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The determination of stress intensity factors (SIF) is of fundamental importance in prediction of brittle failure using linear elastic fracture mechanics. The presence of a crack in the vicinity of another crack induces an interaction effect. The purpose of this paper is to determine the SIF for an orthotropic lamina subjected to uniaxial loading and containing two cracks. The solution is obtained for one crack being horizontal and located in the centre of lamina while the other crack is inclined to first one. The effect of angle of the second crack, fibre angle is studied. Also, for the case of two parallel cracks, effect of eccentricity in x and y directions is observed.

Boundary collocation method is used and stress functions satisfying governing equations in the domain and ensuring stress singularity at the crack tips are defined. The boundary condition on the edges of lamina and the crack is satisfied to determine the complex coefficients in the stress functions.

For the given fibre angle, orientations of second crack which result in increase/decrease in the SIF at the most dangerous crack tip are found out.

Boundary collocation method which is simple and efficient is extended for studying two crack problem in orthotropic materials.

This paper describes progress on the development of theoretical models required for studying failure mechanism, crack initiation and growth around the boreholes driven by hydrofracturing processes in Hot Dry Rock (HDR) reservoirs of geothermal energy. Due to the importance of the stress intensity factor concept (K) in Fracture Mechanics, some advanced modeling techniques for accurate and fast determination of K for relevant problems are proposed. Alternative tools to deal with stress intensity factor determination are developed and assessed from the points of view of accuracy and computational cost. We concentrate on residual strength, crack initiation and crack growth as a means to model and understand experimentally observed behaviors. Several modeling methods such as compounding and weight function techniques, and boundary and finite element modeling for stress intensity factor calculation are discussed. Further to reviews of those techniques, work performed included (i) developing alternative solutions to deal with boundary‐to‐boundary interaction when using the compounding technique, (ii) relating the precision of K calculations with the level of precision of the crack opening displacement of a reference solution, in order to assess the precision of weight function technique, (iii) modeling relevant geometries using the finite element method (FEM), (iv) working on the implementation of direct stress intensity factor K determination in the Higher Order Displacement Discontinuity Method (HODDM), and (v) developing tools to deal with residual stress fields around the boundary of the hydraulically pressurized boreholes.

This paper aims to calculate the mixed‐mode stress intensity factors (SIFs) of a 3D crack meeting the interface in a bimaterial under shear loading by a hypersingular integral equation (HIE) method, And further to assess the accuracy of numerical solutions for the mixed mode SIFs along the crack front.

A 3D crack modeling is reduced to solving a set of HIEs. Based on the analytical solutions of the singular stress field around the crack front, a numerical method for the HIEs is proposed by a finite‐part integral method, where the displacement discontinuities of the crack surface are approximated by the product of basic density functions and polynomials. Using FORTRAN program, numerical solutions of the mixed‐mode SIFs of some examples are presented.

The numerical method is proved to be an effective construction technique. The numerical results show that this numerical technique is successful, and the solution precision is satisfied.

This work takes further steps to improve the fundamental systems of HIE for its application in the fields of arbitrary shape crack problems. Propose several techniques for numerical implementation, which could increase the efficiency and accuracy of computation.

Whenever there is a structure containing the 3D crack, the analysis method described in this paper can be utilized to find the critical configurations under which the structure may be most vulnerable. In such cases, the strength predictions would be safer if the crack could be taken into account.

This paper is the first to apply HIE method to analyzing the mixed‐mode crack meeting the interface in 3D dissimilar materials. Numerical solutions of the mixed‐mode SIFs can give the satisfied solution precision.

Piezoelectric ceramics are often combined with other materials to fabricate composites, which are used for constructions of intelligent systems. This paper is concerned with the fracture of a piezoelectric fiber embedded in an elastic matrix of finite radius. The fiber composite medium is subjected to the axially symmetric mechanical and electrical loads. Fourier and Hankel transforms are used to reduce the problem to the solution of a system of integral equations. Numerical solutions for the crack tip fields are obtained for various crack sizes and different piezoelectric fiber volume fractions. Both impermeable and permeable crack‐face electrical boundary conditions are considered. Applicability and effect of the crack‐face electrical boundary conditions are discussed.

The purpose of this paper is to present special nine‐node quadrilateral elements to discretize the un‐cracked boundary and the inclined surface crack in a transversely isotropic cuboid under a uniform vertical traction along its top and bottom surfaces by a three‐dimensional (3D) boundary element method (BEM) formulation. The mixed‐mode stress intensity factors (SIFs), K_I, K_II and K_III, are calculated.

A 3D dual‐BEM or single‐domain BEM is employed to solve the fracture problems in a linear anisotropic elastic cuboid. The transversely isotropic plane has an arbitrary orientation, and the crack surface is along an inclined plane. The mixed 3D SIFs are evaluated by using the asymptotical relation between the SIFs and the relative crack opening displacements.

Numerical results show clearly the influence of the material and crack orientations on the mixed‐mode SIFs. For comparison, the mode‐I SIF when a horizontal rectangular crack is embedded entirely within the cuboid is calculated also. It is observed that the SIF values along the crack front are larger when the crack is closer to the surface of the cuboid than those when the crack is far away from the surface.

The FORTRAN program developed is limited to regular surface cracks which can be discretized by the quadrilateral shape function; it is not very efficient and suitable for irregular crack shapes.

The evaluation of the 3D mixed‐mode SIFs in the transversely isotropic material may have direct practical applications. The SIFs have been used in engineering design to obtain the safety factor of the elastic structures.

