The first fundamental problems in the infinite plane with cracks and boundary values cyclically symmetric are considered. They are reduced to singular integral equations on a single crack, which would considerably sim...The first fundamental problems in the infinite plane with cracks and boundary values cyclically symmetric are considered. They are reduced to singular integral equations on a single crack, which would considerably simplify the process of method of solution for such problems. Some special cases are illustrated.展开更多
As suggested by the title, this extensive book is concerned with crack and contact prob- lems in linear elasticity. However, in general, it is intended for a wide audience ranging from engineers to mathematical physic...As suggested by the title, this extensive book is concerned with crack and contact prob- lems in linear elasticity. However, in general, it is intended for a wide audience ranging from engineers to mathematical physicists. Indeed, numerous problems of both academic and tech- nological interest in electro-magnetics, acoustics, solid and fluid dynamics, etc. are actually related to each other and governed by the same mixed boundary value problems from a unified mathematical standpoint展开更多
The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cra...The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cracks by a constructive method. Those along the interfaces are further reduced to Fredholm ones.展开更多
Diamond tools have been widely used in national defense military,automobile manufacturing,resource exploitation and other fields.Laser brazing diamond technology is often applied to the preparation of diamond tools.Ho...Diamond tools have been widely used in national defense military,automobile manufacturing,resource exploitation and other fields.Laser brazing diamond technology is often applied to the preparation of diamond tools.However,the formation and expansion of cracks in the process of laser brazing diamond seriously affect the mechanical properties of diamond tools.In order to solve the crack problem of laser brazing diamond,many scholars are committed to the research on improving the solder,optimizing the laser process parameters,improving the laser brazing equipment,optimizing the design of joint form,and developing ultrasonic-assisted laser brazing technology,etc.These studies have achieved certain results.Aiming at the research status of laser brazing diamond crack problem,the crack characteristics of brazing diamond are firstly introduced,and the formation reasons of laser brazing diamond crack are elaborated.Then,the elemental characteristics of brazing filler metals used in brazing diamond are introduced.The influences of Ni-Cr and Ag-Cu-Ti alloy solder and laser process parameters on the crack problem are viewed.Finally,the solutions to the crack problem by scholars at home and abroad in recent years are summarized,and the future research directions to solve crack problem are prospected.展开更多
An oblique edge crack problem in a semi-infinite plane is discussed. Re concentrated forces are applied on the edge crack face, or on the line boundary of the cracked semi-infinite plane. The rational mapping function...An oblique edge crack problem in a semi-infinite plane is discussed. Re concentrated forces are applied on the edge crack face, or on the line boundary of the cracked semi-infinite plane. The rational mapping function approach is suggested to solve the boundary value problem and a solution in a closed form is obtained. Finally, several numerical examples with the calculated results are given.展开更多
A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) bound...A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) boundary integral equations in this paper. The eigen COD is defined as a crack in an infinite domain under fictitious traction acting on the crack surface. Respect to the computational accuracies and efficiencies, the multiple crack problems in finite and infinite plates are solved and compared numerically using three different kinds of boundary integral equations (BIEs): 1) the dual BIEs require crack surface discretization;2) the BIEs with numerical Green’s functions (NGF) without crack surface discretization, but have to solve a complementary matrix;3) the eigen crack opening displacement (COD) BIEs in the present paper. With the concept of eigen COD, the multiple crack problems can be solved by using a conventional displacement discontinuity boundary integral equation in an iterative fashion with a small size of system matrix as that in the NGF approach, but without troubles to determine the complementary matrix. Solution of the stress intensity factors of multiple crack problems is solved and compared in some numerical examples using the above three computational algorithms. Numerical results clearly demonstrate the numerical models of eigen COD BIEs have much higher efficiency, providing a newly numerical technique for multiple crack problems. Not only the accuracy and efficiency of computation can be guaranteed, but also the overall properties and local details can be obtained. In conclusion, the numerical models of eigen COD BIEs realize the simulations for multiple crack problems with large quantity of cracks.展开更多
An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from ...An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from the available experiments that the above assumption will lead to erroneous results. In this paper, the two-dimensional problem of a piezoelectric material with a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions when the material is subjected to uniform loads at infinity. It is shown from these solutions that: (i) the stress intensify factor is the same as that of isotropic material, while the intensity factor of the electric displacement depends on both material properties and the mechanical loads, but not on the electric load. (ii) the energy release rate in a piezoelectric material is larger than that in a pure elastic-anisotropic material, i.e., it is always positive, and independent of the electric loads. (iii) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack.展开更多
The interfacial crack problem of a class of spliced materials is discussed. Using plane elastic complex variable method and integral equation theory, one method of solving the complex stress functions is given.
