Several studies indicate that Eringen's nonlocal model may lead to some inconsistencies for both Euler-Bernoulli and Timoshenko beams, such as cantilever beams subjected to an end point force and fixed-fixed beams...Several studies indicate that Eringen's nonlocal model may lead to some inconsistencies for both Euler-Bernoulli and Timoshenko beams, such as cantilever beams subjected to an end point force and fixed-fixed beams subjected a uniform distributed load. In this paper, the elastic buckling behavior of nanobeams, including both EulerBernoulli and Timoshenko beams, is investigated on the basis of a stress-driven nonlocal integral model. The constitutive equations are the Fredholm-type integral equations of the first kind, which can be transformed to the Volterra integral equations of the first kind. With the application of the Laplace transformation, the general solutions of the deflections and bending moments for the Euler-Bernoulli and Timoshenko beams as well as the rotation and shear force for the Timoshenko beams are obtained explicitly with several unknown constants. Considering the boundary conditions and extra constitutive constraints, the characteristic equations are obtained explicitly for the Euler-Bernoulli and Timoshenko beams under different boundary conditions, from which one can determine the critical buckling loads of nanobeams. The effects of the nonlocal parameters and buckling order on the buckling loads of nanobeams are studied numerically, and a consistent toughening effect is obtained.展开更多
In this work,the static tensile and free vibration of nanorods are studied via both the strain-driven(Strain D)and stress-driven(Stress D)two-phase nonlocal models with a bi-Helmholtz averaging kernel.Merely adjusting...In this work,the static tensile and free vibration of nanorods are studied via both the strain-driven(Strain D)and stress-driven(Stress D)two-phase nonlocal models with a bi-Helmholtz averaging kernel.Merely adjusting the limits of integration,the integral constitutive equation of the Fredholm type is converted to that of the Volterra type and then solved directly via the Laplace transform technique.The unknown constants can be uniquely determined through the standard boundary conditions and two constrained conditions accompanying the Laplace transform process.In the numerical examples,the bi-Helmholtz kernel-based Strain D(or Stress D)two-phase model shows consistently softening(or stiffening)effects on both the tension and the free vibration of nanorods with different boundary edges.The effects of the two nonlocal parameters of the bi-Helmholtz kernel-based two-phase nonlocal models are studied and compared with those of the Helmholtz kernel-based models.展开更多
We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law ...We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.展开更多
A torsional static and free vibration analysis of the functionally graded nanotube(FGNT)composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-He...A torsional static and free vibration analysis of the functionally graded nanotube(FGNT)composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-Helmholtz kernel based stress-driven nonlocal integral model.The differential governing equation and boundary conditions are deduced on the basis of Hamilton’s principle,and the constitutive relationship is expressed as an integral equation with the bi-Helmholtz kernel.Several nominal variables are introduced to simplify the differential governing equation,integral constitutive equation,and boundary conditions.Rather than transforming the constitutive equation from integral to differential forms,the Laplace transformation is used directly to solve the integro-differential equations.The explicit expression for nominal torsional rotation and torque contains four unknown constants,which can be determined with the help of two boundary conditions and two extra constraints from the integral constitutive relation.A few benchmarked examples are solved to illustrate the nonlocal influence on the static torsion of a clamped-clamped(CC)FGNT under torsional constraints and a clamped-free(CF)FGNT under concentrated and uniformly distributed torques as well as the torsional free vibration of an FGNT under different boundary conditions.展开更多
With additional functions of osteocytes being identified, the concept that osteocytes are just "static lacunar-dwelling cells" is no longer accepted. We reviewed most of the relevant literature on osteocyte's funct...With additional functions of osteocytes being identified, the concept that osteocytes are just "static lacunar-dwelling cells" is no longer accepted. We reviewed most of the relevant literature on osteocyte's function in the direct remodeling of the perilucunar matrix, discussing the advantages and disadvantages. Special attention was paid to how the negative researchers argue about the "osteocytic osteolysis" principle, and how the positive side addressed the arguments. We also discussed the newly found data of osteocytic remodeling function from our group. With more biotechnology in hand, there is increased excitement in the prospect of now being able to answer the two important questions: do osteocytes have the capability to remove mineral from the perilacunar matrix and if so what are the molecular and cellular mechanisms? do osteocytes have the capability to deposit new mineral on the perilacunar matrix and if so what are the cellular and molecular mechanisms?展开更多
