This paper evaluates the performance of anisotropic yield functions based on mathematical methods which consider the prediction accuracy of yield stresses and values.The anisotropic yield functions being evaluated inc...This paper evaluates the performance of anisotropic yield functions based on mathematical methods which consider the prediction accuracy of yield stresses and values.The anisotropic yield functions being evaluated include one quadratic yield function and six nonquadratic ones.These yield functions are applied to describe the anisotropy of st eel sheets and aluminum alloy sheets to evaluate their predictability.The root-mean-square errors(RMSEs)are computed to quantitatively assess their performance.The computation results of RMSEs demonstrate that the Yld2004-18p yield function exhibits the highest accuracy but requires extensive tests to calculate anisotropic parameters.The Yld2000-2d and BBC2000 yield functions are the same and thus have the same prediction accuracy.The application to cylindrical cup drawing shows that,associated with the Yld2004-18p and Yld2000-2d yield functions,the finite element(FE)simulations of cup drawing process can predict cups with six or eight ears.Considering both efficiency and accuracy,the Yld2000-2d and BBC2000 yield functions,which have less anisotropic parameters to be calculated,are recommended for metals with intermediate anisotropy.展开更多
The equi-biaxial tensile test is often required for parameter identification of anisotropic yield function and it demands thespecial testing technique or device. Instead of the equi-biaxial tensile test, the plane str...The equi-biaxial tensile test is often required for parameter identification of anisotropic yield function and it demands thespecial testing technique or device. Instead of the equi-biaxial tensile test, the plane strain test carried out with the traditional uniaxialtesting machine is suggested to provide the experimental data for calibration of anisotropic yield function. This simplified method byusing plane strain test was adopted to identify the parameters of Yld2000-2d yield function for 5xxx aluminum alloy and AlMgSialloy sheets. The predicted results of yield stresses, anisotropic coefficients and yield loci by the proposed method were very similarwith the experimental data and those by the equi-biaxial tensile test. It is validated that the plane strain test is effective to provideexperimental data instead of equi-biaxial tensile test for calibration of Yld2000-2d yield function.展开更多
A quadratic yield function which can describe the anisotropic behaviors of sheet metals with tension/compression symmetry and asymmetry is proposed.Five mechanical properties are adopted to determine the coefficients ...A quadratic yield function which can describe the anisotropic behaviors of sheet metals with tension/compression symmetry and asymmetry is proposed.Five mechanical properties are adopted to determine the coefficients of each part of the yield function.For particular cases,the proposed yield function can be simplified to Mises or Hill’s quadratic yield function.The anisotropic mechanical properties are expressed by defining an angle between the current normalized principal stress space and the reference direction with the assumption of orthotropic anisotropy.The accuracy of the proposed yield function in describing the anisotropy under tension and compression is demonstrated.展开更多
The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordin...The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.展开更多
This paper establishes an anisotropic plastic material model to analyze the elasto-plastic behavior of masonry in plane stress state.Being an anisotropic material,masonry has different constitutive relation and fractu...This paper establishes an anisotropic plastic material model to analyze the elasto-plastic behavior of masonry in plane stress state.Being an anisotropic material,masonry has different constitutive relation and fracture energies along each orthotropic axes.Considering the unique material properties of masonry,a new yield criterion for masonry is proposed combining the Hill's yield criterion and the Rankine's yield criterion.The new yield criterion not only introduces compression friction coefficient of shear but also considers yield functions for independent stress state along two material axes of tension.To solve the involved nonlinear equations in numerical analysis,several nonlinear methods are implemented,including Newton-Raphson method for nonlinear equations and Implicit Euler backward mapping algorithm to update stresses.To verify the proposed material model of masonry,a series of tests are operated.The simulation results show that the new developed material model implements successfully.Compared with isotropic material model,the proposed model performs better in elasto-plastic analysis of masonry in plane stress state.The proposed anisotropic model is capable of simulating elasto-plastic behavior of masonry and can be used in related applications.展开更多
