In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved c...In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved complex variable element-free Galerkin（ICVEFG） method is presented for two-dimensional（2D） elastoplasticity problems. Compared with the previous complex variable moving least-squares approximation, the new approximation has greater computational precision and efficiency. Using the penalty method to apply the essential boundary conditions, and using the constrained Galerkin weak form of 2D elastoplasticity to obtain the system equations, we obtain the corresponding formulae of the ICVEFG method for 2D elastoplasticity. Three selected numerical examples are presented using the ICVEFG method to show that the ICVEFG method has the advantages such as greater precision and computational efficiency over the conventional meshless methods.展开更多
We present the hybrid natural element method（HNEM） for two-dimensional elastoplastic large deformation problems. Sibson interpolation is adopted to construct the shape functions of nodal incremental displacements an...We present the hybrid natural element method（HNEM） for two-dimensional elastoplastic large deformation problems. Sibson interpolation is adopted to construct the shape functions of nodal incremental displacements and incremental stresses. The incremental form of Hellinger–Reissner variational principle for elastoplastic large deformation problems is deduced to obtain the equation system. The total Lagrangian formulation is used to describe the discrete equation system.Compared with the natural element method（NEM）, the HNEM has higher computational precision and efficiency in solving elastoplastic large deformation problems. Some numerical examples are selected to demonstrate the advantage of the HNEM for large deformation elastoplasticity problems.展开更多
Dual variational extremum principles for rate problems of classical elastoplasticitv at finite deformation are studied in Updated Lagrangian rate forms. It is proved that the convexity of the variational functionals a...Dual variational extremum principles for rate problems of classical elastoplasticitv at finite deformation are studied in Updated Lagrangian rate forms. It is proved that the convexity of the variational functionals are closely related to a so-called gap function, which plavs an important role in nonlinear variational problems.展开更多
This paper presents a simple damage-gradient based elastoplastic model with non linear isotropic hardening in order to regularize the associated initial and boundary value problem (IBVP). Using the total energy equiva...This paper presents a simple damage-gradient based elastoplastic model with non linear isotropic hardening in order to regularize the associated initial and boundary value problem (IBVP). Using the total energy equivalence hypothesis, fully coupled constitutive equations are used to describe the non local damage induced softening leading to a mesh independent solution. An additional partial differential equation governing the evolution of the non local isotropic damage is added to the classical equilibrium equations and associated weak forms derived. This leads to discretized IBVP governed by two algebric systems. The first one, associated with equilibrium equations, is highly non linear and can be solved by an iterative Newton Raphson method. The second one, related to the non local damage, is a linear algebric system and can be solved directly to compute the non local damage variable at each load increment. Two fields, linear interpolation triangular element with additional degree of freedom is terms of the non local damage variable is constructed. The non local damage variable is then transferred from mesh nodes to the quadrature (or Gauss) points to affect strongly the elastoplastic behavior. Two simple 2D examples are worked out in order to investigate the ability of proposed approach to deliver a mesh independent solution in the softening stage.展开更多
At present, as the easily mining resources are being increasingly depleted, the exploitation of coal under buildings, water-bodies and railways is imminent for the sustainable production. Probability in-tegral method ...At present, as the easily mining resources are being increasingly depleted, the exploitation of coal under buildings, water-bodies and railways is imminent for the sustainable production. Probability in-tegral method is a general method for mining subsidence in the coal system. Because of poor under-standing of mining subsidence for other sections, the authors suggest probability integral method for the study of coal mining under buildings, water-bodies and railways. Moreover, the calculation result of probability integral method should be corrected by numerical simulation method. Based on practical projects, the impact has been evaluated on the security of Xifeihe left embankment under coal mining. Combining with the results of probability integral method, we propose that the 600 m far from em-bankment is a good rationality. This article provides the basis for the rational exploitation of coal re-source which is a major practical problem under the premise of Water Infrastructure Security. Fur-thermore, it also can be served as a reference for the similar projects, such as mining Xiaolangdi res-ervoir area, mining Yuecheng reservoir and mining the major channels of Middle Route South to North Water Transfer.展开更多
New and perhaps unexpected progress in rate-independent elastoplastic modeling is reported with a unified approach toward simulating widely ranging non-elastic effects of various advanced engineering materials such as...New and perhaps unexpected progress in rate-independent elastoplastic modeling is reported with a unified approach toward simulating widely ranging non-elastic effects of various advanced engineering materials such as metals,shape memory alloys,granular materials,fiber-reinforced composites,as well as crystalline solids,etc.This progress originates from a simple idea of bypassing inherent limitations of usual elastoplastic formulations centered on the notion of yielding.With no reference to any yield criteria,the plastic strain-rate should be induced at all stress levels in a more realistic sense that it is small for stresses within a classical yield surface and becomes appreciable for stresses close to and on this surface.A new and unified flow rule for the plastic strain-rate is then proposed of the same smooth form for all cases of both the stress level and the stress rate.Without imposing the ad hoc simplified conditions introduced in usual Prandtl-Reuss equations,new elastoplastic equations are then established by incorporating such small deviations from realistic behaviors as neglected just by postulating these conditions.It turns out that the new equations are not only essentially simpler in both conceptual and structural formulations,but can automatically as inherent response features incorporate significant effects excluded from usual Prandtl-Reuss equations,such as the yielding and unloading behaviors with smooth transitions,the pseudo-elastic effect with hysteresis loops,the non-elastic recovery during unloading as well as failure effects under either monotone or cyclic loading conditions,etc.Since such effects not only go beyond the scope of usual elastoplastic equations but can be only partially simulated even if augmented constitutive equations are postulated toward further characterizing damaging and fracturing effects resulting from evolving micro-defects and macro-cracks,it may be probably surprising that now the new equations of essentially simpler structure not only can in a unified manner simulate all these effects but also can bypass numerical complexities in integrating various rate constitutive equations of complex structures.New results in treating long-standing issues in a few respects are presented,including(i)the yielding and the unloading behaviors with smooth transitions,(ii)the non-elastic recovery during unloading,(iii)the pseudo-elastic effect as extraordinary Bauschinger effect,(iv)failure effects under monotone and cyclic loading,(v)anisotropic multi-mode failure effects of unidirectional composites,(vi)new formulation of crystal elastoplasticity without involving non-uniqueness and singularity issues,(vii)non-normality effects for non-proportional multi-axial loading cases,and(viii)high efficiency algorithms for simulating multi-axial fatigue effects.展开更多
