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
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
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
Currently,there is a lack of research on the impact of excavation damage on the stability of underground compressed air energy storage(CAES)chambers.This study presents a comprehensive analytical framework for evaluat...Currently,there is a lack of research on the impact of excavation damage on the stability of underground compressed air energy storage(CAES)chambers.This study presents a comprehensive analytical framework for evaluating the elastic and elastoplastic stress fields in CAES chambers surrounding rock,incorporating excavation-induced centripetal reduction of rock stiffness and strength.A proposed model introduces exponential reduction functions for the deformation modulus and cohesion within the excavation disturbed zone(EDZ),deriving analytical solutions for both elastic and elastoplastic stress distributions.A case study of a practical engineering project validates the theoretical formulations through comparative analysis with numerical simulations,demonstrating strong consistency in stress field predictions.The main findings indicate that the EDZ causes a significant non-monotonic variation in the elastic hoop stress distribution.While it does not significantly affect the range of the plastic zone,it reduces the permeability and bearing capacity of the surrounding rock,highlighting the necessity of integrating the centripetal reduction of mechanical properties and strictly controlling excavation-induced damage in the design practice.Furthermore,this study provides a new approach for the selection of lining materials and structural design for CAES chambers:the radial stiffness smoothly increases to match the EDZ surrounding rock stiffness,and the cohesion exceeds that of the surrounding rock,which can significantly optimize the overall system's stress distribution.This study provides valuable insights and references for the selection of excavation methods,stability assessment,and support structure design for CAES engineering,and holds significant importance for improving the CAES technology system.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
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
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
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
Nanoindentation can effectively evaluate the mechanical properties of materials in the form of bulk and coating.However,the relationship between the indentation response and the stress–strain curve of thin-film elast...Nanoindentation can effectively evaluate the mechanical properties of materials in the form of bulk and coating.However,the relationship between the indentation response and the stress–strain curve of thin-film elastoplastic materials is complex and thus difficult to be elucidated using traditional physics-based,empirical or statistical models.In this study,the convolutional neural network(CNN),as a practical machine learning method,is adopted and trained to rapidly obtain the mechanical properties of thin-film elastoplastic materials using nanoindentation.The proposed method is targeted for efficiently predicting mechanical properties of thin-film materials from the applied load–penetration depth curve.Combined with the power-law model to describe the elastoplastic characteristics,a dataset comprising 228 nanoindentation cases with wide ranges of material properties is numerically simulated by ABAQUS and the corresponding results are adopted for the CNN training and validating.By addressing the important elastoplastic properties characterized by elastic modulus,yield strength,and hardening exponent,the impacts of CNN’s architecture and training epochs on the predicting performance are investigated in detail.By varying the number of convolutional layers,the influence of mechanical parameters of thin-film materials on the CNN prediction accuracy is discussed.The results show that compared with the traditional reverse algorithm,CNN can greatly reduce the computational complexity and computation time and has better prediction accuracy for the constitutive parameters of thin-film elastoplastic materials.展开更多
The elastoplastic field near crack tips is investigated through finite element simulation.A refined mesh model near the crack tip is proposed. In the mesh refining area, element size continuously varies from the nanom...The elastoplastic field near crack tips is investigated through finite element simulation.A refined mesh model near the crack tip is proposed. In the mesh refining area, element size continuously varies from the nanometer scale to themicrometer scale and the millimeter scale. Graphics of the plastic zone, the crack tip blunting, and the deformed crack tip elements are given in the paper.Based on the curves of stress and plastic strain, closely near the crack tip, the stresssingularity index and the stress intensity factor,as well as the plastic strain singularity index and the plastic strain intensity factor are determined.Thestress and plastic strainsingular index vary with the load, while the dimensions of the stress and the plastic strain intensity factorsdependon the stress and the plastic strain singularity index, respectively. The singular field near the elastoplastic crack tip is characterized by the stress singularity index and the stress intensity factor, or alternativelythe plastic strain singularity index and the plastic strain intensityfactor.At the end of the paper, following Irwin’s concept of fracture mechanics,σδKσδKcriterion andεδQεδQcriterion are proposed.Besides, crack tip angle criterion is also presented.展开更多