A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientat...A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientational motion on the material behavior and neglecting the influence,the constitutive equation is applied to a simple case for the hydrodynamic motion when the orientational contribution is neglected in it and the anisotropic relaxation,retardation times and anisotropic viscosi- ties are introduced to describe the macroscopic behavior of the anisotropic LC polymer fluid.Using the equation for the shear flow of LC polymer fluid,the analytical expressions of the apparent viscosity and the normal stress differences are given which are in a good agreement with the experimental results of Baek et al.For the fiber spinning flow of the fluid,the analytical expression of the extensional viscosity is given.展开更多
Sheet metal formed of lightweight materials such as aluminum sheeting has received great attention related to the reduction of vehicle emissions. This paper evaluates the anisotropic yield locus using Kuwabara＇s biax...Sheet metal formed of lightweight materials such as aluminum sheeting has received great attention related to the reduction of vehicle emissions. This paper evaluates the anisotropic yield locus using Kuwabara＇s biaxial tensile tester and stretches formability using Hecker＇s hemispheri- cal punch stretching test for aluminum 6016-T4 sheet material. The anisotropic yield locus of the A16016-T4 sheet measured is fitted well by the modified Drucker yield func- tion. Moreover the best fitting to the experimental stress- strain curve from the tensile test was obtained by taking an appropriate hardening model. Analytical study to predict the stretch formability by using Hora＇s Modified Maximum Force Criterion （MMFC） was performed. The predicted forming limit curves （FLC） based on various yield functions were compared with the experiments and discussed.展开更多
The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assu...The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli's gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.展开更多
The sensitivity problem to mesh distortion and the low accuracy problem of the stress solutions are two inherent difficulties in the finite element method.By applying the fundamental analytical solutions (in global Ca...The sensitivity problem to mesh distortion and the low accuracy problem of the stress solutions are two inherent difficulties in the finite element method.By applying the fundamental analytical solutions (in global Cartesian coordinates) to the Airy stress function of the anisotropic materials,8-and 12-node plane quadrilateral hybrid stress-function (HS-F) elements are successfully developed based on the principle of the minimum complementary energy.Numerical results show that the present new elements exhibit much better and more robust performance in both displacement and stress solutions than those obtained from other models.They can still perform very well even when the element shapes degenerate into a triangle and a concave quadrangle.It is also demonstrated that the proposed construction procedure is an effective way for developing shape-free finite element models which can completely overcome the sensitivity problem to mesh distortion and can produce highly accurate stress solutions.展开更多
A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic an...A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic and piezoelectric materials, respectively. Di?erent from previous research, the complex argument separation technique is not required so that cumbersome manipulations are avoided. Moreover, it is shown, di?erent from the previous research too, that the orthogonal properties of the material characteristic matrices A and B are no longer necessary in obtaining the POP of EEF in cracked piezoelectric materials. Of the greatest signi?cance is that the method presented in this paper can be widely extended to treat many kinds of problems concerning path- independent integrals with multi-variables.展开更多