The oil and gas industry is increasingly focusing on exploring and developing resources in deep earth layers.At high temperatures,confining pressures,and geostress differences,rock has the mechanical characteristics o...The oil and gas industry is increasingly focusing on exploring and developing resources in deep earth layers.At high temperatures,confining pressures,and geostress differences,rock has the mechanical characteristics of plastic enhancement,which leads to the unclear mechanism of hydraulic fracture expansion.The current fracturing model and construction design lack pertinence,and the fracturing reform is difficult to achieve the expected effect.This paper established a model of elastoplastic hydraulic fracture propagation in deep reservoirs.It considered the enhancement of plasticity by examining the elastoplastic deformation and nonlinear fracturing characteristics of the rock.The results confirmed that the hydraulic fractures in deep reservoirs propagated due to plastic energy dissipation after fracture tip passivation,while the stress concentration declined,which increased propagation resistance.The relationship between geology,engineering factors,degree of plasticity,and fracture propagation is discussed,while the conditions that promote fracture propagation are analyzed to provide theoretical support for deep reservoir fracturing design.展开更多
A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional ...A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional flow rule.The yield function includes parameters that govern the evolution of yield surface,enabling an accurate description of three-dimensional stress states.The direction of plastic flow is governed by the two different fractional orders,which are functions of the plastic internal variable.Additionally,a detailed process is proposed for identifying the yield function parameters and fractional orders.Subsequently,the relationship between the fractional order and the direction of plastic flow in the meridian and deviatoric planes is examined,characterized by the dilation angle and the plastic deflection angle,respectively.The non-orthogonal flow rule,also referred to as the fractional flow rule,allows for a border range of plastic deflection and dilation angles compared to the orthogonal flow rule,thereby significantly enhancing its applicability.The validity and accuracy of proposed model are verified by comparing the analytical solution of the constitutive model with the experimental data.A comparison between the non-orthogonal flow rule and orthogonal flow rule is conducted in both the deviatoric and meridian planes.The further comparison of the stress-strain curves for the non-orthogonal and orthogonal flow rules demonstrates the superiority of the fractional constitutive model.展开更多
Hydraulic fracturing is a key technology for the efficient development of deep oil and gas reservoirs.However,fracture propagation behavior is influenced by rock elastoplasticity and thermal stress,making it difficult...Hydraulic fracturing is a key technology for the efficient development of deep oil and gas reservoirs.However,fracture propagation behavior is influenced by rock elastoplasticity and thermal stress,making it difficult for traditional linear elastic models to accurately describe its dynamic response.To address this,this study employs the Continuum-Discontinuum Element Method(CDEM),incorporating an elastoplastic constitutive model,thermo-hydro-mechanical(THM)coupling effects,and cohesive zone characteristics at the fracture tip to establish a numerical model for hydraulic fracture propagation in deep elastoplastic reservoirs.A systematic investigation was conducted into the effects of fluid viscosity,reservoir temperature,injection rate,elastic modulus,and horizontal stress difference on fracture propagation.The findings show that a larger horizontal stress differential results in a more rectangular fracture geometry,a shorter fracture length,and a wider fracture.An increase in elastic modulus has a negligible impact on fracture length but reduces fracture width,resulting in a rounded rectangular morphology.Elevated reservoir temperature induces thermal tensile stress around the fracture,mitigating in-situ stress effects and reducing both breakdown and propagation pressures.Higher injection rates and fluid viscosity increase fracture initiation difficulty,promoting shorter but wider fractures with enhanced height growth beyond interlayer barriers.Additionally,horizontal stress significantly affects near-fracture plastic deformation:when the stress difference increases from 10 to 25 MPa,the maximum cumulative plastic strain in the surrounding rock rises by 66.67%.By integrating elastoplasticity and thermal stress effects,this study overcomes the limitations of conventional hydraulic fracturing simulations,offering novel insights for optimizing extraction strategies in deep unconventional reservoirs.展开更多
In the framework of elastoplastic theory,by introducing dissipative plastic energy(instead of cumulative plastic strain)and dissipative plastic energy rate(instead of cumulative plastic strain rate)into the ratchettin...In the framework of elastoplastic theory,by introducing dissipative plastic energy(instead of cumulative plastic strain)and dissipative plastic energy rate(instead of cumulative plastic strain rate)into the ratchetting parameter evolution equation and isotropic evolution rules respectively,a cyclic elastoplastic constitutive model based on dissipative plastic energy is established.This model,termed the WDP model,describes the physical meaning and evolution rule of the unclosed stress–strain hysteresis loop using an energy method.A comparison of numerical implementation results with experimental data demonstrates the capability of the WDP model to predict the cyclic deformation of EA4T steel,effectively capturing the cyclic softening characteristics and ratchetting behaviors of axle steel EA4T.展开更多
