The Experts below are selected from a list of 2010 Experts worldwide ranked by ideXlab platform
Lei Jiao - One of the best experts on this subject based on the ideXlab platform.
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The computation of the J integral with the traction boundary integral equation
International Journal for Numerical Methods in Engineering, 2004Co-Authors: Songying Chen, Leqin Wang, Lei JiaoAbstract:The solutions of the displacement boundary integral equation (BIE) are not uniquely determined in certain types of boundary conditions. Traction boundary integral equations that have unique solutions in these traction and mixed boundary cases are established. For two-dimensional linear elasticity problems, the divergence-free property of the traction boundary integral equation is established. By applying Stokes' theorem, unknown tractions or displacements can be reduced to computation of traction integral potential functions at the boundary points. The same is true of the J integral: it is divergence-free and the evaluation of the J integral can be inverted into the computation of the J integral potential functions at the boundary points of the Cracked Body. The J integral can be expressed as the linear combination of the tractions and displacements from the traction BIE on the boundary of the Cracked Body. Numerical integrals are not needed at all. Selected examples are presented to demonstrate the validity of the traction boundary integral and J integral. Copyright © 2004 John Wiley & Sons, Ltd.
Václav Veselý - One of the best experts on this subject based on the ideXlab platform.
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Analysis of accuracy of Williams series approximation of stress field in Cracked Body – influence of area of interest around crack-tip on multi-parameter regression performance
Frattura ed Integrità Strutturale, 2016Co-Authors: Jakub Sobek, Petr Frantík, Václav VeselýAbstract:A study on the accuracy of an approximation of the stress field in a Cracked Body is presented. Crack-tip stress tensor is expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams power series (WPS). Determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over-deterministic method (ODM) for which results from finite element (FE) method computation are usually taken as inputs. Main attention is paid to a detailed analysis of a suitable selection of FE nodes whose results serve as the inputs to the employed method. Two different ways of FE nodal selection are compared – nodes selected from the crack tip vicinity lying at a ring of a certain radius versus nodes selected more or less uniformly from a specified part of the test specimen Body. Comparison of these approaches is made with the help of procedures developed by the authors which enable both the determination of the coefficients of terms of the analytical WPS approximation of the stress field based on the FE results and the backward reconstruction of the field (again using WPS) from those determined terms’ coefficients/functions. The wedge-splitting test (WST) specimen with a crack is taken as example for the study.
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analysis of accuracy of williams series approximation of stress field in Cracked Body influence of area of interest around crack tip on multi parameter regression performance
Fracture and Structural Integrity, 2016Co-Authors: Jakub Sobek, Petr Frantík, Václav VeselýAbstract:A study on the accuracy of an approximation of the stress field in a Cracked Body is presented. Crack-tip stress tensor is expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams power series (WPS). Determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over-deterministic method (ODM) for which results from finite element (FE) method computation are usually taken as inputs. Main attention is paid to a detailed analysis of a suitable selection of FE nodes whose results serve as the inputs to the employed method. Two different ways of FE nodal selection are compared – nodes selected from the crack tip vicinity lying at a ring of a certain radius versus nodes selected more or less uniformly from a specified part of the test specimen Body. Comparison of these approaches is made with the help of procedures developed by the authors which enable both the determination of the coefficients of terms of the analytical WPS approximation of the stress field based on the FE results and the backward reconstruction of the field (again using WPS) from those determined terms’ coefficients/functions. The wedge-splitting test (WST) specimen with a crack is taken as example for the study.
