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
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
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
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
Finite dement formulations are used to simulate the evolution of the elastoplastic response of functionally graded cemented carbides （FGCC） due to thermal loading. The geometry of specimens is an axisymmetric solid ...Finite dement formulations are used to simulate the evolution of the elastoplastic response of functionally graded cemented carbides （FGCC） due to thermal loading. The geometry of specimens is an axisymmetric solid cylinder with a two-dimensional gradient. The elastoplastic constitutive relationship is developed by constraint factors. Numerical results show that compressive stresses occur in the surface zone and tensile stresses in the cobalt rich zone when the temperature drops from the initial stress-free temperature of 800 to 0℃. The maximum value of the surface compressive stress is 254 MPa and the maximum value of the tensile stress is 252 MPa in the cobalt rich zones. When the cobalt concentration difference in the specimens is equal to or greater than 0.3, there is pronounced plastic flow in cobalt rich zone. When the temperature heats up from 0 to 800 ℃, the total plastic strain reaches 0.001 4. Plastic flow has a significant effect on the reduction of thermal stress concentration.展开更多
Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact con...Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact conditions are relaxed totally. First, the coerciveness of the functional is proved. Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated. The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality. A mathematical foundation is developed for the variational extremum principle of elastoplastic contact problems. The developed variational extremum forms can give an effective and strict mathematical modeling to solve contact problems with mathematical programming.展开更多
The elastoplastic mechanical properties of the weld and heat affected zone metals have comparatively major impact on the forming process of tailor-welded blanks. A few scholars investigated the elastoplastic mechanica...The elastoplastic mechanical properties of the weld and heat affected zone metals have comparatively major impact on the forming process of tailor-welded blanks. A few scholars investigated the elastoplastic mechanical properties of the weld and heat affected zone, but they only simply assumed that it was a uniform distribution elastoplastic material different from the base materials. Four types of tailor-welded blanks which consist of ST12 and 304 stainless steel plates are selected as the research objects, the elastoplastic mechanical properties of the tailor-welded blanks weld and heat affected zone metals are obtained based on the nanoindentation tests, and the Erichsen cupping tests are conducted by combining numerical simulation with physical experiment. The nanoindentation tests results demonstrate that the elastoplastic mechanical properties of the weld and heat affected zone metals are not only different from the base materials, but also varying between the weld metals and the heat affected zone metals. Comparing the Erichsen cupping test resulted from numerical with that from experimental method, it is found that the numerical value of Erichsen cupping test which consider the elastoplastic mechanical properties of the weld and heat affected zone metals have a good agreement with the experimental result, and the relative error is only 4.8%. The proposed research provides good solutions for the inhomogeneous elastoplastic mechanical properties of the tailor-welded blanks weld and heat affected zone metals, and improves the control performance of tailor-welded blanks forming accuracy.展开更多
An elastoplastic method for analyzing the 3D deformation, stress and transverse distribution of tension stress during cold strip rolling is developed. The analysis is based on the elastoplastic variational principle i...An elastoplastic method for analyzing the 3D deformation, stress and transverse distribution of tension stress during cold strip rolling is developed. The analysis is based on the elastoplastic variational principle in which a kinematically admissible velocity field is constructed with the lateral flow function as an unknown function. The stress distribution and volume strain distribution are obtained by solving the simultaneous equations formed by the longitudinal differential equation of equilibrium and constitutive equations. The lateral flow function is determined by minimizing the total energy dissipation rate. Experimental investigation was carried out on a reversible cold mill. The front tension stress distributions in cold rolled strips were measured by a multi roll segmented tension sensing shapemeter. The calculated results are in good agreement with the measured ones.展开更多
As a new technique in ground improvement, geosynthetic-encased columns (GECs) have promising applications in soft soil foundation. By assuming yielding occurs in the columns while the surrounding soil and the geosynth...As a new technique in ground improvement, geosynthetic-encased columns (GECs) have promising applications in soft soil foundation. By assuming yielding occurs in the columns while the surrounding soil and the geosynthetic remain elastic, an elastoplastic analytical procedure for foundations improved by GECs is proposed. The radial stresses that the geosynthetic provides and the elastoplastic deformations of the foundation resting on a rigid base are derived. A comparison with finite element analysis shows that the proposed method is effective and can provide a reasonable prediction of a GEC's deformation. Subsequent parametric analysis indicates that higher geosynthetic stiffness leads to better performance of the composite foundation. The optimum length of encasement is related to the load acting on the foundation and the permissible vertical and radial displacements of the column. Moreover, as the dilation angle of the column increases, the settlement decreases, especially under high loading. The influence of the encasement is more significant in soils with smaller elastic modulus.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