Analytical and semi-analytical solutions are presented for anisotropic functionally graded beams subject to an arbitrary load,which can be expanded in terms of sinusoidal series.For plane stress problems,the stress fu...Analytical and semi-analytical solutions are presented for anisotropic functionally graded beams subject to an arbitrary load,which can be expanded in terms of sinusoidal series.For plane stress problems,the stress function is assumed to consist of two parts,one being a product of a trigonometric function of the longitudinal coordinate(x)and an undetermined function of the thickness coordinate(y),and the other a linear polynomial of x with unknown coefficients depending on y.The governing equations satisfied by these y-dependent functions are derived.The expressions for stresses,resultant forces and displacements are then deduced,with integral constants determinable from the boundary conditions.While the analytical solution is derived for the beam with material coefficients varying exponentially or in a power law along the thickness,the semi-analytical solution is sought by making use of the sub-layer approximation for the beam with an arbitrary variation of material parameters along the thickness.The present analysis is applicable to beams with various boundary conditions at the two ends.Three numerical examples are presented for validation of the theory and illustration of the effects of certain parameters.展开更多
Decoupling electrical and thermal properties to enhance the figure of merit of thermoelectric materials underscores an in-depth understanding of the mechanisms that govern the transfer of charge carriers.Typically,a f...Decoupling electrical and thermal properties to enhance the figure of merit of thermoelectric materials underscores an in-depth understanding of the mechanisms that govern the transfer of charge carriers.Typically,a factor that contributes to the optimization of thermal conductivity is often found to be detrimental to the electrical transport properties.Here,we systematically investigated 26 dimeric MX_(2)-type compounds(where M represents a metal and X represents a nonmetal element)to explore the influence of the electronic configurations of metal cations on lattice thermal transport and thermoelectric performance using first-principles calculations.A principled scheme has been identified that the filled outer orbitals of the cation lead to a significantly lower lattice thermal conductivity compared to that of the partly occupied case for MX_(2),due to the much weakened bonds manifested by the shallow potential well,smaller interatomic force constants,and higher atomic displacement parameters.Based on these findings,we propose two ionic compounds,BaAs and BaSe_(2),to realize reasonable high electrical conductivities through the structural anisotropy caused by the inserted covalent X_(2) dimers while still maintaining the large lattice anharmonicity.The combined superior electrical and thermal properties of BaSe_(2) lead to a high n-type thermoelectric ZT value of 2.3 at 500 K.This work clarifies the structural origin of the heat transport properties of dimeric MX_(2)-type compounds and provides an insightful strategy for developing promising thermoelectric materials.展开更多
文摘This paper evaluates the performance of anisotropic yield functions based on mathematical methods which consider the prediction accuracy of yield stresses and values.The anisotropic yield functions being evaluated include one quadratic yield function and six nonquadratic ones.These yield functions are applied to describe the anisotropy of st eel sheets and aluminum alloy sheets to evaluate their predictability.The root-mean-square errors(RMSEs)are computed to quantitatively assess their performance.The computation results of RMSEs demonstrate that the Yld2004-18p yield function exhibits the highest accuracy but requires extensive tests to calculate anisotropic parameters.The Yld2000-2d and BBC2000 yield functions are the same and thus have the same prediction accuracy.The application to cylindrical cup drawing shows that,associated with the Yld2004-18p and Yld2000-2d yield functions,the finite element(FE)simulations of cup drawing process can predict cups with six or eight ears.Considering both efficiency and accuracy,the Yld2000-2d and BBC2000 yield functions,which have less anisotropic parameters to be calculated,are recommended for metals with intermediate anisotropy.
基金Project(P2018-013)supported by the Open Foundation of State Key Laboratory of Materials Processing and Die&Mould Technology,Huazhong University of Science and Technology,China
文摘The equi-biaxial tensile test is often required for parameter identification of anisotropic yield function and it demands thespecial testing technique or device. Instead of the equi-biaxial tensile test, the plane strain test carried out with the traditional uniaxialtesting machine is suggested to provide the experimental data for calibration of anisotropic yield function. This simplified method byusing plane strain test was adopted to identify the parameters of Yld2000-2d yield function for 5xxx aluminum alloy and AlMgSialloy sheets. The predicted results of yield stresses, anisotropic coefficients and yield loci by the proposed method were very similarwith the experimental data and those by the equi-biaxial tensile test. It is validated that the plane strain test is effective to provideexperimental data instead of equi-biaxial tensile test for calibration of Yld2000-2d yield function.