Due to the conflict between equilibrium and constitutive requirements,Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest.As an alternative,the stress-driven mo...Due to the conflict between equilibrium and constitutive requirements,Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest.As an alternative,the stress-driven model has been recently developed.In this paper,for higher-order shear deformation beams,the ill-posed issue(i.e.,excessive mandatory boundary conditions(BCs)cannot be met simultaneously)exists not only in strain-driven nonlocal models but also in stress-driven ones.The well-posedness of both the strain-and stress-driven two-phase nonlocal(TPN-Strain D and TPN-Stress D)models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded(FG)materials.The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions.By using the generalized differential quadrature method(GDQM),the coupling governing equations are solved numerically.The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.展开更多
An integral nonlocal stress gradient viscoelastic model is proposed on the basis of the integral nonlocal stress gradient model and the standard viscoelastic model,and is utilized to investigate the free damping vibra...An integral nonlocal stress gradient viscoelastic model is proposed on the basis of the integral nonlocal stress gradient model and the standard viscoelastic model,and is utilized to investigate the free damping vibration analysis of the viscoelastic BernoulliEuler microbeams in thermal environment.Hamilton's principle is used to derive the differential governing equations and corresponding boundary conditions.The integral relations between the strain and the nonlocal stress are converted into a differential form with constitutive constraints.The size-dependent axial thermal stress due to the variation of the environmental temperature is derived explicitly.The Laplace transformation is utilized to obtain the explicit expression for the bending deflection and moment.Considering the boundary conditions and constitutive constraints,one can get a nonlinear equation with complex coefficients,from which the complex characteristic frequency can be determined.A two-step numerical method is proposed to solve the elastic vibration frequency and the damping ratio.The effects of length scale parameters,viscous coefficient,thermal stress,vibration order on the vibration frequencies,and critical viscous coefficient are investigated numerically for the viscoelastic Bernoulli-Euler microbeams under different boundary conditions.展开更多
A nonlocal study of the vibration responses of functionally graded(FG)beams supported by a viscoelastic Winkler-Pasternak foundation is presented.The damping responses of both the Winkler and Pasternak layers of the f...A nonlocal study of the vibration responses of functionally graded(FG)beams supported by a viscoelastic Winkler-Pasternak foundation is presented.The damping responses of both the Winkler and Pasternak layers of the foundation are considered in the formulation,which were not considered in most literature on this subject,and the bending deformation of the beams and the elastic and damping responses of the foundation as nonlocal by uniting the equivalently differential formulation of well-posed strain-driven(ε-D)and stress-driven(σ-D)two-phase local/nonlocal integral models with constitutive constraints are comprehensively considered,which can address both the stiffness softening and toughing effects due to scale reduction.The generalized differential quadrature method(GDQM)is used to solve the complex eigenvalue problem.After verifying the solution procedure,a series of benchmark results for the vibration frequency of different bounded FG beams supported by the foundation are obtained.Subsequently,the effects of the nonlocality of the foundation on the undamped/damping vibration frequency of the beams are examined.展开更多
Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along...Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along the radial and circumferential directions,we propose nonlocal integral polar models in this work.The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates.The governing differential equations and boundary conditions(BCs)as well as constitutive constraints are deduced.It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected.Meanwhile,the purely strain-and stress-driven nonlocal integral polar models are ill-posed,because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints.Several nominal variables are introduced to simplify the mathematical expression,and the general differential quadrature method(GDQM)is applied to obtain the numerical solutions.The results from the current models(CMs)are compared with the data in the literature.It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models,respectively.The proposed two-phase local/nonlocal integral polar models(TPNIPMs)may provide an efficient method to design and optimize the plate-like structures for microelectro-mechanical systems.展开更多
In this paper,we propose general strain-and stress-driven two-phase local/nonlocal piezoelectric integral models,which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of n...In this paper,we propose general strain-and stress-driven two-phase local/nonlocal piezoelectric integral models,which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of nanostructures.The nonlocal piezoelectric model is transformed from integral to an equivalent differential form with four constitutive boundary conditions due to the difficulty in solving intergro-differential equations directly.The nonlocal piezoelectric integral models are used to model the static bending of the Euler-Bernoulli piezoelectric beam on the assumption that the nonlocal elastic and piezoelectric parameters are coincident with each other.The governing differential equations as well as constitutive and standard boundary conditions are deduced.It is found that purely strain-and stress-driven nonlocal piezoelectric integral models are ill-posed,because the total number of differential orders for governing equations is less than that of boundary conditions.Meanwhile,the traditional nonlocal piezoelectric differential model would lead to inconsistent bending response for Euler-Bernoulli piezoelectric beam under different boundary and loading conditions.Several nominal variables are introduced to normalize the governing equations and boundary conditions,and the general differential quadrature method(GDQM)is used to obtain the numerical solutions.The results from current models are validated against results in the literature.It is clearly established that a consistent softening and toughening effects can be obtained for static bending of the Euler-Bernoulli beam based on the general strain-and stress-driven local/nonlocal piezoelectric integral models,respectively.