This paper presents a closed form solution and numerical analysis for Es- helby＇s elliptic inclusion in an infinite plate. The complex variable method and the confor- real mapping technique are used. The continuity c...This paper presents a closed form solution and numerical analysis for Es- helby＇s elliptic inclusion in an infinite plate. The complex variable method and the confor- real mapping technique are used. The continuity conditions for the traction and displace- ment along the interface in the physical plane are reduced to the similar conditions along the unit circle of the mapping plane. The properties of the complex potentials defined in the finite elliptic region are analyzed. From the continuity conditions, one can separate and obtain the relevant complex potentials defined in the inclusion and the matrix. From the obtained complex potentials, the dependence of the real strains and stresses in the inclusion from the assumed eigenstrains is evaluated. In addition, the stress distribution on the interface along the matrix side is evaluated. The results are obtained in the paper for the first time.展开更多
A closed-form solution for predicting the tangential stress of an inclusion located in mixed mode Ⅰ and Ⅱ crack tip field was developed based on the Eshelby equivalent inclusion theory. Then a mixed mode fracture cr...A closed-form solution for predicting the tangential stress of an inclusion located in mixed mode Ⅰ and Ⅱ crack tip field was developed based on the Eshelby equivalent inclusion theory. Then a mixed mode fracture criterion, including the fracture direction and the critical load, was established based on the maximum tangential stress in the inclusion for brittle inclusioninduced fracture materials. The proposed fracture criterion is a function of the inclusion fracture stress, its size and volume fraction, as well as the elastic constants of the inclusion and the matrix material. The present criterion will reduce to the conventional one as the inclusion having the same elastic behavior as the matrix material. The proposed solutions are in good agreement with detailed finite element analysis and measurement.展开更多
The identification of multiple interacting inclusions with uniform internal stresses in an infinite elastic matrix subjected to a uniform remote loading is of fundamental importance in the mechanics and design of part...The identification of multiple interacting inclusions with uniform internal stresses in an infinite elastic matrix subjected to a uniform remote loading is of fundamental importance in the mechanics and design of particulate composite materials.In anti-plane shear and plane deformations,certain sufficient conditions have been established in the literature which guarantee uniform internal stresses inside multiple interacting inclusions displaying various symmetries when the matrix is subjected to specific uniform remote loading.Correspondingly,sufficient conditions which allow for the design of multiple interacting inclusions independent of any specific form of(uniform)remote loading have also been established.In this paper,we demonstrate rigorously that,in all cases,these sufficient conditions are also necessary conditions and indeed allow for the identification of all possible collections of such inclusions.展开更多
A plastic deformation zone near a screw dislocation is treated as an equivalent transformation inclusion by means of the Eshelby inclusion theory. A closed form solution for determining the interaction between a screw...A plastic deformation zone near a screw dislocation is treated as an equivalent transformation inclusion by means of the Eshelby inclusion theory. A closed form solution for determining the interaction between a screw dislocation and a plastically deformed zone of an arbitrary shape is obtained by using the solution between a dislocation and an equivalent transformation inclusion.展开更多
Since piezoelectric ceramic/polymer composites have been widely used as smart materials and smart structures, it is more and more important to obtain the closed-from solutions of the effective properties of piezocompo...Since piezoelectric ceramic/polymer composites have been widely used as smart materials and smart structures, it is more and more important to obtain the closed-from solutions of the effective properties of piezocomposites with piezoelectric ellipsoidal inclusions. Based on the closed-from solutions of the electroe- lastic Eshelby's tensors obtained in the part I of this paper and the generalized Bu- diansky's energy-equivalence framework, the closed-form general relations of effective electroelastic moduli of the piezocomposites with piezoelectric ellipsoidal inclusions are given. The relations can be applicable for several micromechanics models, such as the dilute solution and the Mori-Tanaka's method. The difference among the various models is shown to be the way in which the average strain and the average electric field of the inclusion phase are evaluated. Comparison between predicted and exper- imental results shows that the theoretical values in this paper agree quite well with the experimental results. These expressions can be readily utilized in analysis and design of piezocomposites.展开更多
By means of asymptotic fixed point theory,it is established that every dissipative functional differential inclusion (probably with infinite delay) has a periodic solution.This provides a theoretical basis for the app...By means of asymptotic fixed point theory,it is established that every dissipative functional differential inclusion (probably with infinite delay) has a periodic solution.This provides a theoretical basis for the applications of Liapunov’s second method to multivalued systems.As a result,a positive answer to Hutson’s open problem is given for more general multivalued systems.展开更多
Coherent second phase often exhibits anisotropic morphology with specifi c orientations with respect to both the second and the matrix phases.As a key feature of microstructure,the morphology of the coherent particles...Coherent second phase often exhibits anisotropic morphology with specifi c orientations with respect to both the second and the matrix phases.As a key feature of microstructure,the morphology of the coherent particles is essential for understanding the second-phase strengthening eff ect in various industrial alloys.This letter reports anisotropic growth of coherent ferrite from austenite matrix in pure iron based on molecular dynamics simulation.We found that the ferrite grain tends to grow into an elongated plate-like shape,independent of its initial confi guration.The fi nal shape of the ferrite is closely related to the misfi t between the two phases,with the longest direction and the broad facet of the plate being,respectively,consistent with the best matching direction and the best matching plane calculated via the Burgers vector content(BVC)method.The strain energy calculation in the framework of Eshelby’s inclusion theory verifi es that the simulated orientation of the coherent ferrite is energetically favorable.It is anticipated that the BVC method will be applicable in analysis of anisotropic growth and morphology of coherent second phase in other phase transformation systems.展开更多
文摘This paper presents a closed form solution and numerical analysis for Es- helby＇s elliptic inclusion in an infinite plate. The complex variable method and the confor- real mapping technique are used. The continuity conditions for the traction and displace- ment along the interface in the physical plane are reduced to the similar conditions along the unit circle of the mapping plane. The properties of the complex potentials defined in the finite elliptic region are analyzed. From the continuity conditions, one can separate and obtain the relevant complex potentials defined in the inclusion and the matrix. From the obtained complex potentials, the dependence of the real strains and stresses in the inclusion from the assumed eigenstrains is evaluated. In addition, the stress distribution on the interface along the matrix side is evaluated. The results are obtained in the paper for the first time.
