence, and stress state under reciprocating loading. The results show that the model can reasonably simulate the mechanical state of concrete under compression and tension and can effectively solve the mesh-dependence problem in finite element problems. The simulation results were still consistent when the mesh size was 2.5 mm. The low cycle reciprocating simulation test of the concrete column also proves that the model has better hysteretic and bidirectional coupling performance. It is verified that the VUMAT material subroutine can meet the analysis requirements of reinforced concrete structures and can be used to simulate the dynamic response of structures with strong nonlinear stages.

Hoek Brown Elastoplastic Damage Model Considering Pore Water Pressure and Its Application to Subsea Tunnel Engineering

Compared with land tunnels, subsea tunnels are more prone to disasters such as water inrush. In order to calculate the deformation and the excavation damage zone (EDZ) of subsea tunnel, an elastoplastic damage constitutive model based on Hoek Brown (HB) criterion is proposed. Moreover, the modified effective stress principle considering pore water pressure is introduced and a finite element constitutive integral algorithm is established. To overcome the “singularity” problem in the numerical implementation, a complete implicit return mapping algorithm is deduced for solving the elastic-plastic HB damage (HBD) model, the plasticity correction process for three cases in which the flow vector returns to the main plane, the left and right prisms, and the tip, respectively. Furthermore, the 3D numerical program is then developed based on Abaqus' user subroutine interface. And the stability and accuracy of the algorithm is verified by uniaxial and triaxial laboratory compression tests. Finally, based on the proposed HBD model and program, the three-dimensional numerical calculations were carried out for the shield tunnel of the Dalian subsea project of China, which can reasonably reflect the displacement and damage evolution of the surrounding rock with different shield construction sequence, different pore water pressure and different support pressure. The model and program provided an effective means to analyze the EDZ of the surrounding rock for subsea tunnel engineering.

An elastoplastic damage constitutive model for rock-like materials with a fractional plastic flow rule

An elastoplastic damage constitutive model is constructed in this work to describe the macroscopic mechanical behaviors of geomaterials with a “porous matrix - inclusion” microstructure. In order to consider the influences of microstructure on its nonlinear behavior , such as the porosity, volume fraction of inclusions and the properties of the solid phase, the macroscopic yield criterion derived in Shen et al. (2013) is adopted. By introducing a general damage factor, this criterion is extended phenomenologically to describe the elastoplastic damage behavior of the studied geomaterial. A plastic hardening law of the solid phase is considered to capture the hardening behavior. Then, a complete constitutive model is constructed by using a fractional plastic flow rule to calculate the macroscopic plastic deformation . The degree of non-associativity of the plastic flow rule can be controlled by the fractional derivative of the yield function, which avoids the introduction of macroscopic phenomenological plastic potential. The proposed model is implemented and applied to describe the mechanical behavior of claystone . Comparisons between the numerical predictions and experimental data show that the proposed model is able to capture the main mechanical features of the studied geomaterial, such as the damage procedure, the transition from volumetric contractancy to dilatancy and the brittle to ductile transition with the increase of confining pressure.

An elastoplastic damage constitutive model for hybrid steel-polypropylene fiber reinforced concrete

An appropriate constitutive model to characterize the mechanical behavior of fiber reinforced concrete (FRC) plays a critical role in accurate prediction of structural performance. In this study, an elastoplastic damage constitutive model is developed for hybrid steel-polypropylene fiber reinforced concrete (HFRC), which can predict the versatile mechanical responses of HFRC as a result of various hybrid fiber inclusions. For plasticity growth, the Willam-Warnke five-parameter failure envelope is modified in the effective stress space to govern the yield condition of HFRC, while a nonlinear Drucker-Prager type plastic potential function is proposed to control the non-associated plastic flow. Regarding the damage evolution, the damage criterion and evolution laws are established in the Cauchy stress space, in which the plastic hardening and unilateral behaviors are taken into consideration. Upon two parallel integration algorithms to describe the development of plasticity and damage, as well as the identification of fiber-dependent parameters, the proposed model is numerically implemented and then validated by the experimental results from available research. The comparisons between the numerical predictions and the test results at both material scale and structural scale solidly demonstrate the capacity of the model in capturing the main features of HFRC when subjected to different loading paths.