A three-node triangular element fitted to numerical manifold method with continuous nodal stress, called Trig_3-CNS(NMM)element, was recently proposed for linear elastic continuous problems and linear elastic simple c...A three-node triangular element fitted to numerical manifold method with continuous nodal stress, called Trig_3-CNS(NMM)element, was recently proposed for linear elastic continuous problems and linear elastic simple crack problems. The Trig_3-CNS(NMM) element can be considered as a development of both the Trig_3-CNS element and the numerical manifold method(NMM).Inheriting all the advantages of Trig_3-CNS element, calculations using Trig_3-CNS(NMM) element can obtain higher accuracy than Trig_3 element without extra degrees of freedom(DOFs) and yield continuous nodal stress without stress smoothing. Inheriting all the advantages of NMM, Trig_3-CNS(NMM) element can conveniently treat crack problems without deploying conforming mathematical mesh. In this paper,complex problems such as a crucifix crack and a star-shaped crack with many branches are studied to exhibit the advantageous features of the Trig_3-CNS(NMM) element. Numerical results show that the Trig_3-CNS(NMM) element is prominent in modeling complex crack problems.展开更多
The generalized 2D problem in piezoelectric media with collinear cracks is addressed based on Stroh's formulation and the exact electric boundary conditions on the crack faces. Exact solutions are obtained, respec...The generalized 2D problem in piezoelectric media with collinear cracks is addressed based on Stroh's formulation and the exact electric boundary conditions on the crack faces. Exact solutions are obtained, respectively, for two special cases: one is that a piezoelectric solid withN collinear cracks is subjected to uniform loads at infinity, and the other is that a piezoelectric solid containing a single crack is subjected to a line load at an arbitrary point. It is shown when uniform loads are applied at infinity or on the crack faces that, the stress intensity factors are the same as those of isotropic materials, while the intensity factor of electric displacement is dependent on the material constants and the applied mechanical loads, but not on the applied electric loads. Moreover, it is found that the electric field inside any crack is not equal to zero, which is related to the material properties and applied mechanical-electric loads.展开更多
The equilibrium problem for the infinite elastic plane consisting of two different media with many cracks on the interface is discussed. It is transferred to a boundary value problem for analytic functions and then fu...The equilibrium problem for the infinite elastic plane consisting of two different media with many cracks on the interface is discussed. It is transferred to a boundary value problem for analytic functions and then further reduced to a singular integral equation, the unique solvability and an effective method of solution for which are established. A practical example in applications is illustrated, the solution of which is obtained in closed form.展开更多
Using complex variable methods in elasticity, this paper deals with the plane problems ot a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of Complex str...Using complex variable methods in elasticity, this paper deals with the plane problems ot a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of Complex stress functions and stress-intensity tactors expressed in terms of series, and to these problems disiusses three sposial cases,i.e.the cases of the crack under a uniform pressure, a uniform shear stress and the use of the dise rotating uniformly. In these cases the approximate formulas calcidating the stress-intensity factors are also presented. The calculated results shun that for the middle and.small orachs situated inside the disc and not near the external boundary,these approximate formulas give good or better approximation.展开更多
The time-domain BEM was developed to analyze the dynamic stress intensity factor ( DSIF) of 3-D elastodynamic crack problems. To simulate the stress singularity along the front of a crack, eight-node isoparametric sin...The time-domain BEM was developed to analyze the dynamic stress intensity factor ( DSIF) of 3-D elastodynamic crack problems. To simulate the stress singularity along the front of a crack, eight-node isoparametric singular elements were used, and the DSIF for a semi-circular surface crack was firstly calculated based on displacement equation using the time-domain BEM formulation. The new scheme to determine the time step was brought forward. By the dynamic analysis program of time-domain BEM compiled by its, several numerical examples are presented, which demonstrate the unconditional stability and high accuracy of time-domain BEM applied to 3-D elastodynamic crack problems.展开更多
