A hybrid attention deep learning network for refined segmentation of cracks from shield tunnel lining images

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.

Interactions of penny-shaped cracks in three-dimensional solids

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.

On Cyclically Symmetric Crack Problems

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.

Book Review “Fabrikant,V.I.Contact and Crack Problems in Linear Theory of Elasticity,Bentham Science Publishers,Sharjah,UAE(2010)”

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

ON CRACK PROBLEMS IN AN INFINITE PLANE CONSISTING OF THREE DIFFERENT MEDIA

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.

Numerical Comparison Research on the Solution of Stress Intensity Factors of Multiple Crack Problems

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.

Comments on “General solutions of plane problem for power function curved cracks”

An error has been found in Ref. [1]. In the case of n = 2, authors of Ref. [1] suggested the following conformal mapping function：

THE ANALYSIS OF DYNAMIC STRESS INTENSITY FACTOR FOR SEMI-CIRCULAR SURFACE CRACK USING TIME-DOMAIN BEM FORMULATION

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.

AN EDGE CRACK PROBLEM IN A SEMI-INFINITE PLANE SUBJECTED TO CONCENTRATED FORCES

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.

Modeling complex crack problems using the three-node triangular element fitted to numerical manifold method with continuous nodal stress

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.

Application of the extended traction boundary element-free method to the fracture of two-dimensional infinite magnetoelectroelastic solid

A novel extended traction boundary element-free method is proposed to analyze the crack problems of two-dimensional infinite magnetoelectroelastic solid.An extended traction boundary integral equation only involving Cauchy singularity is firstly derived.Then,the extended dislocation densities on the crack surface are expressed as the combination of a characteristic term and unknown weight functions,and the radial point interpolation method is adopted to approximate the unknown weight functions.The numerical scheme of the extended traction boundary element-free method is further established,and an effective numerical procedure is used to evaluate the Cauchy singular integrals.Finally,the stress intensity factor,electric displacement intensity factor and magnetic induction intensity factor are computed for some selected crack problems that contain straight,curved and branched cracks,and good numerical results are obtained.At the same time,the fracture properties of these crack problems are discussed.

Research status of crack problem in laser brazing diamond

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.