A Simple Elastoplastic Damage Constitutive Model of Porous Rock Materials

Traditional macroscopic phenomenon constitutive model is not easy to describe in the non-linear mechanical properties of porous rock materials, since the effect of porosity does not incorporate into the strength criterion. This paper presents a simple elastoplastic damage constitutive model of porous rock material based on micromechanical theory. To consider the heterogeneities of the studied porous rock, a simplified representative volume element is introduced, and it is assumed that it is made up of randomly distributed spherical pores embedded in a solid matrix obeying Drucker-Prager yield function. Thus, a homogenized plastic criterion considering the effect of porosity is introduced to describe the macroscopic plastic mechanical properties of porous rock materials. In this model, the non-associated flow rule and isotropic strain hardening law are used, and then the degradation of elastic and plastic properties is employed by adopting a damage criterion. This criterion is related to the evolution of equivalent plastic strain. In order to verify the accuracy of the model, the corresponding numerical program was used to realize the micro-macro constitutive model, and the results were compared with the triaxial compression test results of sandstone under different confining pressures. It is observed that the numerical simulation results are in great agreement with the experimental data, indicating that the proposed model is able to predict the main mechanical behavior of porous sandstone.

Investigation of ultimate bearing capacity of shield tunnel based on concrete damage model

Shield tunnel is usually treated as an underground permanent facility with a design service life of 100 years, its bearing capacity and service performance has attracted extensive attention. Previous studies on the mechanical behavior of shield tunnel are mostly carried out within the framework of elastic or elastoplastic theories. However, when these theories are used to explore the ultimate bearing capacity of shield tunnels, large structural deformation is bound to occur, which leads to crack or damage development and finally structural failure. Therefore, to analyze the damage and failure of shield tunnels, the damage and deterioration characteristics of concrete materials should be considered. Also, the damage mechanics theory is more appropriate to deal with this problem. In this paper, a damage–based analysis method for investigating the ultimate bearing capacity of shield tunnels is proposed. A bi–scalar elastoplastic damage constitutive model based on energy–based stress decomposition is introduced to describe the damage and deterioration behavior of concrete materials. Then, an elaborate numerical model of shield tunnel is developed based on the 3D discontinuous contact model. Moreover, the validity of the proposed method is verified by comparing the simulations with the full–scale experimental results. Then, the ultimate bearing capacity and damage characteristics of shield tunnels in practical underground service conditions are discussed. It is found that the numerical results are generally in good agreement with the experimental data, so that the proposed model can effectively reflect the characteristics of structural deformation, internal force transfer, damage evolution process, failure mode and stress redistribution in the loading process. Also, it is found that the failure process of the tunnel structure can be divided into linear elastic phase, yield–damage phase and failure phase. The range of each phase depends on the loading conditions and surrounding soil constraints. In addition, the integrated stiffness and bearing capacity of the tunnel–soil coupled structure increase with the increase of soil elastic modulus and lateral coefficient of earth pressure. The increase of coupled structural stiffness will also shorten the yield–damage phase and decrease the structural toughness (or ductility). The failure modes of the shield tunnel structure are manifested by the bolt yielding, concrete cracking, and finally, the forming joint plastic hinges on the tunnel crown and waist joints.

Research on Dynamic Response Characteristics for Basement Structure of Heavy Haul Railway Tunnel with Defects

Based on the basic principle of thermodynamics, an elastoplastic damage constitutive model of concrete is constructed in this paper. The model is realized and verified in FLAC3D, which provides a solid foundation for the study of dynamic response and fatigue damage to the base structure of a heavy haul railway tunnel. The dynamic response and damage distribution of the base structure of a heavy-duty railway tunnel with defects were numerically simulated by the concrete elastic-plastic damage constitutive model. Then, by analyzing the response characteristics of the tunnel basement structure under different surrounding rock softening degrees, different foundation suspension range and different foundation structure damage degree are determined. The results show the following: (1) The elastoplastic damage constitutive model of concrete can well describe the stress–strain relationship of materials, especially with the simulation results of post peak softening being in good agreement with the test results, and the simulation effect of the unloading–reloading process of the cyclic loading and unloading test also meet the requirements. (2) The initial stress field and dynamic response of the tunnel basement structure under the action of train vibration load are very different from the ideal state of the structure design when the surrounding rock of the base is softened, the base is suspended, or the basement structure is damaged. With the surrounding rock softening, basement hanging, or basement structure damage developing to a certain extent, the basement structure will be damaged. (3) The horizontal dynamic stress amplitude increases with the increase in the softening degree of the basement surrounding rock. The horizontal dynamic stress of the measuring point increases with the increase in the width of the hanging out area when the hanging out area is located directly below the loading line. When the degree of damage to the basement structure is aggravated, the horizontal dynamic tensile stress of each measuring point gradually decreases. (4) The maximum principal stress increment increases with the increase in the fracture degree of the basement structure, while the minimum principal stress increment decreases with the increase in the fracture degree of the basement structure, but the variation range of the large and minimum principal stress increments is small. The research results have important theoretical and practical significance for further analysis of the damage mechanism and control technology of the foundation structure of a heavy haul railway tunnel with defects.