In road and bridge construction, the use of concrete materials has become an important method. Although the construction and application of this concrete material has strong superiority and use value, the problem is m...In road and bridge construction, the use of concrete materials has become an important method. Although the construction and application of this concrete material has strong superiority and use value, the problem is more prominent, especially the occurrence of cracks will seriously affect the safety of roads and bridges, which must arouse people's attention. In view of the most common cracks in road and bridge construction, the main influencing factors and corresponding preventive measures are briefly analyzed and discussed.展开更多
This research developed a hybrid position-channel network (named PCNet) through incorporating newly designed channel and position attention modules into U-Net to alleviate the crack discontinuity problem in channel an...This research developed a hybrid position-channel network (named PCNet) through incorporating newly designed channel and position attention modules into U-Net to alleviate the crack discontinuity problem in channel and spatial dimensions. In PCNet, the U-Net is used as a baseline to extract informative spatial and channel-wise features from shield tunnel lining crack images. A channel and a position attention module are designed and embedded after each convolution layer of U-Net to model the feature interdependencies in channel and spatial dimensions. These attention modules can make the U-Net adaptively integrate local crack features with their global dependencies. Experiments were conducted utilizing the dataset based on the images from Shanghai metro shield tunnels. The results validate the effectiveness of the designed channel and position attention modules, since they can individually increase balanced accuracy (BA) by 11.25% and 12.95%, intersection over union (IoU) by 10.79% and 11.83%, and F1 score by 9.96% and 10.63%, respectively. In comparison with the state-of-the-art models (i.e. LinkNet, PSPNet, U-Net, PANet, and Mask R–CNN) on the testing dataset, the proposed PCNet outperforms others with an improvement of BA, IoU, and F1 score owing to the implementation of the channel and position attention modules. These evaluation metrics indicate that the proposed PCNet presents refined crack segmentation with improved performance and is a practicable approach to segment shield tunnel lining cracks in field practice.展开更多
The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped i...The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.展开更多
This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained...This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained with some unknown constants. The satisfactions of all boundary conditions are then checked, the condition at infinity is considered and the unknown constants are determined. Further study may focus on the case with different shear moduli and the influence of the large deformation.展开更多
文摘The first fundamental problems in the infinite plane with cracks and boundary values cyclically symmetric are considered. They are reduced to singular integral equations on a single crack, which would considerably simplify the process of method of solution for such problems. Some special cases are illustrated.
文摘As suggested by the title, this extensive book is concerned with crack and contact prob- lems in linear elasticity. However, in general, it is intended for a wide audience ranging from engineers to mathematical physicists. Indeed, numerous problems of both academic and tech- nological interest in electro-magnetics, acoustics, solid and fluid dynamics, etc. are actually related to each other and governed by the same mixed boundary value problems from a unified mathematical standpoint
基金Project supported by the Science Fund of the Chinese Academy of Sciences
文摘The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cracks by a constructive method. Those along the interfaces are further reduced to Fredholm ones.
基金supported by Central Plain's leading talent fund for Science,Technology and Innovation of China(Grant No.234200510015).
文摘Diamond tools have been widely used in national defense military,automobile manufacturing,resource exploitation and other fields.Laser brazing diamond technology is often applied to the preparation of diamond tools.However,the formation and expansion of cracks in the process of laser brazing diamond seriously affect the mechanical properties of diamond tools.In order to solve the crack problem of laser brazing diamond,many scholars are committed to the research on improving the solder,optimizing the laser process parameters,improving the laser brazing equipment,optimizing the design of joint form,and developing ultrasonic-assisted laser brazing technology,etc.These studies have achieved certain results.Aiming at the research status of laser brazing diamond crack problem,the crack characteristics of brazing diamond are firstly introduced,and the formation reasons of laser brazing diamond crack are elaborated.Then,the elemental characteristics of brazing filler metals used in brazing diamond are introduced.The influences of Ni-Cr and Ag-Cu-Ti alloy solder and laser process parameters on the crack problem are viewed.Finally,the solutions to the crack problem by scholars at home and abroad in recent years are summarized,and the future research directions to solve crack problem are prospected.