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
Water distribution networks are essential components of water supply systems. The combination of pipe structural deterioration and mechanics leads to the failure of pipelines. A physical model for estimating the pipe ...Water distribution networks are essential components of water supply systems. The combination of pipe structural deterioration and mechanics leads to the failure of pipelines. A physical model for estimating the pipe failure must include both the pipe deterioration model and mechanics model. Winkler pipe-soil interaction (WPSI), an analytical mechanics model developed by Rajani and Tesfamariam (2004), takes external and internal loads, temperature changes, loss of bedding support, and the elastoplastic effect of soil into consideration. Based on the WPSI model, a method to evaluate the elastic and plastic areas was proposed in the present study. An FEM model based on pipe-soil interaction (PSI) element was used to verify the analytical model. Sensitivity analyses indicate that the soft soil, long pipe and high temperature induced the axial plastic deformation more likely, which, however, may not occur in normal scenarios. The soft soil, pipes in small diameters, long unsupported bedding are prone to form flexural plastic area. The results show that the pipes subjected to the same loads have smaller stresses in the elastoplastic analysis than elastic analysis. The difference, however, is slight.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
Due to differences in the properties of composition materials and construction techniques,unreinforced masonry is characterized by low strength,anisotropy,nonuniformity,and low ductility.In order to accurately simulat...Due to differences in the properties of composition materials and construction techniques,unreinforced masonry is characterized by low strength,anisotropy,nonuniformity,and low ductility.In order to accurately simulate the mechanical behavior of unreinforced brick masonry walls under static and dynamic loads,a new elastoplastic damage constitutive model was proposed and the corresponding subroutine was developed based on the concrete material constitutive model.In the proposed constitutive model,the Rankine strength theory and the Drucker-Prager strength theory were used to define the tensile and compressive yield surface function of materials,respectively.Moreover,the stress updating algorithm was modified to consider the tensile plastic permanent deformation of masonry materials.To verify the accuracy of the proposed constitutive model,numerical simulations of the brick masonry under monotonic and cyclic uniaxial tension and compression loads were carried out.Comparisons among the numerical and theoretical and experimental results show that the proposed model can properly reflect the masonry material mechanical properties.Furthermore,the numerical models of four pieces of masonry walls with different mortar strengths were established.Low cyclic loadings were applied and the results show that the proposed constitutive model can properly simulate the wall shear failure characteristics,and the force-displacement hysteretic curves obtained by numerical simulation are in good agreement with the tests.Overall,the proposed elastic-plastic damage constitutive model can simulate the nonlinear behavior of unreinforced brick masonry walls very well,and can be used to predict the structural response of masonry walls.展开更多
An isotropic hardening elastoplastic model for soil is presented, which takes into consideration the influence of structure and overconsolidation on strength and deformation of clays. Based on the superloading concept...An isotropic hardening elastoplastic model for soil is presented, which takes into consideration the influence of structure and overconsolidation on strength and deformation of clays. Based on the superloading concept and subloading concept, the inner structural variable ω and overconsolidation variable ρ are introduced to describe the structure and overconsolidation of soil. The present model requires three additional parameters which can be obtained by conventional triaxial test, and the other parameters are same as those of modified Cam-clay(MCC) model. The performance of the proposed model is verified by undrained and drained triaxial tests.展开更多
The elastoplastic pure bending problem of a curved beam with material inhomo- geneity is investigated based on Tresca＇s yield criterion and its associated flow rule. Suppose that the material is elastically isotropic...The elastoplastic pure bending problem of a curved beam with material inhomo- geneity is investigated based on Tresca＇s yield criterion and its associated flow rule. Suppose that the material is elastically isotropic, ideally elastic-plastic and its elastic modulus and yield limit vary radially according to exponential functions. Closed-form solutions to the stresses and radial displacement in both purely elastic stress state and partially plastic stress state are presented. Numerical examples reveal the distinct characteristics of elastoplastic bending of a curved beam composed of inhomogeneous materials. Due to the inhomogeneity of materials, the bearing capac- ity of the curved beam can be improved greatly and the initial yield mode can also be dominated. Closed-form solutions presented here can serve as benchmark results for evaluating numerical solutions.展开更多