This is the first time that the special nine‐node quadrilateral shape function has been applied to the boundary containing the crack mouth. The numerical method developed can be applied to the SIF calculation in a finite transversely isotropic cuboid within an inclined surface crack. The computational approach and the results of SIFs are of great value for the modeling and design of anisotropic elastic structures.

The elastodynamic response of two coplanar finite cracks in an infinite orthotropic strip due to longitudinal waves incident normally on the cracks has been investigated in this paper. Fourier transforms are used to reduce the mixed boundary value problem to Cauchy‐type singular integral equation, which is solved numerically. The stress intensity factors at the edges of the cracks have been derived and plotted against dimensionless frequency for different geometry parameters. Also normal stress out side the cracks has been calculated numerically and plotted for different parameters and different materials.

The purpose of this paper is to develop a methodology for in situ stress intensity factor (SIF) determination that can be used for the analysis of cracked structures. The technique is based on digital image correlation (DIC) combined with an overdetermined algorithm.

The linear overdeterministic algorithm for calculating the SIF based on stress values around the crack tip is applied to a strain field obtained by DIC.

As long as the image quality is sufficiently high, a good accuracy can be obtained for the measured SIF. The crack tip can be automatically detected based on the same strain field. The use of the strain field instead of the displacement field, eliminates problems related to the rigid body motion of the analysed structure.

In future works, based on the applied techniques, the SIF of complex cracked plane stress structures can be accurately determined in real engineering applications.

The paper demonstrates application of known techniques, refined for other applications, also the use of stress field for SIF overdeterministic calculations.

The purpose of this paper is to introduce a computational time dependent modeling to investigate propagation of elastic-viscoplastic zones in the shock wave loaded circular plates.

Constitutive equations are implemented incrementally by the Von-Kármán finite deflection system which is coupled with a mixed strain hardening rule and physical-base viscoplastic models. Time integrations of the equations are done by the return mapping technique through the cutting-plane algorithm. An integrated solution is established by pseudo-spectral collocation methodology. The Chebyshev basis functions are utilized to evaluate the coefficients of displacement fields. Temporal terms are discretized by the Houbolt marching method. Spatial linearizations are accomplished by the quadratic extrapolation technique.

Results of the center point deflections, effective plastic strain and stress (dynamic flow stress) and temperature rise are compared for three features of the Von-Kármán system. Identifying time history of resultant stresses, propagations of the viscoplastic plastic zones are illustrated for two circumstances; with considering strain rate and hardening effects, and without them. Some of modeling and computation aspects are discussed, carefully. When the results are compared with experimental data of shock wave loadings and finite element simulations, good agreements between them are observed.

This computational approach makes coupling the structural equations with the physical descriptions of the high rate deformation through step-by-step spectral solution of the constitutive equations.

This paper aims to develop a new isogeometric boundary element formulation based on non-uniform rational basis splines (NURBS) curves for solving Reissner’s shear-deformable plates.

The generalized displacements and tractions along the problem boundary are approximated as NURBS curves having the same rational B-spline basis functions used to describe the geometrical boundary of the problem. The source points positions are determined over the problem boundary by the well-known Greville abscissae definition. The singular integrals are accurately evaluated using the singularity subtraction technique.

Numerical examples are solved to demonstrate the validity and the accuracy of the developed formulation.

This formulation is considered to preserve the exact geometry of the problem and to reduce or cancel mesh generation time by using NURBS curves employed in computer aided designs as a tool for isogeometric analysis. The present formulation extends such curves to be implemented as a stress analysis tool.

This paper aims to assess the effectiveness of Hall currents and power-law slip condition on the hydromagnetic convective flow of an electrically conducting power-law fluid over an exponentially stretching sheet under the effect of a strong variable magnetic field and thermal radiation. Flow formation is developed using the rheological expression of a power-law fluid.

The nonlinear partial differential equations describing the flow are transformed into the nonlinear ordinary differential equations by employing the local similarity transformations and then solved numerically by an effective numerical approach, namely, fourth-order Runge–Kutta integration scheme, along with the shooting iteration technique. The numerical solution is computed for different parameters by using the computational software MATLAB bvp4c. The bvp4c function uses the finite difference code as the default. This method is a fourth-order collocation method. The impacts of thermophysical parameters on velocity and temperature distributions, skin friction coefficients and Nusselt number in the boundary layer regime are exhibited through graphs and tables and deliberated with proper physical justification.

Our investigation conveys that Hall current has an enhancing behavior on velocity profiles and reduces skin friction coefficients. An increase in the power-law index is observed to deplete velocity and temperature evolution. The temperature for the pseudo-plastic (shear-thinning) fluid is relatively higher than the corresponding temperature of the dilatant (shear-thickening) fluid. The streamlines are more distorted and have low intensity near the surface of the sheet for the dilatant fluid than the pseudo-plastic fluid.

The study is pertinent to the expulsion of polymer sheet and photographic films, hydrometallurgical industry, electrically conducting polymer dynamics, magnetic material processing, solutions and melts of polymer processing, purification of molten metals from nonmetallic. The results obtained in this work can be relevant in fluid mechanics and heat transfer applications.

The present problem has, to the authors' knowledge, not communicated thus far in the scientific literature. A comparative study with the published works is conducted to verify the accuracy of the present study. The results obtained in this analysis are significant in providing the standards for validating the accuracies of some numerical or empirical methods.