文摘An oblique edge crack problem in a semi-infinite plane is discussed. Re concentrated forces are applied on the edge crack face, or on the line boundary of the cracked semi-infinite plane. The rational mapping function approach is suggested to solve the boundary value problem and a solution in a closed form is obtained. Finally, several numerical examples with the calculated results are given.
文摘A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) boundary integral equations in this paper. The eigen COD is defined as a crack in an infinite domain under fictitious traction acting on the crack surface. Respect to the computational accuracies and efficiencies, the multiple crack problems in finite and infinite plates are solved and compared numerically using three different kinds of boundary integral equations (BIEs): 1) the dual BIEs require crack surface discretization;2) the BIEs with numerical Green’s functions (NGF) without crack surface discretization, but have to solve a complementary matrix;3) the eigen crack opening displacement (COD) BIEs in the present paper. With the concept of eigen COD, the multiple crack problems can be solved by using a conventional displacement discontinuity boundary integral equation in an iterative fashion with a small size of system matrix as that in the NGF approach, but without troubles to determine the complementary matrix. Solution of the stress intensity factors of multiple crack problems is solved and compared in some numerical examples using the above three computational algorithms. Numerical results clearly demonstrate the numerical models of eigen COD BIEs have much higher efficiency, providing a newly numerical technique for multiple crack problems. Not only the accuracy and efficiency of computation can be guaranteed, but also the overall properties and local details can be obtained. In conclusion, the numerical models of eigen COD BIEs realize the simulations for multiple crack problems with large quantity of cracks.
文摘An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from the available experiments that the above assumption will lead to erroneous results. In this paper, the two-dimensional problem of a piezoelectric material with a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions when the material is subjected to uniform loads at infinity. It is shown from these solutions that: (i) the stress intensify factor is the same as that of isotropic material, while the intensity factor of the electric displacement depends on both material properties and the mechanical loads, but not on the electric load. (ii) the energy release rate in a piezoelectric material is larger than that in a pure elastic-anisotropic material, i.e., it is always positive, and independent of the electric loads. (iii) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack.
文摘The interfacial crack problem of a class of spliced materials is discussed. Using plane elastic complex variable method and integral equation theory, one method of solving the complex stress functions is given.
基金the National Natural Science Foundation of China(Grant Nos 51609240,11572009&51538001)and the National Basic Research Program of China(Grant No 2014CB047100)
文摘A three-node triangular element fitted to numerical manifold method with continuous nodal stress, called Trig_3-CNS(NMM)element, was recently proposed for linear elastic continuous problems and linear elastic simple crack problems. The Trig_3-CNS(NMM) element can be considered as a development of both the Trig_3-CNS element and the numerical manifold method(NMM).Inheriting all the advantages of Trig_3-CNS element, calculations using Trig_3-CNS(NMM) element can obtain higher accuracy than Trig_3 element without extra degrees of freedom(DOFs) and yield continuous nodal stress without stress smoothing. Inheriting all the advantages of NMM, Trig_3-CNS(NMM) element can conveniently treat crack problems without deploying conforming mathematical mesh. In this paper,complex problems such as a crucifix crack and a star-shaped crack with many branches are studied to exhibit the advantageous features of the Trig_3-CNS(NMM) element. Numerical results show that the Trig_3-CNS(NMM) element is prominent in modeling complex crack problems.
基金The project supported by the National Natural Science Foundation of China(19772004)
文摘The generalized 2D problem in piezoelectric media with collinear cracks is addressed based on Stroh's formulation and the exact electric boundary conditions on the crack faces. Exact solutions are obtained, respectively, for two special cases: one is that a piezoelectric solid withN collinear cracks is subjected to uniform loads at infinity, and the other is that a piezoelectric solid containing a single crack is subjected to a line load at an arbitrary point. It is shown when uniform loads are applied at infinity or on the crack faces that, the stress intensity factors are the same as those of isotropic materials, while the intensity factor of electric displacement is dependent on the material constants and the applied mechanical loads, but not on the applied electric loads. Moreover, it is found that the electric field inside any crack is not equal to zero, which is related to the material properties and applied mechanical-electric loads.