Numerical challenges,incorporating non-uniqueness,non-convexity,undefined gradients,and high curvature,of the positive level sets of yield function are encountered in stress integration when utilizing the return-mappi...Numerical challenges,incorporating non-uniqueness,non-convexity,undefined gradients,and high curvature,of the positive level sets of yield function are encountered in stress integration when utilizing the return-mapping algorithm family.These phenomena are illustrated by an assessment of four typical yield functions:modified spatially mobilized plane criterion,Lade criterion,Bigoni-Piccolroaz criterion,and micromechanics-based upscaled Drucker-Prager criterion.One remedy to these issues,named the"Hop-to-Hug"(H2H)algorithm,is proposed via a convexification enhancement upon the classical cutting-plane algorithm(CPA).The improved robustness of the H2H algorithm is demonstrated through a series of integration tests in one single material point.Furthermore,a constitutive model is implemented with the H2H algorithm into the Abaqus/Standard finite-element platform.Element-level and structure-level analyses are carried out to validate the effectiveness of the H2H algorithm in convergence.All validation analyses manifest that the proposed H2H algorithm can offer enhanced stability over the classical CPA method while maintaining the ease of implementation,in which evaluations of the second-order derivatives of yield function and plastic potential function are circumvented.展开更多
Concrete materials are employed extensively in a variety of large-scale structures due to their economic viability and superior mechanical properties.During the service life of concrete structures,they are inevitably ...Concrete materials are employed extensively in a variety of large-scale structures due to their economic viability and superior mechanical properties.During the service life of concrete structures,they are inevitably subjected to damage from impact loading from natural disasters,such as earthquakes and storms.In recent years,the phasefield model has demonstrated exceptional capability in predicting the stochastic initiation,propagation,and bifurcation of cracks in materials.This study employs a phase-field model to focus on the rate dependency and failure response of concrete under impact deformation.A viscosity coefficient is introduced within the phase-field model to characterize the viscous behavior of dynamic crack propagation in concrete.The rate-dependent cohesive strength is defined within the yield function of concrete,where the rate sensitivity of cohesive strength facilitates the accumulation of the plastic driving force in the phase-field model.This process effectively captures the impact failure response of concrete.The applicability of the model was validated through unit cell experiments and numerical simulations of concrete under impact compression.Furthermore,the mechanical response and damage evolution mechanisms of concrete under impact loading were analyzed.It was observed that crack propagation in concrete initiates at material defects and,with increasing load,eventually develops in a direction perpendicular to the loading axis.展开更多
Electrically Assisted Forming(EAF)technology has obvious advantages in material forming.To develop an effective constitutive model considering electrical effects,room temperature and electrically assisted quasi-static...Electrically Assisted Forming(EAF)technology has obvious advantages in material forming.To develop an effective constitutive model considering electrical effects,room temperature and electrically assisted quasi-static uniaxial tensile tests were conducted using ultrathin nickelbased superalloy plates with a thickness of 0.25 mm.The research focused on the two most widely recognized effects:the Joule thermal and the electric athermal effects.The mechanism of current action can be divided into two scenarios:one considering the Joule thermal effect only,and the other considering both effects simultaneously.Two basic constitutive models,namely the Modified-Hollomon model and the Johnson-Cook(J-C)model,were selected to be optimized through the classification of two different situations,and four optimized constitutive models were proposed.It was found that the J-C model with simultaneous consideration of the Joule thermal effect and electric athermal effect had the best prediction effect by comparing the results of these four models.Finally,the accuracy of the optimization model was verified by finite element simulation of the electrically assisted stretching optimization model.The results show that the constitutive model can effectively predict the temperature effect caused by the Joule heat effect and the athermal effect of current on the material.展开更多
An elastoplastic constitutive model based on the Modified Cam Clay(MCC)model is developed to describe the mechanical behaviour of soils cemented via microbially induced calcite precipitation(MICP).It considers the inc...An elastoplastic constitutive model based on the Modified Cam Clay(MCC)model is developed to describe the mechanical behaviour of soils cemented via microbially induced calcite precipitation(MICP).It considers the increase of the elastic stiffness,the change of the yield surface due to MICP cementation and the degradation of calcium carbonate bonds during shearing.Specifically,to capture the typical contraction-dilation transition in MICP soils,the original volumetric hardening rule in the MCC model is modified to a combined deviatoric and volumetric hardening rule.The model could reproduce a series of drained triaxial tests on MICP-treated soils with different calcium carbonate contents.Further,we carry out a parametric study and observe numerical instability in some cases.In combination with an analytical analysis,our numerical modelling has identified the benefits and limitations of using MCCbased models in the simulation of MICP-cemented soils,leading to suggestions for further model development.展开更多
This paper presents a micromechanics-based Cosserat continuum model for microstructured granular materials.By utilizing this model,the macroscopic constitutive parameters of granular materials with different microstru...This paper presents a micromechanics-based Cosserat continuum model for microstructured granular materials.By utilizing this model,the macroscopic constitutive parameters of granular materials with different microstructures are expressed as sums of microstructural information.The microstructures under consideration can be classified into three categories:a medium-dense microstructure,a dense microstructure consisting of one-sized particles,and a dense microstructure consisting of two-sized particles.Subsequently,the Cosserat elastoplastic model,along with its finite element formulation,is derived using the extended Drucker-Prager yield criteria.To investigate failure behaviors,numerical simulations of granular materials with different microstructures are conducted using the ABAQUS User Element(UEL)interface.It demonstrates the capacity of the proposed model to simulate the phenomena of strain-softening and strain localization.The study investigates the influence of microscopic parameters,including contact stiffness parameters and characteristic length,on the failure behaviors of granularmaterials withmicrostructures.Additionally,the study examines themesh independence of the presented model and establishes its relationship with the characteristic length.A comparison is made between finite element simulations and discrete element simulations for a medium-dense microstructure,revealing a good agreement in results during the elastic stage.Somemacroscopic parameters describing plasticity are shown to be partially related to microscopic factors such as confining pressure and size of the representative volume element.展开更多