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Multi-parameter approximation of the stress field in a Cracked Body in the more distant surroundings of the crack tip
International Journal of Fatigue, 2016Co-Authors: Václav Veselý, Jakub Sobek, Petr Frantík, Stanislav SeitlAbstract:Abstract The accuracy of the multi-parameter approximation of the stress fields in a Cracked Body is studied in the paper. This approximation, which uses the Williams power series expansion (WE), is intended to be used to estimate the extent of the nonlinear zone, which plays a significant role within tensile failure and the fatigue assessment of non-brittle materials. The characteristics of this zone could be potentially incorporated into methods of determining the true values of fracture parameters and the fatigue behaviour descriptors of materials exhibiting nonlinear failure. Considering the fact that in the case of elastic–plastic and especially quasi-brittle materials the size of this zone is substantial in comparison to specimen dimensions, it is necessary to consider a large region around the crack tip for this task. An automatic routine implemented as a Java application was created to determine the values of coefficients of the higher order terms of the WE that describe crack-tip fields. These values are calculated using the Over-Deterministic Method (ODM), which is applied to the results of the finite element (FE) analysis of an arbitrary mode I test geometry. Furthermore, another Java application developed by the authors provides an analytical reconstruction of the crack-tip stress field by means of the truncated WE, and enables detailed analysis of the crack-tip stress field approximation. The developed procedures simplify the analysis of the description of mechanical fields at a greater distance from the crack tip considerably. The presented research is focused on the optimisation of the selection of FE nodal results entering the ODM procedure used to determine the values of coefficients of the higher order terms of the WE. The aim is to improve the accuracy of the approximation.
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Accuracy of Approximation of Stress and Displacement Fields in Cracked Body for Estimation of Failure Zone Extent / Přesnost Aproximace Polí Napětí A Posunů V Tělese S Trhlinou Pro Odhad Rozsahu Zóny Porušení
Transactions of the VŠB – Technical University of Ostrava Civil Engineering Series, 2012Co-Authors: Jakub Sobek, Václav Veselý, Lucie ŠestákováAbstract:Abstract The paper deals with an analysis of the stress and displacement fields in a Cracked Body. The intention of the authors is to determine the sufficient number of terms of the Williams power series for an accurate approximation of the near-crack-tip fields which can be subsequently used e.g. for estimation of the extent of the fracture process zone in quasi-brittle materials. Values of coefficients of these terms are determined via regression from results of numerical simulations; the coefficients are expressed as functions of the relative crack length. The analysis is conducted on a 2D numerical model of the wedge-splitting test on a modified standard cube-shaped specimen used commonly for testing of cementitious composites; ANSYS FE computational system is employed.
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convergence study on application of the over deterministic method for determination of near tip fields in a Cracked plate loaded in mixed mode
Applied Mechanics and Materials, 2012Co-Authors: Lucie Šestáková, Václav VeselýAbstract:Multi-parameter description of crack behavior in quasi-brittle materials offers still enough space for investigations. Several studies have been carried out by the authors in this field [1-3]. One part of the publications by the authors (this work included) contain analyses of the accuracy, convergence and/or tuning of the over-deterministic method that enables determination of the coefficients of the higher-order terms in Williams expansion approximating the stress and displacement fields in a Cracked Body without any complicated FE formulations. These intermediate studies should bring together a list of recommendations how to use the ODM as effectively as possible and obtain reliable enough values of coefficients of the higher-order terms. Thus, the stress/displacement field can be determined precisely even in a larger distance from the crack tip, which is crucial for assessment of the fracture occurring in quasi-brittle materials.
Songying Chen - One of the best experts on this subject based on the ideXlab platform.
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The computation of the J integral with the traction boundary integral equation
International Journal for Numerical Methods in Engineering, 2004Co-Authors: Songying Chen, Leqin Wang, Lei JiaoAbstract:The solutions of the displacement boundary integral equation (BIE) are not uniquely determined in certain types of boundary conditions. Traction boundary integral equations that have unique solutions in these traction and mixed boundary cases are established. For two-dimensional linear elasticity problems, the divergence-free property of the traction boundary integral equation is established. By applying Stokes' theorem, unknown tractions or displacements can be reduced to computation of traction integral potential functions at the boundary points. The same is true of the J integral: it is divergence-free and the evaluation of the J integral can be inverted into the computation of the J integral potential functions at the boundary points of the Cracked Body. The J integral can be expressed as the linear combination of the tractions and displacements from the traction BIE on the boundary of the Cracked Body. Numerical integrals are not needed at all. Selected examples are presented to demonstrate the validity of the traction boundary integral and J integral. Copyright © 2004 John Wiley & Sons, Ltd.
Dietmar Gross - One of the best experts on this subject based on the ideXlab platform.