基金Project supported by the National Basic Research Program of China (No. 2004CB619303).
文摘A closed-form solution for predicting the tangential stress of an inclusion located in mixed mode Ⅰ and Ⅱ crack tip field was developed based on the Eshelby equivalent inclusion theory. Then a mixed mode fracture criterion, including the fracture direction and the critical load, was established based on the maximum tangential stress in the inclusion for brittle inclusioninduced fracture materials. The proposed fracture criterion is a function of the inclusion fracture stress, its size and volume fraction, as well as the elastic constants of the inclusion and the matrix material. The present criterion will reduce to the conventional one as the inclusion having the same elastic behavior as the matrix material. The proposed solutions are in good agreement with detailed finite element analysis and measurement.
基金Project supported by the National Natural Science Foundation of China(Nos.11902147,11872203,and 51921003)the Natural Science Foundation of Jiangsu Province of China(No.BK20190393)and the Natural Sciences and Engineering Research Council of Canada(No.RGPIN–2017-03716115112)。
文摘The identification of multiple interacting inclusions with uniform internal stresses in an infinite elastic matrix subjected to a uniform remote loading is of fundamental importance in the mechanics and design of particulate composite materials.In anti-plane shear and plane deformations,certain sufficient conditions have been established in the literature which guarantee uniform internal stresses inside multiple interacting inclusions displaying various symmetries when the matrix is subjected to specific uniform remote loading.Correspondingly,sufficient conditions which allow for the design of multiple interacting inclusions independent of any specific form of(uniform)remote loading have also been established.In this paper,we demonstrate rigorously that,in all cases,these sufficient conditions are also necessary conditions and indeed allow for the identification of all possible collections of such inclusions.
基金Project supported by the National Basic Research Program of China (No.2004CB619303)the National Science Foundation of China (No.10572088).
文摘A plastic deformation zone near a screw dislocation is treated as an equivalent transformation inclusion by means of the Eshelby inclusion theory. A closed form solution for determining the interaction between a screw dislocation and a plastically deformed zone of an arbitrary shape is obtained by using the solution between a dislocation and an equivalent transformation inclusion.
基金The project supported by the National Natural Science Foundation of China
文摘Since piezoelectric ceramic/polymer composites have been widely used as smart materials and smart structures, it is more and more important to obtain the closed-from solutions of the effective properties of piezocomposites with piezoelectric ellipsoidal inclusions. Based on the closed-from solutions of the electroe- lastic Eshelby's tensors obtained in the part I of this paper and the generalized Bu- diansky's energy-equivalence framework, the closed-form general relations of effective electroelastic moduli of the piezocomposites with piezoelectric ellipsoidal inclusions are given. The relations can be applicable for several micromechanics models, such as the dilute solution and the Mori-Tanaka's method. The difference among the various models is shown to be the way in which the average strain and the average electric field of the inclusion phase are evaluated. Comparison between predicted and exper- imental results shows that the theoretical values in this paper agree quite well with the experimental results. These expressions can be readily utilized in analysis and design of piezocomposites.
基金Project supported by the National Natural Science Foundation of China and doctoral Fund of Educational Comnission.
文摘By means of asymptotic fixed point theory,it is established that every dissipative functional differential inclusion (probably with infinite delay) has a periodic solution.This provides a theoretical basis for the applications of Liapunov’s second method to multivalued systems.As a result,a positive answer to Hutson’s open problem is given for more general multivalued systems.
基金financially supported by the National Natural Science Foundation of China (Grant Nos. 51471097 and 51671111)the National Key Research and Development Program of China (Grant No. 2016YFB0701304)
文摘Coherent second phase often exhibits anisotropic morphology with specifi c orientations with respect to both the second and the matrix phases.As a key feature of microstructure,the morphology of the coherent particles is essential for understanding the second-phase strengthening eff ect in various industrial alloys.This letter reports anisotropic growth of coherent ferrite from austenite matrix in pure iron based on molecular dynamics simulation.We found that the ferrite grain tends to grow into an elongated plate-like shape,independent of its initial confi guration.The fi nal shape of the ferrite is closely related to the misfi t between the two phases,with the longest direction and the broad facet of the plate being,respectively,consistent with the best matching direction and the best matching plane calculated via the Burgers vector content(BVC)method.The strain energy calculation in the framework of Eshelby’s inclusion theory verifi es that the simulated orientation of the coherent ferrite is energetically favorable.It is anticipated that the BVC method will be applicable in analysis of anisotropic growth and morphology of coherent second phase in other phase transformation systems.