A new finite strain elastoplastic J2-flow model is established with an explicit formulation of work-hardening and softening effects up to eventual failure,in which both a new flow rule free of yielding and an asymptot...A new finite strain elastoplastic J2-flow model is established with an explicit formulation of work-hardening and softening effects up to eventual failure,in which both a new flow rule free of yielding and an asymptotically vanishing stress limit are incorporated.The novelties of this new model are as follows:(i)Fatigue failure effects under repeated loading conditions with either constant or varying amplitudes are automatically characterized as inherent response features;(ii)neither additional damage-like variables nor failure criteria need to be involved;and(iii)both high-and low-cycle fatigue effects may be simultaneously treated.A fast and efficient algorithm of high accuracy is proposed for directly simulating high-and medium-high-cycle fatigue failure effects under repeated loading conditions.Toward this goal,a direct and explicit relationship between the fatigue life and the stress amplitude is obtained by means of explicit and direct procedures of integrating the coupled elastoplastic rate equations for any given number of loading-unloading cycles with varying stress amplitudes.Numerical examples suggest that the new algorithm is much more fast and efficient than usual tedious and very time-consuming integration procedures.展开更多
An exploratory discussion is presented on the application of egg-shaped function in elasto-plastic constitutive analysis for soft clay.Two main tasks of the paper are:1)to propose a complete yield criterion based on e...An exploratory discussion is presented on the application of egg-shaped function in elasto-plastic constitutive analysis for soft clay.Two main tasks of the paper are:1)to propose a complete yield criterion based on egg-shaped function and supplement its definition in the deviatoric section,and then a yield criterion suitable for 3D stress conditions is obtained;2)to elaborate its numerical implementation based on the drained triaxial tests.During the above discussion,a non-associated flow rule is proposed,in which the stress-dilatancy relationship in most classical theory is replaced by a linear dependence between the stress state parameterηand the rotation angleγof the plastic potential surface.Thereafter,isotropic and kinematic hardening behavior is considered by employing the hardening parameter H,which can be expressed as the function of plastic work Wp.Finally,comparisons between numerical results and test data on Taizhou soft clay are made to verify the effectiveness of the proposed model.展开更多
The combined self-consistent and Mori-Tanaka approach proposed for the evaluation of the effective elastic property of particulate composites is extended to evMuate the effective elastoplastic property of particulate ...The combined self-consistent and Mori-Tanaka approach proposed for the evaluation of the effective elastic property of particulate composites is extended to evMuate the effective elastoplastic property of particulate composites. Suppose there are sufficient identical particle inclusions with total volume fraction c in a representative volume element （RVE） of a particulate composite, these inclusions are separated into two groups, with volume fractions （1 -A-1）c and c/A over the RVE, respectively. We assume that the first group of inclusions has already been embedded in the original matrix to form a fictitious matrix, and the RVE of the composite consists of the fictitious matrix and the second group of particle inclusions. The property of the fictitious matrix is determined by the conventional self-consistent scheme, while the effective elastoplastic property of the composite is determined by the conventional Mori-Tanaka scheme. Analysis shows that, the conventional Mori-Tanaka scheme and self-consistent scheme can be obtained as the two limit cases of the extended approach as A = 1 and A = c~, respectively. The constitutive behavior of the inclusions in either Group I or Group II is identical, indicating the consistency in the description of the constitutive behavior in the two steps. ~klrthermore, the effective elastoplastic behavior of some typical particulate composites is analyzed, and the satisfactory agreement between the computational and experimental results demonstrates the validity of the extended approach. The introduced A can serve reasonably as a parameter, which is related to the actual property of composites and can be identified by experiments, for a more accurate evaluation of the effective elastoplastic property of particulate composites.展开更多
Nonlinear behaviors are commonplace in many complex engineering applications,e.g.,metal forming,vehicle crash test and so on.This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear ...Nonlinear behaviors are commonplace in many complex engineering applications,e.g.,metal forming,vehicle crash test and so on.This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear problems including general large deformation hyperelastic problems and small deformation elastoplastic problems,to reveal the advantages of local refinement property of T-splines in describing nonlinear behavior of materials.By applying the adaptive refinement capability of T-splines during the iteration process of analysis,the numerical simulation accuracy of the nonlinear model could be increased dramatically.The Bézier extraction of the T-splines provides an element structure for isogeometric analysis that can be easily incorporated into existing nonlinear finite element codes.In addition,T-splines show great superiority of modeling complex geometries especially when the model is irregular and with hole features.Several numerical examples have been tested to validate the accuracy and convergence of the proposed method.The obtained results are compared with those from NURBS-based isogeometric analysis and commercial software ABAQUS.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Science and Technology Commission of Shanghai Municipality,Grant/Award Number:22dz1205300。