A fully coupling model for the diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries is proposed. The effect of the mechanical stress on the lithium diffusion is accounted for b...A fully coupling model for the diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries is proposed. The effect of the mechanical stress on the lithium diffusion is accounted for by the mechanical part of the chemical potential derived from the Gibbs free energy along with the logarithmic stress and strain. Eight dimensionless parameters, governing the stress-assisted diffusion and the diffusion induced elastoplastic bending, are identified. It is found that the finite plasticity starting from the interface of the bilayer increases the chemical potential gradient and thereby facilitates the lithium diffusion. The full plastic flow makes the abnormal lithium concentration distribution possible, i.e., the concentration at the lithium inlet can be lower than the concentration at the interface(downstream). The increase in the thickness of the active layer during charging is much larger than the eigen-stretch due to lithiation, and this excess thickening is found to be caused by the lithiation induced plastic yield.展开更多
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
Based on the ABAQUS platform for finite element analysis, the extended finite element method (XFEM) considering elastoplastic constitutive relationship is developed, by which the displacement discontinuity across the ...Based on the ABAQUS platform for finite element analysis, the extended finite element method (XFEM) considering elastoplastic constitutive relationship is developed, by which the displacement discontinuity across the crack surface and the strong nonlinearity near the crack tip can be described more accurately. The strip specimens with unilateral cracks and central cracks under uniaxial tension are simulated using the XFEM and the FEM, respectively. The J-integral across the crack on each incremen t is calcula ted using the equivale nt domain integral met hod (EDIM), the interaction integral met hod and the FEM, respectively. The effec ts of mesh size and mesh shape near the crack tip, element type and different calculation methods on the accuracy of J-integral are analyzed. The simulation results show that the XFEM is more accurate than the FEM with the same element size and type. The fracture tests of cast iron specimens with unilateral cracks under uniaxial tension are performed, and the J-integral criterion is valid to predict the fracture initiation in numerical simulation. The critical value of J-integral is calculated using the EDIM of the XFEM. The comparisons demonstrate that the simulated elastoplastic load-displacement curves with the XFEM are in good agreement with the experimental results.展开更多
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The National Natural Science Foundation of China(No.50323008,31070517)Scientific Research Foundation of Guangxi Education Department(No.201203YB097)
文摘Finite dement formulations are used to simulate the evolution of the elastoplastic response of functionally graded cemented carbides （FGCC） due to thermal loading. The geometry of specimens is an axisymmetric solid cylinder with a two-dimensional gradient. The elastoplastic constitutive relationship is developed by constraint factors. Numerical results show that compressive stresses occur in the surface zone and tensile stresses in the cobalt rich zone when the temperature drops from the initial stress-free temperature of 800 to 0℃. The maximum value of the surface compressive stress is 254 MPa and the maximum value of the tensile stress is 252 MPa in the cobalt rich zones. When the cobalt concentration difference in the specimens is equal to or greater than 0.3, there is pronounced plastic flow in cobalt rich zone. When the temperature heats up from 0 to 800 ℃, the total plastic strain reaches 0.001 4. Plastic flow has a significant effect on the reduction of thermal stress concentration.
基金The National Natural Science Foundation of China(No.10672039)the Key Project of Ministry of Education of China(No.105083)
文摘Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact conditions are relaxed totally. First, the coerciveness of the functional is proved. Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated. The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality. A mathematical foundation is developed for the variational extremum principle of elastoplastic contact problems. The developed variational extremum forms can give an effective and strict mathematical modeling to solve contact problems with mathematical programming.
基金Supported by National Natural Science Foundation of China(Grant No.51275444)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20121333110003)Natural Science Foundation-Steel and Iron Foundation of Hebei Province,China(Grant No.E2014203271)
文摘The elastoplastic mechanical properties of the weld and heat affected zone metals have comparatively major impact on the forming process of tailor-welded blanks. A few scholars investigated the elastoplastic mechanical properties of the weld and heat affected zone, but they only simply assumed that it was a uniform distribution elastoplastic material different from the base materials. Four types of tailor-welded blanks which consist of ST12 and 304 stainless steel plates are selected as the research objects, the elastoplastic mechanical properties of the tailor-welded blanks weld and heat affected zone metals are obtained based on the nanoindentation tests, and the Erichsen cupping tests are conducted by combining numerical simulation with physical experiment. The nanoindentation tests results demonstrate that the elastoplastic mechanical properties of the weld and heat affected zone metals are not only different from the base materials, but also varying between the weld metals and the heat affected zone metals. Comparing the Erichsen cupping test resulted from numerical with that from experimental method, it is found that the numerical value of Erichsen cupping test which consider the elastoplastic mechanical properties of the weld and heat affected zone metals have a good agreement with the experimental result, and the relative error is only 4.8%. The proposed research provides good solutions for the inhomogeneous elastoplastic mechanical properties of the tailor-welded blanks weld and heat affected zone metals, and improves the control performance of tailor-welded blanks forming accuracy.