Complexities in mechanical behaviours of rock masses mainly stem from inherent discontinuities,which calls for advanced bolt-grouting techniques for stability enhancement.Understanding the mechanical properties of bol...Complexities in mechanical behaviours of rock masses mainly stem from inherent discontinuities,which calls for advanced bolt-grouting techniques for stability enhancement.Understanding the mechanical properties of bolt-grouted fractured rock mass(BGFR)and developing accurate prediction methods are crucial to optimize the BGFR support strategies.This paper establishes a new elastoplastic(E-P)model based on the orthotropic and the Mohr-Coulomb(M-C)plastic-yielding criteria.The elastic parameters of the model were derived through a meso-mechanical analysis of composite materials mechanics(CMM).Laboratory BGFR specimens were prepared and uniaxial compression test and variable-angle shear test considering different bolt arrangements were carried out to obtain the mechanical parameters of the specimens.Results showed that the anisotropy of BGFR mainly depends on the relative volume content of each component material in a certain direction.Moreover,the mechanical parameters deduced from the theory of composite materials which consider the short fibre effect are shown to be in good agreement with those determined by laboratory experiments,and the variation rules maintained good consistency.Last,a case study of a real tunnel project is provided to highlight the effectiveness,validity and robustness of the developed E-P model in prediction of stresses and deformations.展开更多
The recoverable strain of rock is completely classified as elastic strain in the conventional elastic-plastic theory,which often results in poor agreement between theoretical and experimental curves.This work proposes...The recoverable strain of rock is completely classified as elastic strain in the conventional elastic-plastic theory,which often results in poor agreement between theoretical and experimental curves.This work proposes an improved elastoplastic model of rock materials considering the evolutions of crack deformation and elastic modulus to better characterize the nonlinear mechanical behavior of rock in the post-peak stage.In this model,the recoverable strain is assumed to be a combination of elastic and crack strain,and the constitutive relationship between crack strain and rock stress is deduced.Based on the proposed assumption,the evolutions of the mechanical parameters including strength parameters,elastic,plastic,and crack deformation parameters versus the plastic strain and confining stress were investigated.The developed elastoplastic model was validated by comparing the theoretical values with the results of the triaxial cyclic loading and unloading test.The theoretical calculation results show a good agreement with the laboratory test,which indicates that the improved elastoplastic model can effectively reflect the nonlinear mechanical behavior of the rock materials.The research results are expected to provide a valuable reference for further understanding the evolution of rock crack deformation.展开更多
The lining and surrounding rock around tunnels constructed in cold areas exhibit nonuniform material properties due to the existence of a temperature field.This study considered the effects of these properties on the ...The lining and surrounding rock around tunnels constructed in cold areas exhibit nonuniform material properties due to the existence of a temperature field.This study considered the effects of these properties on the integrity of tunnel structures.By establishing an elastoplastic mechanical model,analytical solutions to the stress and displacement under five different elastoplastic states were derived and compared based on distinct yield criteria.The findings showed that with increasing relative radius,the displacement in the lining elastic zone initially decreased before increasing,whereas the shift in the plastic zone continued to increase.The displacement in the elastic zone of the frozen surrounding rock intensified with increasing relative radius,whereas the shift in the plastic zone experienced a gradual decline.The displacement of the inner wall of the lining was always greater than that of the outer wall,and this phenomenon occurred only after the frozen surrounding rock exhibited a plastic zone.The maximum displacements of the liner in its elastically limited and plastically limited states were 1.39,1.77,2.28,and 2.37 mm and 15.93,25.51,44.28,and 48.58 mm based on the Drucker-Prager(DP),Mohr-Coulomb(MC),Tresca,and double-shear strength criteria,respectively;the maximum limit displacements of the frozen surrounding rock were 12.74,20.41,35.43,and 38.87 mm and 85.32,103.38,569.23,and 680.43 mm,respectively.With increasing relative radius,the radial stresses within both the lining and the frozen surrounding rock intensified;and the tangential stress in the elastic zone of the lining decreased whereas the opposite change rule was observed in the plastic zone.The tangential stresses in the frozen surrounding rock and lining exhibited the same variation trend.Based on calculations with four distinct strength criteria,the elastic and plastic ultimate bearing capacities of the lining were 1.81,2.31,2.95,and 3.07 MPa,and 3.31,4.84,7.48,and 8.05 MPa,while those of the frozen surrounding rock were 8.52,13.24,22.17,and 24.18 MPa,and 16.76,32.46,74.15,and 85.64 MPa.In addition,with the expansion of the plastic zone,the phenomenon of a sudden change in the tangential stress at location r2 became progressively attenuated.The study findings can provide some theoretical guidance for the design and construction of tunnels in cold areas.展开更多
The stability of dams and their foundations is an important problem to which dam engineers have paid close attention over the years. This paper presented two methods to analyze the stability of a gravity dam and its f...The stability of dams and their foundations is an important problem to which dam engineers have paid close attention over the years. This paper presented two methods to analyze the stability of a gravity dam and its foundation. The direct analysis method was based on a rigid limit equilibrium method which regarded both dam and the rock foundation as undeformable rigid bodies. In this method, the safety factor of potential sliding surfaces was computed directly. The second method, the indirect analysis method, was based on elasto-plastic theory and employs nonlinear finite element method (FEM) in the analysis of stresses and deformation in the dam and its foundation. The determination of the safety degree of the structure was based on the convergence and abrupt the change criterion. The results obtained showed that structures' constituent material behavior played an active role in the failure of engineered structures in addition to the imposed load.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11171208 and U1433104)
文摘In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved complex variable element-free Galerkin（ICVEFG） method is presented for two-dimensional（2D） elastoplasticity problems. Compared with the previous complex variable moving least-squares approximation, the new approximation has greater computational precision and efficiency. Using the penalty method to apply the essential boundary conditions, and using the constrained Galerkin weak form of 2D elastoplasticity to obtain the system equations, we obtain the corresponding formulae of the ICVEFG method for 2D elastoplasticity. Three selected numerical examples are presented using the ICVEFG method to show that the ICVEFG method has the advantages such as greater precision and computational efficiency over the conventional meshless methods.