文摘Currently,there is a lack of research on the impact of excavation damage on the stability of underground compressed air energy storage(CAES)chambers.This study presents a comprehensive analytical framework for evaluating the elastic and elastoplastic stress fields in CAES chambers surrounding rock,incorporating excavation-induced centripetal reduction of rock stiffness and strength.A proposed model introduces exponential reduction functions for the deformation modulus and cohesion within the excavation disturbed zone(EDZ),deriving analytical solutions for both elastic and elastoplastic stress distributions.A case study of a practical engineering project validates the theoretical formulations through comparative analysis with numerical simulations,demonstrating strong consistency in stress field predictions.The main findings indicate that the EDZ causes a significant non-monotonic variation in the elastic hoop stress distribution.While it does not significantly affect the range of the plastic zone,it reduces the permeability and bearing capacity of the surrounding rock,highlighting the necessity of integrating the centripetal reduction of mechanical properties and strictly controlling excavation-induced damage in the design practice.Furthermore,this study provides a new approach for the selection of lining materials and structural design for CAES chambers:the radial stiffness smoothly increases to match the EDZ surrounding rock stiffness,and the cohesion exceeds that of the surrounding rock,which can significantly optimize the overall system's stress distribution.This study provides valuable insights and references for the selection of excavation methods,stability assessment,and support structure design for CAES engineering,and holds significant importance for improving the CAES technology system.
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 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 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.
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.
基金supported by the National Natural Science Foundation of China(No.52175148)the Natural Science Foundation of Shaanxi Province(No.2021KW-25)+1 种基金the Open Cooperation Innovation Fund of Xi’an Modern Chemistry Research Institute(No.SYJJ20210409)the Fundamental Research Funds for the Central Universities(No.3102018ZY015).
文摘Nanoindentation can effectively evaluate the mechanical properties of materials in the form of bulk and coating.However,the relationship between the indentation response and the stress–strain curve of thin-film elastoplastic materials is complex and thus difficult to be elucidated using traditional physics-based,empirical or statistical models.In this study,the convolutional neural network(CNN),as a practical machine learning method,is adopted and trained to rapidly obtain the mechanical properties of thin-film elastoplastic materials using nanoindentation.The proposed method is targeted for efficiently predicting mechanical properties of thin-film materials from the applied load–penetration depth curve.Combined with the power-law model to describe the elastoplastic characteristics,a dataset comprising 228 nanoindentation cases with wide ranges of material properties is numerically simulated by ABAQUS and the corresponding results are adopted for the CNN training and validating.By addressing the important elastoplastic properties characterized by elastic modulus,yield strength,and hardening exponent,the impacts of CNN’s architecture and training epochs on the predicting performance are investigated in detail.By varying the number of convolutional layers,the influence of mechanical parameters of thin-film materials on the CNN prediction accuracy is discussed.The results show that compared with the traditional reverse algorithm,CNN can greatly reduce the computational complexity and computation time and has better prediction accuracy for the constitutive parameters of thin-film elastoplastic materials.
基金The work was supported by the National Natural Science Foundation of China (Grant 11572226).
文摘The elastoplastic field near crack tips is investigated through finite element simulation.A refined mesh model near the crack tip is proposed. In the mesh refining area, element size continuously varies from the nanometer scale to themicrometer scale and the millimeter scale. Graphics of the plastic zone, the crack tip blunting, and the deformed crack tip elements are given in the paper.Based on the curves of stress and plastic strain, closely near the crack tip, the stresssingularity index and the stress intensity factor,as well as the plastic strain singularity index and the plastic strain intensity factor are determined.Thestress and plastic strainsingular index vary with the load, while the dimensions of the stress and the plastic strain intensity factorsdependon the stress and the plastic strain singularity index, respectively. The singular field near the elastoplastic crack tip is characterized by the stress singularity index and the stress intensity factor, or alternativelythe plastic strain singularity index and the plastic strain intensityfactor.At the end of the paper, following Irwin’s concept of fracture mechanics,σδKσδKcriterion andεδQεδQcriterion are proposed.Besides, crack tip angle criterion is also presented.
基金This study was carried out under the joint support of the fund from NSFC(No.11372172)and the start-up fund from Jinan University,Guangzhou,China.