基金supported by the National Natural Science Foundation of China (Grant Nos.51475003 and 51205004)Beijing Natural Science Foundation (Grant No.3152010)+1 种基金open project of "State Key Laboratory of Solidification Processing" of Northwestern Polytechnical University (No.SKLSP201635)Beijing Education Committee Science and Technology Program (Grant No.KM201510009004)
文摘A quadratic yield function which can describe the anisotropic behaviors of sheet metals with tension/compression symmetry and asymmetry is proposed.Five mechanical properties are adopted to determine the coefficients of each part of the yield function.For particular cases,the proposed yield function can be simplified to Mises or Hill’s quadratic yield function.The anisotropic mechanical properties are expressed by defining an angle between the current normalized principal stress space and the reference direction with the assumption of orthotropic anisotropy.The accuracy of the proposed yield function in describing the anisotropy under tension and compression is demonstrated.
基金Project supported by the National Natural Science Foundation of China (Nos. 10472102 and 1043203)the Foundation of Ningbo University (No. 2005014), China
文摘The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.
基金Sponsored by Changjiang Scholars Program of China (Grant No.2009-37)PhD Programs Foundation of Ministry of Education of China (Grant No.20092302110046)Natural Science Foundation of Heilongjiang Province (Grant No.E200916)
文摘This paper establishes an anisotropic plastic material model to analyze the elasto-plastic behavior of masonry in plane stress state.Being an anisotropic material,masonry has different constitutive relation and fracture energies along each orthotropic axes.Considering the unique material properties of masonry,a new yield criterion for masonry is proposed combining the Hill's yield criterion and the Rankine's yield criterion.The new yield criterion not only introduces compression friction coefficient of shear but also considers yield functions for independent stress state along two material axes of tension.To solve the involved nonlinear equations in numerical analysis,several nonlinear methods are implemented,including Newton-Raphson method for nonlinear equations and Implicit Euler backward mapping algorithm to update stresses.To verify the proposed material model of masonry,a series of tests are operated.The simulation results show that the new developed material model implements successfully.Compared with isotropic material model,the proposed model performs better in elasto-plastic analysis of masonry in plane stress state.The proposed anisotropic model is capable of simulating elasto-plastic behavior of masonry and can be used in related applications.
基金The project supported by the National Natural Science Foundation of China(19832050 and 10372100)
文摘A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientational motion on the material behavior and neglecting the influence,the constitutive equation is applied to a simple case for the hydrodynamic motion when the orientational contribution is neglected in it and the anisotropic relaxation,retardation times and anisotropic viscosi- ties are introduced to describe the macroscopic behavior of the anisotropic LC polymer fluid.Using the equation for the shear flow of LC polymer fluid,the analytical expressions of the apparent viscosity and the normal stress differences are given which are in a good agreement with the experimental results of Baek et al.For the fiber spinning flow of the fluid,the analytical expression of the extensional viscosity is given.
基金Supported by National Research Foundation of Korea(NFR)grant funded by the Korea Government(MEST)(No.2014R1A2A2A01005903)Priority Research Center Program(No.2010-0020089)
文摘Sheet metal formed of lightweight materials such as aluminum sheeting has received great attention related to the reduction of vehicle emissions. This paper evaluates the anisotropic yield locus using Kuwabara＇s biaxial tensile tester and stretches formability using Hecker＇s hemispheri- cal punch stretching test for aluminum 6016-T4 sheet material. The anisotropic yield locus of the A16016-T4 sheet measured is fitted well by the modified Drucker yield func- tion. Moreover the best fitting to the experimental stress- strain curve from the tensile test was obtained by taking an appropriate hardening model. Analytical study to predict the stretch formability by using Hora＇s Modified Maximum Force Criterion （MMFC） was performed. The predicted forming limit curves （FLC） based on various yield functions were compared with the experiments and discussed.
文摘The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli's gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.