基金supported by the Natural Science Foundation of Shanghai,China(Grant No.13ZR1415900)
文摘We present the hybrid natural element method（HNEM） for two-dimensional elastoplastic large deformation problems. Sibson interpolation is adopted to construct the shape functions of nodal incremental displacements and incremental stresses. The incremental form of Hellinger–Reissner variational principle for elastoplastic large deformation problems is deduced to obtain the equation system. The total Lagrangian formulation is used to describe the discrete equation system.Compared with the natural element method（NEM）, the HNEM has higher computational precision and efficiency in solving elastoplastic large deformation problems. Some numerical examples are selected to demonstrate the advantage of the HNEM for large deformation elastoplasticity problems.
文摘Dual variational extremum principles for rate problems of classical elastoplasticitv at finite deformation are studied in Updated Lagrangian rate forms. It is proved that the convexity of the variational functionals are closely related to a so-called gap function, which plavs an important role in nonlinear variational problems.
文摘This paper presents a simple damage-gradient based elastoplastic model with non linear isotropic hardening in order to regularize the associated initial and boundary value problem (IBVP). Using the total energy equivalence hypothesis, fully coupled constitutive equations are used to describe the non local damage induced softening leading to a mesh independent solution. An additional partial differential equation governing the evolution of the non local isotropic damage is added to the classical equilibrium equations and associated weak forms derived. This leads to discretized IBVP governed by two algebric systems. The first one, associated with equilibrium equations, is highly non linear and can be solved by an iterative Newton Raphson method. The second one, related to the non local damage, is a linear algebric system and can be solved directly to compute the non local damage variable at each load increment. Two fields, linear interpolation triangular element with additional degree of freedom is terms of the non local damage variable is constructed. The non local damage variable is then transferred from mesh nodes to the quadrature (or Gauss) points to affect strongly the elastoplastic behavior. Two simple 2D examples are worked out in order to investigate the ability of proposed approach to deliver a mesh independent solution in the softening stage.
基金Technology Innovation Fund of the Ministry of Water Resources (Grant No. Scxc2005-11)
文摘At present, as the easily mining resources are being increasingly depleted, the exploitation of coal under buildings, water-bodies and railways is imminent for the sustainable production. Probability in-tegral method is a general method for mining subsidence in the coal system. Because of poor under-standing of mining subsidence for other sections, the authors suggest probability integral method for the study of coal mining under buildings, water-bodies and railways. Moreover, the calculation result of probability integral method should be corrected by numerical simulation method. Based on practical projects, the impact has been evaluated on the security of Xifeihe left embankment under coal mining. Combining with the results of probability integral method, we propose that the 600 m far from em-bankment is a good rationality. This article provides the basis for the rational exploitation of coal re-source which is a major practical problem under the premise of Water Infrastructure Security. Fur-thermore, it also can be served as a reference for the similar projects, such as mining Xiaolangdi res-ervoir area, mining Yuecheng reservoir and mining the major channels of Middle Route South to North Water Transfer.
基金the German Science Foundation(DFG)for supportFuyao University of Science and Technology of Fujian,China+1 种基金supported by the National Natural Science Foundation of China(Grant Nos.12172149 and 12172151)the Ministry of Science and Technology of China(Grant No.G20221990122)。
文摘New and perhaps unexpected progress in rate-independent elastoplastic modeling is reported with a unified approach toward simulating widely ranging non-elastic effects of various advanced engineering materials such as metals,shape memory alloys,granular materials,fiber-reinforced composites,as well as crystalline solids,etc.This progress originates from a simple idea of bypassing inherent limitations of usual elastoplastic formulations centered on the notion of yielding.With no reference to any yield criteria,the plastic strain-rate should be induced at all stress levels in a more realistic sense that it is small for stresses within a classical yield surface and becomes appreciable for stresses close to and on this surface.A new and unified flow rule for the plastic strain-rate is then proposed of the same smooth form for all cases of both the stress level and the stress rate.Without imposing the ad hoc simplified conditions introduced in usual Prandtl-Reuss equations,new elastoplastic equations are then established by incorporating such small deviations from realistic behaviors as neglected just by postulating these conditions.It turns out that the new equations are not only essentially simpler in both conceptual and structural formulations,but can automatically as inherent response features incorporate significant effects excluded from usual Prandtl-Reuss equations,such as the yielding and unloading behaviors with smooth transitions,the pseudo-elastic effect with hysteresis loops,the non-elastic recovery during unloading as well as failure effects under either monotone or cyclic loading conditions,etc.Since such effects not only go beyond the scope of usual elastoplastic equations but can be only partially simulated even if augmented constitutive equations are postulated toward further characterizing damaging and fracturing effects resulting from evolving micro-defects and macro-cracks,it may be probably surprising that now the new equations of essentially simpler structure not only can in a unified manner simulate all these effects but also can bypass numerical complexities in integrating various rate constitutive equations of complex structures.New results in treating long-standing issues in a few respects are presented,including(i)the yielding and the unloading behaviors with smooth transitions,(ii)the non-elastic recovery during unloading,(iii)the pseudo-elastic effect as extraordinary Bauschinger effect,(iv)failure effects under monotone and cyclic loading,(v)anisotropic multi-mode failure effects of unidirectional composites,(vi)new formulation of crystal elastoplasticity without involving non-uniqueness and singularity issues,(vii)non-normality effects for non-proportional multi-axial loading cases,and(viii)high efficiency algorithms for simulating multi-axial fatigue effects.