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a hyper singular traction boundary integral equation method for stress intensity factor computation in a finite Cracked Body
Engineering Analysis With Boundary Elements, 2003Co-Authors: Tsviatko Rangelov, Petia Dineva, Dietmar GrossAbstract:Abstract This paper attempts to answer the commonly raised question: what are the parameters controlling the solution accuracy and stability when the hyper-singular traction boundary-integral equations (BIEs) are used for the dynamic (time-harmonic) linear elastic fracture analysis of a finite Cracked structure. The usage of the traction BIEs together with the parabolic discretization mesh leads to hyper-singularity, when the crack lies on the boundary, even after application of a regularization procedure. In this paper two new ways, average method and shifted point method to overcome this difficulty, are proposed and compared. It is shown by numerical experiments on the examples of a Cracked rectangular plate and of a Cracked infinite plane that the accuracy and the convergence of the method solution depends mainly on the smoothness requirements of the solution at all collocation points.
C. K. Chao - One of the best experts on this subject based on the ideXlab platform.
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5685 - ON THE ENERGY RELEASE RATE OF FINITE Cracked BODIES
2013Co-Authors: C. K. Chao, R C ChangAbstract:C. K. Chao Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 10672 and R. C. Chang Department of Mechanical Engineering, St. John’s & St. Mary’s Institute of Technology Taipei, Taiwan 25135 Abstract A new concept of the energy release rate of a finite Cracked Body is proposed. Considering the global view of the strain energy density field, the new fracture parameter presented here is different from the conventional definition that only depends on the stress field around the crack tip but neglects the influences induced by the boundary conditions on the far field. Based on the hypothesis of the energy density theory, the fracture initiation, trajectory, and destination can be predicted from the strain energy density field of the finite Cracked Body. The new energy release rate defined here is the integration of the strain energy density along the fracture trajectory that begins at the crack initiation and ends to the cracking destination point. Moreover, some interesting comparisons between the new and the conventional energy release rate are discussed.
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Time-Dependent Effect of Viscoelastic Substrate on a Cracked Body under Inplane Load
Key Engineering Materials, 2006Co-Authors: R. C. Chang, C. K. Chao, C.t. Chuang, P.h. YangAbstract:Theoretical and experimental methods dealing with the effect of a viscoelastic substrate on a Cracked Body under inplane load are presented in this article. A generalized trimaterial solution is solved as a convergent series in terms of complex potentials via the successive iterations of the alternating technique in order to satisfy the continuity condition along the interfaces between dissimilar media. This trimaterial solution is then applied to the problem of a finite thickness layer bonded to a half-plane substrate. Using a standard solid model to formulate the viscoelastic constitutive equation, the real time stress intensity factors can be directly obtained from the Laplace domain. In the experiment, an aluminum Cracked plate bonded to a polymer substrate is tested in a tension machine, where the displacement of the specimen is recorded by a high precision digital camera. The time-dependent stress intensity factor is determined by an inverse calculation through the crack opening displacement. The comparisons between the theoretical and experimental results are discussed in the final.
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Effects of a viscoelastic substrate on a Cracked Body under in-plane concentrated loading
Acta Mechanica, 2001Co-Authors: R. C. Chang, S. C. Wang, C. K. ChaoAbstract:The effect of a viscoelastic substrate on an anisotropic elastic Cracked Body under in-plane concentrated loading is studied in this paper. Based on the correspondence principle, the viscoelastic solution is directly obtained from the corresponding elastic one. The fundamental elastic solution is solved as three complex potentials via the property of analytical continuation to satisfy the continuity condition along the interface between dissimilar media. A singular integral technique in association with the dual coordinate transformation is applied to obtain the stress intensity factors for various crack orientations. Using the standard solid model to formulate the viscoelastic constitutive equation, some numerical examples are considered to demonstrate the use of the present approach.
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Thermal Stress Analysis of a Subsurface Inclined Crack Subjected to a Point Heat Source
Journal of Energy Resources Technology-transactions of The Asme, 1997Co-Authors: C. K. Chao, J. W. WangAbstract:The thermoelastic response of a subsurface inclined crack under the application of a point heat source is studied in this paper. Based on the complex variable theory and the method of analytical continuation, the problem is formulated by two stress functions and a temperature function which are enforced to satisfy the interface condition. The singular integral equations for both the temperature field and thermoelastic field are derived by taking dislocation junctions along the crack border such that both the insulated condition and traction-free condition are satisfied on the crack surface. Numerical results of the thermal stress intensity factors for different geometric configurations are discussed in detail and provided in graphical form. The results obtained in this study will be helpful in understanding the problems of seismology generated by thermal loading in a Cracked Body.