基金granted by China Postdoctoral Science Foundation
文摘An elastoplastic method for analyzing the 3D deformation, stress and transverse distribution of tension stress during cold strip rolling is developed. The analysis is based on the elastoplastic variational principle in which a kinematically admissible velocity field is constructed with the lateral flow function as an unknown function. The stress distribution and volume strain distribution are obtained by solving the simultaneous equations formed by the longitudinal differential equation of equilibrium and constitutive equations. The lateral flow function is determined by minimizing the total energy dissipation rate. Experimental investigation was carried out on a reversible cold mill. The front tension stress distributions in cold rolled strips were measured by a multi roll segmented tension sensing shapemeter. The calculated results are in good agreement with the measured ones.
基金Project (No. 2011FZA4021) supported by the Fundamental Research Funds for the Central Universities, China
文摘As a new technique in ground improvement, geosynthetic-encased columns (GECs) have promising applications in soft soil foundation. By assuming yielding occurs in the columns while the surrounding soil and the geosynthetic remain elastic, an elastoplastic analytical procedure for foundations improved by GECs is proposed. The radial stresses that the geosynthetic provides and the elastoplastic deformations of the foundation resting on a rigid base are derived. A comparison with finite element analysis shows that the proposed method is effective and can provide a reasonable prediction of a GEC's deformation. Subsequent parametric analysis indicates that higher geosynthetic stiffness leads to better performance of the composite foundation. The optimum length of encasement is related to the load acting on the foundation and the permissible vertical and radial displacements of the column. Moreover, as the dilation angle of the column increases, the settlement decreases, especially under high loading. The influence of the encasement is more significant in soils with smaller elastic modulus.
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Project supported by the National Natural Science Foundation of China (No. 50278088)the Program for New Century Excellent Talents in University (No. NCET-04-0525), China
文摘Water distribution networks are essential components of water supply systems. The combination of pipe structural deterioration and mechanics leads to the failure of pipelines. A physical model for estimating the pipe failure must include both the pipe deterioration model and mechanics model. Winkler pipe-soil interaction (WPSI), an analytical mechanics model developed by Rajani and Tesfamariam (2004), takes external and internal loads, temperature changes, loss of bedding support, and the elastoplastic effect of soil into consideration. Based on the WPSI model, a method to evaluate the elastic and plastic areas was proposed in the present study. An FEM model based on pipe-soil interaction (PSI) element was used to verify the analytical model. Sensitivity analyses indicate that the soft soil, long pipe and high temperature induced the axial plastic deformation more likely, which, however, may not occur in normal scenarios. The soft soil, pipes in small diameters, long unsupported bedding are prone to form flexural plastic area. The results show that the pipes subjected to the same loads have smaller stresses in the elastoplastic analysis than elastic analysis. The difference, however, is slight.
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National Key Research and Development Program of China under Grant Nos.2018YFC1504400 and 2019YFC1509301Natural Science Foundation of China under Grant No.52078471Scientific Research Fund of Institute of Engineering Mechanics,China Earthquake Administration under Grant No.2019EEEVL0402。
文摘Due to differences in the properties of composition materials and construction techniques,unreinforced masonry is characterized by low strength,anisotropy,nonuniformity,and low ductility.In order to accurately simulate the mechanical behavior of unreinforced brick masonry walls under static and dynamic loads,a new elastoplastic damage constitutive model was proposed and the corresponding subroutine was developed based on the concrete material constitutive model.In the proposed constitutive model,the Rankine strength theory and the Drucker-Prager strength theory were used to define the tensile and compressive yield surface function of materials,respectively.Moreover,the stress updating algorithm was modified to consider the tensile plastic permanent deformation of masonry materials.To verify the accuracy of the proposed constitutive model,numerical simulations of the brick masonry under monotonic and cyclic uniaxial tension and compression loads were carried out.Comparisons among the numerical and theoretical and experimental results show that the proposed model can properly reflect the masonry material mechanical properties.Furthermore,the numerical models of four pieces of masonry walls with different mortar strengths were established.Low cyclic loadings were applied and the results show that the proposed constitutive model can properly simulate the wall shear failure characteristics,and the force-displacement hysteretic curves obtained by numerical simulation are in good agreement with the tests.Overall,the proposed elastic-plastic damage constitutive model can simulate the nonlinear behavior of unreinforced brick masonry walls very well,and can be used to predict the structural response of masonry walls.