基金The Youth Science Fund Project of National Natural Science Foundation of China,52404027,Jinbo Lithe General Program of the National Natural Science Foundation of China,52274036,Suling Wang。
文摘The oil and gas industry is increasingly focusing on exploring and developing resources in deep earth layers.At high temperatures,confining pressures,and geostress differences,rock has the mechanical characteristics of plastic enhancement,which leads to the unclear mechanism of hydraulic fracture expansion.The current fracturing model and construction design lack pertinence,and the fracturing reform is difficult to achieve the expected effect.This paper established a model of elastoplastic hydraulic fracture propagation in deep reservoirs.It considered the enhancement of plasticity by examining the elastoplastic deformation and nonlinear fracturing characteristics of the rock.The results confirmed that the hydraulic fractures in deep reservoirs propagated due to plastic energy dissipation after fracture tip passivation,while the stress concentration declined,which increased propagation resistance.The relationship between geology,engineering factors,degree of plasticity,and fracture propagation is discussed,while the conditions that promote fracture propagation are analyzed to provide theoretical support for deep reservoir fracturing design.
基金sponsored by the National Natural Science Foundation of China(Grant No.42141010).
文摘A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional flow rule.The yield function includes parameters that govern the evolution of yield surface,enabling an accurate description of three-dimensional stress states.The direction of plastic flow is governed by the two different fractional orders,which are functions of the plastic internal variable.Additionally,a detailed process is proposed for identifying the yield function parameters and fractional orders.Subsequently,the relationship between the fractional order and the direction of plastic flow in the meridian and deviatoric planes is examined,characterized by the dilation angle and the plastic deflection angle,respectively.The non-orthogonal flow rule,also referred to as the fractional flow rule,allows for a border range of plastic deflection and dilation angles compared to the orthogonal flow rule,thereby significantly enhancing its applicability.The validity and accuracy of proposed model are verified by comparing the analytical solution of the constitutive model with the experimental data.A comparison between the non-orthogonal flow rule and orthogonal flow rule is conducted in both the deviatoric and meridian planes.The further comparison of the stress-strain curves for the non-orthogonal and orthogonal flow rules demonstrates the superiority of the fractional constitutive model.
基金supported by the Shandong Provincial Natural Science Foundation for Distinguished Young Scholars(Grant No.ZR2024JQ012)This research was financially supported by the National Natural Science Foundation of China(General Program,Grant No.52474069)This research was financially supported by the Natural Gas Research Institute of Shaanxi Yanchang Petroleum(Group)Co.,Ltd.(Grant No.TYTY0824SFW0003).
文摘Hydraulic fracturing is a key technology for the efficient development of deep oil and gas reservoirs.However,fracture propagation behavior is influenced by rock elastoplasticity and thermal stress,making it difficult for traditional linear elastic models to accurately describe its dynamic response.To address this,this study employs the Continuum-Discontinuum Element Method(CDEM),incorporating an elastoplastic constitutive model,thermo-hydro-mechanical(THM)coupling effects,and cohesive zone characteristics at the fracture tip to establish a numerical model for hydraulic fracture propagation in deep elastoplastic reservoirs.A systematic investigation was conducted into the effects of fluid viscosity,reservoir temperature,injection rate,elastic modulus,and horizontal stress difference on fracture propagation.The findings show that a larger horizontal stress differential results in a more rectangular fracture geometry,a shorter fracture length,and a wider fracture.An increase in elastic modulus has a negligible impact on fracture length but reduces fracture width,resulting in a rounded rectangular morphology.Elevated reservoir temperature induces thermal tensile stress around the fracture,mitigating in-situ stress effects and reducing both breakdown and propagation pressures.Higher injection rates and fluid viscosity increase fracture initiation difficulty,promoting shorter but wider fractures with enhanced height growth beyond interlayer barriers.Additionally,horizontal stress significantly affects near-fracture plastic deformation:when the stress difference increases from 10 to 25 MPa,the maximum cumulative plastic strain in the surrounding rock rises by 66.67%.By integrating elastoplasticity and thermal stress effects,this study overcomes the limitations of conventional hydraulic fracturing simulations,offering novel insights for optimizing extraction strategies in deep unconventional reservoirs.
基金supported by the Science&Technology Development Fund of Tianjin Education Commission for Higher Education(No.2023KJ250).
文摘In the framework of elastoplastic theory,by introducing dissipative plastic energy(instead of cumulative plastic strain)and dissipative plastic energy rate(instead of cumulative plastic strain rate)into the ratchetting parameter evolution equation and isotropic evolution rules respectively,a cyclic elastoplastic constitutive model based on dissipative plastic energy is established.This model,termed the WDP model,describes the physical meaning and evolution rule of the unclosed stress–strain hysteresis loop using an energy method.A comparison of numerical implementation results with experimental data demonstrates the capability of the WDP model to predict the cyclic deformation of EA4T steel,effectively capturing the cyclic softening characteristics and ratchetting behaviors of axle steel EA4T.
基金supported by the National Natural Science Foundation of China (Grant Nos.12372376 and U22A20596).
