Anti-Plane Elasticity Problem and Mode Ⅲ Crack Problem of Cubic Quasicrystal

The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.

Dynamic anti-plane analysis for two symmetrically interfacial cracks near circular cavity in piezoelectric bi-materials

The present paper is exposed theoretically to the influence on the dynamic stress intensity factor （DSIF） in the piezoelectric bi-materials model with two symmet- rically permeable interracial cracks near the edges of a circular cavity, subjected to the dynamic incident anti-plane shearing wave （SH-wave）. An available theoretical method to dynamic analysis in the related research field is provided. The formulations are based on Green＇s function method. The DSIFs at the inner and outer tips of the left crack are obtained by solving the boundary value problems with the conjunction and crack- simulation technique. The numerical results are obtained by the FORTRAN language program and plotted to show the influence of the variations of the physical parameters, the structural geometry, and the wave frequencies of incident wave on the dimensionless DSIFs. Comparisons with previous work and between the inner and outer tips are con- cluded.

ELECTRIC FIELD GRADIENT EFFECTS IN ANTI-PLANE PROBLEMS OF A CIRCULAR CYLINDRICAL HOLE IN PIEZOELECTRIC MATERIALS OF 6 mm SYMMETRY

We study electromechanical felds in the anti-plane deformation of an infnite medium of piezoelectric materials of 6 mm symmetry with a circular cylindrical hole. The theory of electro- elastic dielectrics with electric feld gradient in the constitutive relations is used. Special attention is paid to the felds near the surface of the hole.

STRESS INTENSITY FACTORS CALCULATION IN ANTI-PLANE FRACTURE PROBLEM BY ORTHOGONAL INTEGRAL EXTRACTION METHOD BASED ON FEMOL

For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions （or between the derivatives of eigenfunctions） of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors （SIFs）, so any order SIF can be extracted based on a certain known solution of displacement （an analytic result or a numerical result）. Many numerical examples based on the finite element method of lines （FEMOL） show that the present method is very powerful and efficient.

ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE

Electroelastic behavior of a cracked piezoelectric ceramics plate subjected to four Cases of combined mechanical-electrical loads is analyzed. The integral transform method is applied to convert the problem involving an impermeable anti-plane crack to dual integral equations. Solving the resulting equations, the explicit analytic expressions for electroelastic field along the crack line and the intensity factors of relevant quantities near the crack tip and the mechanical strain energy release rate we obtained, The known results for an infinite piezoelectric ceramics plane containing an impermeable anti-plane crack are recovered from the present results only if the thickness of the plate h --> infinity.

ANTI-PLANE CRACK MOVING ALONG THE INTERFACE OF DISSIMILAR PIEZOELECTRIC MATERIALS

The problem of an anti-plane Griffith crack moving along the interface of dissimilar piezoelectric materials is solved by using the integral transform technique. It is shown from the result that the intensity factors of anti-plane stress and electric displacement around the crack tip are dependent on the speed of the Griffith crack as well as the material coefficients. When the two piezoelectric materials are identical, the present result will be reduced to the result far the problem of an anti-plane moving Griffith crack in homogeneous piezoelectric materials.

New Formulation for Arbitrary Cracks Problem and Its Stress Intensity Factor of Plane Elasticity

Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.

GENERALIZED 2D PROBLEM OF PIEZOELECTRIC MEDIA CONTAINING COLLINEAR CRACKS

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.

AN EXACT SOLUTION OF CRACK PROBLEMS IN PIEZOELECTRIC MATERIALS

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.

PLANE ELASTIC PROBLEMS OF DIFFERENT MEDIA WITH CRACKS ON THE INTERFACE

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.

Spline Fictitious Boundary Element Alternating Method for Edge Crack Problems with Mixed Boundary Conditions

The alternating method based on the fundamental solutions of the infinite domain containing a crack,namely Muskhelishvili’s solutions,divides the complex structure with a crack into a simple model without crack which can be solved by traditional numerical methods and an infinite domain with a crack which can be solved by Muskhelishvili’s solutions.However,this alternating method cannot be directly applied to the edge crack problems since partial crack surface of Muskhelishvili’s solutions is located outside the computational domain.In this paper,an improved alternating method,the spline fictitious boundary element alternating method(SFBEAM),based on infinite domain with the combination of spline fictitious boundary element method(SFBEM)and Muskhelishvili’s solutions is proposed to solve the edge crack problems.Since the SFBEM and Muskhelishvili’s solutions are obtained in the framework of infinite domain,no special treatment is needed for solving the problem of edge cracks.Different mixed boundary conditions edge crack problems with varies of computational parameters are given to certify the high precision,efficiency and applicability of the proposed method compared with other alternating methods and extend finite element method.

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.

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.

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

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.

PLANE PROBLEMS OF A FINITE DISC CONTAINING AN INTERNAL CRACK

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.

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.

PROBLEMS OF COLLINEAR CRACKS BETWEEN BONDED DISSIMILAR MATERIALS UNDER ANTIPLANE CONCENTRATED FORCES

In this paper problems of collinear cracks between bonded dissimilar materials under antiplane concentrated forces are dealt with. General solutions of the problems are formulated by applying extended Schwarz principle integrated with the analysis of the singularity of complex stress functions. Closed-form solutions of several typical problems are obtained and the stress intensity factors are given. These solutions include a series of original results and some results of previous researches. It is found that under symmetrical loads the solutions for the dissimilar materials are the same as those for the homogeneous materia[7]

General solutions of plane problem for power function curved cracks

A new exact and universal conformal mapping is proposed. Using Muskhelishvili＇s complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors （SIFs） for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.

Interfacial Crack Problem of a Class of Spliced Materials

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.