基金the National Natural Science Foundation of China(No.41602282)
文摘An isotropic hardening elastoplastic model for soil is presented, which takes into consideration the influence of structure and overconsolidation on strength and deformation of clays. Based on the superloading concept and subloading concept, the inner structural variable ω and overconsolidation variable ρ are introduced to describe the structure and overconsolidation of soil. The present model requires three additional parameters which can be obtained by conventional triaxial test, and the other parameters are same as those of modified Cam-clay(MCC) model. The performance of the proposed model is verified by undrained and drained triaxial tests.
基金supported by the Disaster Prevention and Engineering Safety Laboratory in Guangxi and the National NaturalScience Foundation of China(Nos.11072177 and 10872150)the Scientific Research Foundation for the ReturnedOverseas Chinese Scholars,State Education Ministry
文摘The elastoplastic pure bending problem of a curved beam with material inhomo- geneity is investigated based on Tresca＇s yield criterion and its associated flow rule. Suppose that the material is elastically isotropic, ideally elastic-plastic and its elastic modulus and yield limit vary radially according to exponential functions. Closed-form solutions to the stresses and radial displacement in both purely elastic stress state and partially plastic stress state are presented. Numerical examples reveal the distinct characteristics of elastoplastic bending of a curved beam composed of inhomogeneous materials. Due to the inhomogeneity of materials, the bearing capac- ity of the curved beam can be improved greatly and the initial yield mode can also be dominated. Closed-form solutions presented here can serve as benchmark results for evaluating numerical solutions.
基金Project supported by the National Natural Science Foundation of China(No.11332005)
文摘A fully coupling model for the diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries is proposed. The effect of the mechanical stress on the lithium diffusion is accounted for by the mechanical part of the chemical potential derived from the Gibbs free energy along with the logarithmic stress and strain. Eight dimensionless parameters, governing the stress-assisted diffusion and the diffusion induced elastoplastic bending, are identified. It is found that the finite plasticity starting from the interface of the bilayer increases the chemical potential gradient and thereby facilitates the lithium diffusion. The full plastic flow makes the abnormal lithium concentration distribution possible, i.e., the concentration at the lithium inlet can be lower than the concentration at the interface(downstream). The increase in the thickness of the active layer during charging is much larger than the eigen-stretch due to lithiation, and this excess thickening is found to be caused by the lithiation induced plastic yield.
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the National Natural Science Foundation of China (Grant 51465002, 11262001, 51675110, 11632007)the Systematic Project of Guangxi Key Laboratory Project of Disaster Prevention and Engineering Safety (Grant 2016ZDX07).
文摘Based on the ABAQUS platform for finite element analysis, the extended finite element method (XFEM) considering elastoplastic constitutive relationship is developed, by which the displacement discontinuity across the crack surface and the strong nonlinearity near the crack tip can be described more accurately. The strip specimens with unilateral cracks and central cracks under uniaxial tension are simulated using the XFEM and the FEM, respectively. The J-integral across the crack on each incremen t is calcula ted using the equivale nt domain integral met hod (EDIM), the interaction integral met hod and the FEM, respectively. The effec ts of mesh size and mesh shape near the crack tip, element type and different calculation methods on the accuracy of J-integral are analyzed. The simulation results show that the XFEM is more accurate than the FEM with the same element size and type. The fracture tests of cast iron specimens with unilateral cracks under uniaxial tension are performed, and the J-integral criterion is valid to predict the fracture initiation in numerical simulation. The critical value of J-integral is calculated using the EDIM of the XFEM. The comparisons demonstrate that the simulated elastoplastic load-displacement curves with the XFEM are in good agreement with the experimental results.