文摘Numerical challenges,incorporating non-uniqueness,non-convexity,undefined gradients,and high curvature,of the positive level sets of yield function are encountered in stress integration when utilizing the return-mapping algorithm family.These phenomena are illustrated by an assessment of four typical yield functions:modified spatially mobilized plane criterion,Lade criterion,Bigoni-Piccolroaz criterion,and micromechanics-based upscaled Drucker-Prager criterion.One remedy to these issues,named the"Hop-to-Hug"(H2H)algorithm,is proposed via a convexification enhancement upon the classical cutting-plane algorithm(CPA).The improved robustness of the H2H algorithm is demonstrated through a series of integration tests in one single material point.Furthermore,a constitutive model is implemented with the H2H algorithm into the Abaqus/Standard finite-element platform.Element-level and structure-level analyses are carried out to validate the effectiveness of the H2H algorithm in convergence.All validation analyses manifest that the proposed H2H algorithm can offer enhanced stability over the classical CPA method while maintaining the ease of implementation,in which evaluations of the second-order derivatives of yield function and plastic potential function are circumvented.
文摘Concrete materials are employed extensively in a variety of large-scale structures due to their economic viability and superior mechanical properties.During the service life of concrete structures,they are inevitably subjected to damage from impact loading from natural disasters,such as earthquakes and storms.In recent years,the phasefield model has demonstrated exceptional capability in predicting the stochastic initiation,propagation,and bifurcation of cracks in materials.This study employs a phase-field model to focus on the rate dependency and failure response of concrete under impact deformation.A viscosity coefficient is introduced within the phase-field model to characterize the viscous behavior of dynamic crack propagation in concrete.The rate-dependent cohesive strength is defined within the yield function of concrete,where the rate sensitivity of cohesive strength facilitates the accumulation of the plastic driving force in the phase-field model.This process effectively captures the impact failure response of concrete.The applicability of the model was validated through unit cell experiments and numerical simulations of concrete under impact compression.Furthermore,the mechanical response and damage evolution mechanisms of concrete under impact loading were analyzed.It was observed that crack propagation in concrete initiates at material defects and,with increasing load,eventually develops in a direction perpendicular to the loading axis.
基金co-supported by the National Natural Science Foundation of China(No.52105316)the National Natural Foundation of Jiangxi,China(No.2021BAB214046)+1 种基金the Fundamental Research Funds for the Central Universities,China(No.501LKQB2022107021)the Young Elite Scientists Sponsorship Program by the China Association for Science and Technology(No.YESS20200397)。
文摘Electrically Assisted Forming(EAF)technology has obvious advantages in material forming.To develop an effective constitutive model considering electrical effects,room temperature and electrically assisted quasi-static uniaxial tensile tests were conducted using ultrathin nickelbased superalloy plates with a thickness of 0.25 mm.The research focused on the two most widely recognized effects:the Joule thermal and the electric athermal effects.The mechanism of current action can be divided into two scenarios:one considering the Joule thermal effect only,and the other considering both effects simultaneously.Two basic constitutive models,namely the Modified-Hollomon model and the Johnson-Cook(J-C)model,were selected to be optimized through the classification of two different situations,and four optimized constitutive models were proposed.It was found that the J-C model with simultaneous consideration of the Joule thermal effect and electric athermal effect had the best prediction effect by comparing the results of these four models.Finally,the accuracy of the optimization model was verified by finite element simulation of the electrically assisted stretching optimization model.The results show that the constitutive model can effectively predict the temperature effect caused by the Joule heat effect and the athermal effect of current on the material.
基金funded by the German Research Foundation(DFG)(Grant No.NA 330/20e1).
文摘An elastoplastic constitutive model based on the Modified Cam Clay(MCC)model is developed to describe the mechanical behaviour of soils cemented via microbially induced calcite precipitation(MICP).It considers the increase of the elastic stiffness,the change of the yield surface due to MICP cementation and the degradation of calcium carbonate bonds during shearing.Specifically,to capture the typical contraction-dilation transition in MICP soils,the original volumetric hardening rule in the MCC model is modified to a combined deviatoric and volumetric hardening rule.The model could reproduce a series of drained triaxial tests on MICP-treated soils with different calcium carbonate contents.Further,we carry out a parametric study and observe numerical instability in some cases.In combination with an analytical analysis,our numerical modelling has identified the benefits and limitations of using MCCbased models in the simulation of MICP-cemented soils,leading to suggestions for further model development.
基金the National Natural Science Foundation of China through Contract/Grant Numbers 12002245,12172263 and 11772237Chongqing Jiaotong University through Contract/Grant Number F1220038.
文摘This paper presents a micromechanics-based Cosserat continuum model for microstructured granular materials.By utilizing this model,the macroscopic constitutive parameters of granular materials with different microstructures are expressed as sums of microstructural information.The microstructures under consideration can be classified into three categories:a medium-dense microstructure,a dense microstructure consisting of one-sized particles,and a dense microstructure consisting of two-sized particles.Subsequently,the Cosserat elastoplastic model,along with its finite element formulation,is derived using the extended Drucker-Prager yield criteria.To investigate failure behaviors,numerical simulations of granular materials with different microstructures are conducted using the ABAQUS User Element(UEL)interface.It demonstrates the capacity of the proposed model to simulate the phenomena of strain-softening and strain localization.The study investigates the influence of microscopic parameters,including contact stiffness parameters and characteristic length,on the failure behaviors of granularmaterials withmicrostructures.Additionally,the study examines themesh independence of the presented model and establishes its relationship with the characteristic length.A comparison is made between finite element simulations and discrete element simulations for a medium-dense microstructure,revealing a good agreement in results during the elastic stage.Somemacroscopic parameters describing plasticity are shown to be partially related to microscopic factors such as confining pressure and size of the representative volume element.
基金funded by the National Key Research and Development Plan(No.2022YFC3203200)Department of Science and Technology of Guangdong Province(No.2021ZT09G087)the National Natural Science Foundation Project of China(No.42167025).