基金Supported Science Foundation of the National Committee of EducationNatural Science Funds of the National Scientific Committee
文摘The equilibrium problem for the infinite elastic plane consisting of two different media with many cracks on the interface is discussed. It is transferred to a boundary value problem for analytic functions and then further reduced to a singular integral equation, the unique solvability and an effective method of solution for which are established. A practical example in applications is illustrated, the solution of which is obtained in closed form.
文摘Using complex variable methods in elasticity, this paper deals with the plane problems ot a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of Complex stress functions and stress-intensity tactors expressed in terms of series, and to these problems disiusses three sposial cases,i.e.the cases of the crack under a uniform pressure, a uniform shear stress and the use of the dise rotating uniformly. In these cases the approximate formulas calcidating the stress-intensity factors are also presented. The calculated results shun that for the middle and.small orachs situated inside the disc and not near the external boundary,these approximate formulas give good or better approximation.
文摘The time-domain BEM was developed to analyze the dynamic stress intensity factor ( DSIF) of 3-D elastodynamic crack problems. To simulate the stress singularity along the front of a crack, eight-node isoparametric singular elements were used, and the DSIF for a semi-circular surface crack was firstly calculated based on displacement equation using the time-domain BEM formulation. The new scheme to determine the time step was brought forward. By the dynamic analysis program of time-domain BEM compiled by its, several numerical examples are presented, which demonstrate the unconditional stability and high accuracy of time-domain BEM applied to 3-D elastodynamic crack problems.
文摘In road and bridge construction, the use of concrete materials has become an important method. Although the construction and application of this concrete material has strong superiority and use value, the problem is more prominent, especially the occurrence of cracks will seriously affect the safety of roads and bridges, which must arouse people's attention. In view of the most common cracks in road and bridge construction, the main influencing factors and corresponding preventive measures are briefly analyzed and discussed.
基金support from the Ministry of Science and Tech-nology of the:People's Republic of China(Grant No.2021 YFB2600804)the Open Research Project Programme of the State Key Labor atory of Interet of Things for Smart City(University of Macao)(Grant No.SKL-IoTSC(UM)-2021-2023/ORPF/A19/2022)the General Research Fund(GRF)project(Grant No.15214722)from Research Grants Council(RGC)of Hong Kong Special Administrative Re gion Government of China are gratefully acknowledged.
文摘This research developed a hybrid position-channel network (named PCNet) through incorporating newly designed channel and position attention modules into U-Net to alleviate the crack discontinuity problem in channel and spatial dimensions. In PCNet, the U-Net is used as a baseline to extract informative spatial and channel-wise features from shield tunnel lining crack images. A channel and a position attention module are designed and embedded after each convolution layer of U-Net to model the feature interdependencies in channel and spatial dimensions. These attention modules can make the U-Net adaptively integrate local crack features with their global dependencies. Experiments were conducted utilizing the dataset based on the images from Shanghai metro shield tunnels. The results validate the effectiveness of the designed channel and position attention modules, since they can individually increase balanced accuracy (BA) by 11.25% and 12.95%, intersection over union (IoU) by 10.79% and 11.83%, and F1 score by 9.96% and 10.63%, respectively. In comparison with the state-of-the-art models (i.e. LinkNet, PSPNet, U-Net, PANet, and Mask R–CNN) on the testing dataset, the proposed PCNet outperforms others with an improvement of BA, IoU, and F1 score owing to the implementation of the channel and position attention modules. These evaluation metrics indicate that the proposed PCNet presents refined crack segmentation with improved performance and is a practicable approach to segment shield tunnel lining cracks in field practice.
文摘The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.
文摘This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained with some unknown constants. The satisfactions of all boundary conditions are then checked, the condition at infinity is considered and the unknown constants are determined. Further study may focus on the case with different shear moduli and the influence of the large deformation.