展开更多
Scale effects play critical roles in the mechanical responses of microstructures.An isogeometric analysis was developed here to investigate the mechanical responses of an axially functionally graded microbeam.The Eule...Scale effects play critical roles in the mechanical responses of microstructures.An isogeometric analysis was developed here to investigate the mechanical responses of an axially functionally graded microbeam.The Euler–Bernoulli beam model was utilized,and size effects in the structure were modeled with a stress-driven two-phase local/nonlocal integral constitution.The governing equation of microstructures was given in an equivalent differential form with two additional constitutive boundary conditions.The framework was verified and utilized to analyze the microbeam’s static and dynamic mechanical responses.The present work showed great potential for modeling various types of functionally graded microstructures.展开更多
The influence of the shape and spatial distribution of reinforced particles on strength and damage of metal matrix composite (MMC) is investigated through finite element method under uniaxial tensile, simple shear, ...The influence of the shape and spatial distribution of reinforced particles on strength and damage of metal matrix composite (MMC) is investigated through finite element method under uniaxial tensile, simple shear, biaxial tensile, as well as combined tensile/shear loadings. The particle shapes change randomly from circular to regular n-sided polygon (3 ≤ n ≤ 10); the particle alignments are determined through a sequentially random number stream and the particle locations are defined through the random sequential adsorption algorithm. The ductile failure in metal matrix and brittle failure in particles are described through damage models based on the stress triaxial indicator and maximum principal stress criterion, respectively, while the debonding behavior of interface between particles and matrix is simulated through cohesive elements. The simulation results show that, under different loadings, interface debonding is the dominated failure mechanism in MMCs and plastic deformation and ductile failure of matrix also play very important roles on the failure of MMCs.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11672131)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures of China(No.MCMS-0217G02)the Priority Academic Program Development of Jiangsu Higher Education Institutions of China(No.11672131)。
文摘Several studies indicate that Eringen's nonlocal model may lead to some inconsistencies for both Euler-Bernoulli and Timoshenko beams, such as cantilever beams subjected to an end point force and fixed-fixed beams subjected a uniform distributed load. In this paper, the elastic buckling behavior of nanobeams, including both EulerBernoulli and Timoshenko beams, is investigated on the basis of a stress-driven nonlocal integral model. The constitutive equations are the Fredholm-type integral equations of the first kind, which can be transformed to the Volterra integral equations of the first kind. With the application of the Laplace transformation, the general solutions of the deflections and bending moments for the Euler-Bernoulli and Timoshenko beams as well as the rotation and shear force for the Timoshenko beams are obtained explicitly with several unknown constants. Considering the boundary conditions and extra constitutive constraints, the characteristic equations are obtained explicitly for the Euler-Bernoulli and Timoshenko beams under different boundary conditions, from which one can determine the critical buckling loads of nanobeams. The effects of the nonlocal parameters and buckling order on the buckling loads of nanobeams are studied numerically, and a consistent toughening effect is obtained.
基金the National Natural Science Foundation of China(No.12172169)the China Scholarship Council(CSC)(No.202006830038)。
文摘In this work,the static tensile and free vibration of nanorods are studied via both the strain-driven(Strain D)and stress-driven(Stress D)two-phase nonlocal models with a bi-Helmholtz averaging kernel.Merely adjusting the limits of integration,the integral constitutive equation of the Fredholm type is converted to that of the Volterra type and then solved directly via the Laplace transform technique.The unknown constants can be uniquely determined through the standard boundary conditions and two constrained conditions accompanying the Laplace transform process.In the numerical examples,the bi-Helmholtz kernel-based Strain D(or Stress D)two-phase model shows consistently softening(or stiffening)effects on both the tension and the free vibration of nanorods with different boundary edges.The effects of the two nonlocal parameters of the bi-Helmholtz kernel-based two-phase nonlocal models are studied and compared with those of the Helmholtz kernel-based models.