文摘Complexities in mechanical behaviours of rock masses mainly stem from inherent discontinuities,which calls for advanced bolt-grouting techniques for stability enhancement.Understanding the mechanical properties of bolt-grouted fractured rock mass(BGFR)and developing accurate prediction methods are crucial to optimize the BGFR support strategies.This paper establishes a new elastoplastic(E-P)model based on the orthotropic and the Mohr-Coulomb(M-C)plastic-yielding criteria.The elastic parameters of the model were derived through a meso-mechanical analysis of composite materials mechanics(CMM).Laboratory BGFR specimens were prepared and uniaxial compression test and variable-angle shear test considering different bolt arrangements were carried out to obtain the mechanical parameters of the specimens.Results showed that the anisotropy of BGFR mainly depends on the relative volume content of each component material in a certain direction.Moreover,the mechanical parameters deduced from the theory of composite materials which consider the short fibre effect are shown to be in good agreement with those determined by laboratory experiments,and the variation rules maintained good consistency.Last,a case study of a real tunnel project is provided to highlight the effectiveness,validity and robustness of the developed E-P model in prediction of stresses and deformations.
基金supported by the National Natural Science Foundation of China(Grant No.52074269)the Postgraduate Research&Practice Innovation Program of Jiangsu Province,and the Graduate Innovation Program of China University of Mining and Technology(Grant No.2024WLKXJ202).
文摘The recoverable strain of rock is completely classified as elastic strain in the conventional elastic-plastic theory,which often results in poor agreement between theoretical and experimental curves.This work proposes an improved elastoplastic model of rock materials considering the evolutions of crack deformation and elastic modulus to better characterize the nonlinear mechanical behavior of rock in the post-peak stage.In this model,the recoverable strain is assumed to be a combination of elastic and crack strain,and the constitutive relationship between crack strain and rock stress is deduced.Based on the proposed assumption,the evolutions of the mechanical parameters including strength parameters,elastic,plastic,and crack deformation parameters versus the plastic strain and confining stress were investigated.The developed elastoplastic model was validated by comparing the theoretical values with the results of the triaxial cyclic loading and unloading test.The theoretical calculation results show a good agreement with the laboratory test,which indicates that the improved elastoplastic model can effectively reflect the nonlinear mechanical behavior of the rock materials.The research results are expected to provide a valuable reference for further understanding the evolution of rock crack deformation.
基金supported by the Natural Science Foundation of Anhui Province(2408085ME147)Engineering Research Center of the Ministry of Education for Underground Mining Engineering(JYBGCZX2022103)+3 种基金the Key Laboratory of Building Structure and Underground Engineering of Anhui Province(KLBSUE-2023-02)the Key Laboratory of Underground Engineering and Disaster Prevention and Control of Henan Province(KFKT 2023-06)supported by National Natural Science Foundation of China(No.52378384)Natural Science Foundation of Anhui Province(No.2308085ME188).
文摘The lining and surrounding rock around tunnels constructed in cold areas exhibit nonuniform material properties due to the existence of a temperature field.This study considered the effects of these properties on the integrity of tunnel structures.By establishing an elastoplastic mechanical model,analytical solutions to the stress and displacement under five different elastoplastic states were derived and compared based on distinct yield criteria.The findings showed that with increasing relative radius,the displacement in the lining elastic zone initially decreased before increasing,whereas the shift in the plastic zone continued to increase.The displacement in the elastic zone of the frozen surrounding rock intensified with increasing relative radius,whereas the shift in the plastic zone experienced a gradual decline.The displacement of the inner wall of the lining was always greater than that of the outer wall,and this phenomenon occurred only after the frozen surrounding rock exhibited a plastic zone.The maximum displacements of the liner in its elastically limited and plastically limited states were 1.39,1.77,2.28,and 2.37 mm and 15.93,25.51,44.28,and 48.58 mm based on the Drucker-Prager(DP),Mohr-Coulomb(MC),Tresca,and double-shear strength criteria,respectively;the maximum limit displacements of the frozen surrounding rock were 12.74,20.41,35.43,and 38.87 mm and 85.32,103.38,569.23,and 680.43 mm,respectively.With increasing relative radius,the radial stresses within both the lining and the frozen surrounding rock intensified;and the tangential stress in the elastic zone of the lining decreased whereas the opposite change rule was observed in the plastic zone.The tangential stresses in the frozen surrounding rock and lining exhibited the same variation trend.Based on calculations with four distinct strength criteria,the elastic and plastic ultimate bearing capacities of the lining were 1.81,2.31,2.95,and 3.07 MPa,and 3.31,4.84,7.48,and 8.05 MPa,while those of the frozen surrounding rock were 8.52,13.24,22.17,and 24.18 MPa,and 16.76,32.46,74.15,and 85.64 MPa.In addition,with the expansion of the plastic zone,the phenomenon of a sudden change in the tangential stress at location r2 became progressively attenuated.The study findings can provide some theoretical guidance for the design and construction of tunnels in cold areas.
文摘The stability of dams and their foundations is an important problem to which dam engineers have paid close attention over the years. This paper presented two methods to analyze the stability of a gravity dam and its foundation. The direct analysis method was based on a rigid limit equilibrium method which regarded both dam and the rock foundation as undeformable rigid bodies. In this method, the safety factor of potential sliding surfaces was computed directly. The second method, the indirect analysis method, was based on elasto-plastic theory and employs nonlinear finite element method (FEM) in the analysis of stresses and deformation in the dam and its foundation. The determination of the safety degree of the structure was based on the convergence and abrupt the change criterion. The results obtained showed that structures' constituent material behavior played an active role in the failure of engineered structures in addition to the imposed load.