文摘A new finite strain elastoplastic J2-flow model is established with an explicit formulation of work-hardening and softening effects up to eventual failure,in which both a new flow rule free of yielding and an asymptotically vanishing stress limit are incorporated.The novelties of this new model are as follows:(i)Fatigue failure effects under repeated loading conditions with either constant or varying amplitudes are automatically characterized as inherent response features;(ii)neither additional damage-like variables nor failure criteria need to be involved;and(iii)both high-and low-cycle fatigue effects may be simultaneously treated.A fast and efficient algorithm of high accuracy is proposed for directly simulating high-and medium-high-cycle fatigue failure effects under repeated loading conditions.Toward this goal,a direct and explicit relationship between the fatigue life and the stress amplitude is obtained by means of explicit and direct procedures of integrating the coupled elastoplastic rate equations for any given number of loading-unloading cycles with varying stress amplitudes.Numerical examples suggest that the new algorithm is much more fast and efficient than usual tedious and very time-consuming integration procedures.
基金Project(41672264)supported by the National Natural Science Foundation of ChinaProject(2019C03103)supported by the Key Research and Development Program of Zhejiang Province,China。
文摘An exploratory discussion is presented on the application of egg-shaped function in elasto-plastic constitutive analysis for soft clay.Two main tasks of the paper are:1)to propose a complete yield criterion based on egg-shaped function and supplement its definition in the deviatoric section,and then a yield criterion suitable for 3D stress conditions is obtained;2)to elaborate its numerical implementation based on the drained triaxial tests.During the above discussion,a non-associated flow rule is proposed,in which the stress-dilatancy relationship in most classical theory is replaced by a linear dependence between the stress state parameterηand the rotation angleγof the plastic potential surface.Thereafter,isotropic and kinematic hardening behavior is considered by employing the hardening parameter H,which can be expressed as the function of plastic work Wp.Finally,comparisons between numerical results and test data on Taizhou soft clay are made to verify the effectiveness of the proposed model.
基金Project supported by the National Natural Science Foundation of China-NSAF (No. 10976032)Japan Society for the Promotion of Science (No. L08538)
文摘The combined self-consistent and Mori-Tanaka approach proposed for the evaluation of the effective elastic property of particulate composites is extended to evMuate the effective elastoplastic property of particulate composites. Suppose there are sufficient identical particle inclusions with total volume fraction c in a representative volume element （RVE） of a particulate composite, these inclusions are separated into two groups, with volume fractions （1 -A-1）c and c/A over the RVE, respectively. We assume that the first group of inclusions has already been embedded in the original matrix to form a fictitious matrix, and the RVE of the composite consists of the fictitious matrix and the second group of particle inclusions. The property of the fictitious matrix is determined by the conventional self-consistent scheme, while the effective elastoplastic property of the composite is determined by the conventional Mori-Tanaka scheme. Analysis shows that, the conventional Mori-Tanaka scheme and self-consistent scheme can be obtained as the two limit cases of the extended approach as A = 1 and A = c~, respectively. The constitutive behavior of the inclusions in either Group I or Group II is identical, indicating the consistency in the description of the constitutive behavior in the two steps. ~klrthermore, the effective elastoplastic behavior of some typical particulate composites is analyzed, and the satisfactory agreement between the computational and experimental results demonstrates the validity of the extended approach. The introduced A can serve reasonably as a parameter, which is related to the actual property of composites and can be identified by experiments, for a more accurate evaluation of the effective elastoplastic property of particulate composites.
基金support by the Natural Science Foundation of China(Project Nos.61972011 and 61572056).
文摘Nonlinear behaviors are commonplace in many complex engineering applications,e.g.,metal forming,vehicle crash test and so on.This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear problems including general large deformation hyperelastic problems and small deformation elastoplastic problems,to reveal the advantages of local refinement property of T-splines in describing nonlinear behavior of materials.By applying the adaptive refinement capability of T-splines during the iteration process of analysis,the numerical simulation accuracy of the nonlinear model could be increased dramatically.The Bézier extraction of the T-splines provides an element structure for isogeometric analysis that can be easily incorporated into existing nonlinear finite element codes.In addition,T-splines show great superiority of modeling complex geometries especially when the model is irregular and with hole features.Several numerical examples have been tested to validate the accuracy and convergence of the proposed method.The obtained results are compared with those from NURBS-based isogeometric analysis and commercial software ABAQUS.