基金Project supported by the National Natural Science Foundation of China(No.12172169)the Natural Sciences and Engineering Research Council of Canada(No.NSERC RGPIN-2023-03227)。
文摘We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.
基金Project supported by the National Natural Science Foundation of China(No.11672131)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘A torsional static and free vibration analysis of the functionally graded nanotube(FGNT)composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-Helmholtz kernel based stress-driven nonlocal integral model.The differential governing equation and boundary conditions are deduced on the basis of Hamilton’s principle,and the constitutive relationship is expressed as an integral equation with the bi-Helmholtz kernel.Several nominal variables are introduced to simplify the differential governing equation,integral constitutive equation,and boundary conditions.Rather than transforming the constitutive equation from integral to differential forms,the Laplace transformation is used directly to solve the integro-differential equations.The explicit expression for nominal torsional rotation and torque contains four unknown constants,which can be determined with the help of two boundary conditions and two extra constraints from the integral constitutive relation.A few benchmarked examples are solved to illustrate the nonlocal influence on the static torsion of a clamped-clamped(CC)FGNT under torsional constraints and a clamped-free(CF)FGNT under concentrated and uniformly distributed torques as well as the torsional free vibration of an FGNT under different boundary conditions.
基金supported in part by the National Institutes of Health AR-46798
文摘With additional functions of osteocytes being identified, the concept that osteocytes are just "static lacunar-dwelling cells" is no longer accepted. We reviewed most of the relevant literature on osteocyte's function in the direct remodeling of the perilucunar matrix, discussing the advantages and disadvantages. Special attention was paid to how the negative researchers argue about the "osteocytic osteolysis" principle, and how the positive side addressed the arguments. We also discussed the newly found data of osteocytic remodeling function from our group. With more biotechnology in hand, there is increased excitement in the prospect of now being able to answer the two important questions: do osteocytes have the capability to remove mineral from the perilacunar matrix and if so what are the molecular and cellular mechanisms? do osteocytes have the capability to deposit new mineral on the perilacunar matrix and if so what are the cellular and molecular mechanisms?
基金Project supported by the National Natural Science Foundation of China(No.11672131)。
文摘Due to the conflict between equilibrium and constitutive requirements,Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest.As an alternative,the stress-driven model has been recently developed.In this paper,for higher-order shear deformation beams,the ill-posed issue(i.e.,excessive mandatory boundary conditions(BCs)cannot be met simultaneously)exists not only in strain-driven nonlocal models but also in stress-driven ones.The well-posedness of both the strain-and stress-driven two-phase nonlocal(TPN-Strain D and TPN-Stress D)models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded(FG)materials.The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions.By using the generalized differential quadrature method(GDQM),the coupling governing equations are solved numerically.The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.
基金Project supported by the National Natural Science Foundation of China(No.12172169)。
文摘An integral nonlocal stress gradient viscoelastic model is proposed on the basis of the integral nonlocal stress gradient model and the standard viscoelastic model,and is utilized to investigate the free damping vibration analysis of the viscoelastic BernoulliEuler microbeams in thermal environment.Hamilton's principle is used to derive the differential governing equations and corresponding boundary conditions.The integral relations between the strain and the nonlocal stress are converted into a differential form with constitutive constraints.The size-dependent axial thermal stress due to the variation of the environmental temperature is derived explicitly.The Laplace transformation is utilized to obtain the explicit expression for the bending deflection and moment.Considering the boundary conditions and constitutive constraints,one can get a nonlinear equation with complex coefficients,from which the complex characteristic frequency can be determined.A two-step numerical method is proposed to solve the elastic vibration frequency and the damping ratio.The effects of length scale parameters,viscous coefficient,thermal stress,vibration order on the vibration frequencies,and critical viscous coefficient are investigated numerically for the viscoelastic Bernoulli-Euler microbeams under different boundary conditions.