基金supported by the National Natural Science Foundation of China(Grant No.10872108,10876100)the Program for New Century Excellent Talents in University(Grant No. NCET-07-0477)+1 种基金the National Basic Research Program of China(Grant No. 2010CB832701)ASFC
文摘The sensitivity problem to mesh distortion and the low accuracy problem of the stress solutions are two inherent difficulties in the finite element method.By applying the fundamental analytical solutions (in global Cartesian coordinates) to the Airy stress function of the anisotropic materials,8-and 12-node plane quadrilateral hybrid stress-function (HS-F) elements are successfully developed based on the principle of the minimum complementary energy.Numerical results show that the present new elements exhibit much better and more robust performance in both displacement and stress solutions than those obtained from other models.They can still perform very well even when the element shapes degenerate into a triangle and a concave quadrangle.It is also demonstrated that the proposed construction procedure is an effective way for developing shape-free finite element models which can completely overcome the sensitivity problem to mesh distortion and can produce highly accurate stress solutions.
基金Project supported by the Natural Science Foundation of Shaanxi Province (No.2002A18) and the Doctorate Foundation of Xi’an Jiao-Tong University.
文摘A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic and piezoelectric materials, respectively. Di?erent from previous research, the complex argument separation technique is not required so that cumbersome manipulations are avoided. Moreover, it is shown, di?erent from the previous research too, that the orthogonal properties of the material characteristic matrices A and B are no longer necessary in obtaining the POP of EEF in cracked piezoelectric materials. Of the greatest signi?cance is that the method presented in this paper can be widely extended to treat many kinds of problems concerning path- independent integrals with multi-variables.
基金Supported by the National Natural Science Foundation of China(Grant Nos.10472102,10432030,and 10725210)
文摘Analytical and semi-analytical solutions are presented for anisotropic functionally graded beams subject to an arbitrary load,which can be expanded in terms of sinusoidal series.For plane stress problems,the stress function is assumed to consist of two parts,one being a product of a trigonometric function of the longitudinal coordinate(x)and an undetermined function of the thickness coordinate(y),and the other a linear polynomial of x with unknown coefficients depending on y.The governing equations satisfied by these y-dependent functions are derived.The expressions for stresses,resultant forces and displacements are then deduced,with integral constants determinable from the boundary conditions.While the analytical solution is derived for the beam with material coefficients varying exponentially or in a power law along the thickness,the semi-analytical solution is sought by making use of the sub-layer approximation for the beam with an arbitrary variation of material parameters along the thickness.The present analysis is applicable to beams with various boundary conditions at the two ends.Three numerical examples are presented for validation of the theory and illustration of the effects of certain parameters.
基金financial support from the Natural Science Foundation of China(No.11904089,12174092,11674087)the Overseas Expertise Introduction Center for Discipline Innovation(D18025)+1 种基金the Program for Key Research and Development of Science and Technology in Hubei Province(grant No.2023BEB002)supported by the Young Science Foundation of Hubei University(Grant No.430/184303000047).
文摘Decoupling electrical and thermal properties to enhance the figure of merit of thermoelectric materials underscores an in-depth understanding of the mechanisms that govern the transfer of charge carriers.Typically,a factor that contributes to the optimization of thermal conductivity is often found to be detrimental to the electrical transport properties.Here,we systematically investigated 26 dimeric MX_(2)-type compounds(where M represents a metal and X represents a nonmetal element)to explore the influence of the electronic configurations of metal cations on lattice thermal transport and thermoelectric performance using first-principles calculations.A principled scheme has been identified that the filled outer orbitals of the cation lead to a significantly lower lattice thermal conductivity compared to that of the partly occupied case for MX_(2),due to the much weakened bonds manifested by the shallow potential well,smaller interatomic force constants,and higher atomic displacement parameters.Based on these findings,we propose two ionic compounds,BaAs and BaSe_(2),to realize reasonable high electrical conductivities through the structural anisotropy caused by the inserted covalent X_(2) dimers while still maintaining the large lattice anharmonicity.The combined superior electrical and thermal properties of BaSe_(2) lead to a high n-type thermoelectric ZT value of 2.3 at 500 K.This work clarifies the structural origin of the heat transport properties of dimeric MX_(2)-type compounds and provides an insightful strategy for developing promising thermoelectric materials.