基金the National Natural Science Foundation of China(No.12172169)the China Scholarship Council(CSC)(No.202006830038)the Natural Sciences and Engineering Research Council of Canada(No.RGPIN-2017-03716115112)。
文摘A nonlocal study of the vibration responses of functionally graded(FG)beams supported by a viscoelastic Winkler-Pasternak foundation is presented.The damping responses of both the Winkler and Pasternak layers of the foundation are considered in the formulation,which were not considered in most literature on this subject,and the bending deformation of the beams and the elastic and damping responses of the foundation as nonlocal by uniting the equivalently differential formulation of well-posed strain-driven(ε-D)and stress-driven(σ-D)two-phase local/nonlocal integral models with constitutive constraints are comprehensively considered,which can address both the stiffness softening and toughing effects due to scale reduction.The generalized differential quadrature method(GDQM)is used to solve the complex eigenvalue problem.After verifying the solution procedure,a series of benchmark results for the vibration frequency of different bounded FG beams supported by the foundation are obtained.Subsequently,the effects of the nonlocality of the foundation on the undamped/damping vibration frequency of the beams are examined.
基金Project supported by the National Natural Science Foundation of China(No.12172169)the Research Fund of State Key Laboratory of Mechanicsthe Priority Academic Program Development of Jiangsu Higher Education Institutions of China。
文摘Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along the radial and circumferential directions,we propose nonlocal integral polar models in this work.The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates.The governing differential equations and boundary conditions(BCs)as well as constitutive constraints are deduced.It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected.Meanwhile,the purely strain-and stress-driven nonlocal integral polar models are ill-posed,because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints.Several nominal variables are introduced to simplify the mathematical expression,and the general differential quadrature method(GDQM)is applied to obtain the numerical solutions.The results from the current models(CMs)are compared with the data in the literature.It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models,respectively.The proposed two-phase local/nonlocal integral polar models(TPNIPMs)may provide an efficient method to design and optimize the plate-like structures for microelectro-mechanical systems.
基金the National Natural Science Foundation of China(No.12172169)the Scholarship of the China Scholarship Council(No.202106830093)。
文摘In this paper,we propose general strain-and stress-driven two-phase local/nonlocal piezoelectric integral models,which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of nanostructures.The nonlocal piezoelectric model is transformed from integral to an equivalent differential form with four constitutive boundary conditions due to the difficulty in solving intergro-differential equations directly.The nonlocal piezoelectric integral models are used to model the static bending of the Euler-Bernoulli piezoelectric beam on the assumption that the nonlocal elastic and piezoelectric parameters are coincident with each other.The governing differential equations as well as constitutive and standard boundary conditions are deduced.It is found that purely strain-and stress-driven nonlocal piezoelectric integral models are ill-posed,because the total number of differential orders for governing equations is less than that of boundary conditions.Meanwhile,the traditional nonlocal piezoelectric differential model would lead to inconsistent bending response for Euler-Bernoulli piezoelectric beam under different boundary and loading conditions.Several nominal variables are introduced to normalize the governing equations and boundary conditions,and the general differential quadrature method(GDQM)is used to obtain the numerical solutions.The results from current models are validated against results in the literature.It is clearly established that a consistent softening and toughening effects can be obtained for static bending of the Euler-Bernoulli beam based on the general strain-and stress-driven local/nonlocal piezoelectric integral models,respectively.
基金support of the present work from the National Natural Science Foundation of China(12172169,12202135,and 12272724)supported by the Fundamental Research Funds for the Central Universities from Hohai University(423142).
文摘Scale effects play critical roles in the mechanical responses of microstructures.An isogeometric analysis was developed here to investigate the mechanical responses of an axially functionally graded microbeam.The Euler–Bernoulli beam model was utilized,and size effects in the structure were modeled with a stress-driven two-phase local/nonlocal integral constitution.The governing equation of microstructures was given in an equivalent differential form with two additional constitutive boundary conditions.The framework was verified and utilized to analyze the microbeam’s static and dynamic mechanical responses.The present work showed great potential for modeling various types of functionally graded microstructures.
基金financially supported by the Fundamental Research Funds for the Central Universities (No.NE2014401)a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘The influence of the shape and spatial distribution of reinforced particles on strength and damage of metal matrix composite (MMC) is investigated through finite element method under uniaxial tensile, simple shear, biaxial tensile, as well as combined tensile/shear loadings. The particle shapes change randomly from circular to regular n-sided polygon (3 ≤ n ≤ 10); the particle alignments are determined through a sequentially random number stream and the particle locations are defined through the random sequential adsorption algorithm. The ductile failure in metal matrix and brittle failure in particles are described through damage models based on the stress triaxial indicator and maximum principal stress criterion, respectively, while the debonding behavior of interface between particles and matrix is simulated through cohesive elements. The simulation results show that, under different loadings, interface debonding is the dominated failure mechanism in MMCs and plastic deformation and ductile failure of matrix also play very important roles on the failure of MMCs.