scholarly journals MODIFIED DUALITY SCHEME FOR SOLVING MODEL CRACK PROBLEM IN MECHANICS

2017 ◽  
Vol 54 (2) ◽  
pp. 647-654
Author(s):  
Robert V. Namm ◽  
Gyungsoo Woo
Keyword(s):  
Crack Problem ◽  
Duality Scheme ◽  
Model Crack

The Crack Problem for an Orthotropic Half Plane Stiffened by Elastic Films

1992 ◽  
Author(s):  
R. Mahajan ◽  
F. Erdogan ◽  
Y. T. Chou
Keyword(s):  
Half Plane ◽  
Crack Problem

scholarly journals Modified duality methods for solving an elastic crack problem with Coulomb friction on the crack faces

2020 ◽  
Vol 10 (1) ◽  
pp. 276-282
Author(s):  
Robert V. Namm ◽  
Georgiy I. Tsoy
Keyword(s):  
Variational Inequality ◽  
Elastic Body ◽  
Approximation Method ◽  
Coulomb Friction ◽  
Auxiliary Problem ◽  
Crack Problem ◽  
Successive Approximation Method ◽  
Elastic Crack ◽  
Quasi Variational Inequality ◽  
Crack Faces

AbstractWe consider an equilibrium problem for an elastic body with a crack, on the faces of which unilateral non-penetration conditions and Coulomb friction are realized. This problem can be formulated as quasi-variational inequality. To solve it, the successive approximation method is applied. On each outer step of this method, we solve an auxiliary problem with given friction. We solve the auxiliary problem by using modified Lagrange functionals. Numerical results are presented.

Influence of the Material and Thickness of the Specimen on an Infrared Stress Image

2004 ◽  
Vol 261-263 ◽  
pp. 1641-1646
Author(s):  
Kenji Machida ◽  
Mamtimin Gheni
Keyword(s):  
Thermal Conductivity ◽  
Hybrid Method ◽  
Thermal Conduction ◽  
Crack Problem ◽  
High Stress ◽  
High Accuracy ◽  
Problem Analysis ◽  
Principal Stresses ◽  
Distribution Form ◽  
Stress Components

The thickness dependency of the temperature image obtained by an infrared thermography was investigated using specimens with three kinds of materials and four kinds of the thickness of the specimen. Only the sum of the principal stresses which is the first invariant of stress tensor is measured, and it is impossible to measure individual stress components directly. Then, the infrared hybrid method was developed to separate individual stress components. Although the form of the contour line of low stress side differs greatly, the distribution form of high stress side was considerably alike. The stress intensity factor of material with low thermal conductivity can be estimated with high accuracy by the infrared hybrid method. On the crack problem, it was elucidated that the influence of thermal conduction is large and an inverse problem analysis is required.

Delamination of Compressively Stressed Orthotropic Functionally Graded Material Coatings Under Thermal Loading

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Bora Yıldırım ◽  
Suphi Yılmaz ◽  
Suat Kadıoğlu
Keyword(s):  
Functionally Graded Material ◽  
Bond Coat ◽  
Thermal Loading ◽  
Layer Structure ◽  
Crack Problem ◽  
Functionally Graded ◽  
Internal Crack ◽  
Correlation Technique ◽  
Fracture Parameters ◽  
Graded Material

The objective of this study is to investigate a particular type of crack problem in a layered structure consisting of a substrate, a bond coat, and an orthotropic functionally graded material coating. There is an internal crack in the orthotropic coating layer. It is parallel to the coating bond-coat interface and perpendicular to the material gradation of the coating. The position of the crack inside the coating is kept as a variable. Hence, the case of interface crack is also addressed. The top and bottom surfaces of the three layer structure are subjected to different temperatures and a two-dimensional steady-state temperature distribution develops. The case of compressively stressed coating is considered. Under this condition, buckling can occur, the crack can propagate, and the coating is prone to delamination. To predict the onset of delamination, one needs to know the fracture mechanics parameters, namely, Mode I and Mode II stress intensity factors and energy release rates. Hence, temperature distributions and fracture parameters are calculated by using finite element method and displacement correlation technique. Results of this study present the effects of boundary conditions, geometric parameters (crack length and crack position), and the type of gradation on fracture parameters.

An Effective Numerical Approach for Multiple Void-Crack Interaction

2005 ◽  
Vol 73 (4) ◽  
pp. 525-535 ◽  
Author(s):  
Xiangqiao Yan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Elastic Plate ◽  
Homogeneous Problem ◽  
Crack Problem ◽  
General System ◽  
Numerical Approach ◽  
Displacement Discontinuity ◽  
Crack Problems ◽  
Element Method

This paper presents a numerical approach to modeling a general system containing multiple interacting cracks and voids in an infinite elastic plate under remote uniform stresses. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks and voids, the original problem is divided into a homogeneous problem (the one without cracks and voids) subjected to remote loads and a multiple void-crack problem in an unloaded body with applied tractions on the surfaces of cracks and voids. Thus the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Test examples are included to illustrate that the numerical approach is very simple and effective for analyzing multiple crack/void problems in an infinite elastic plate. Specifically, the numerical approach is used to study the microdefect-finite main crack linear elastic interaction. In addition, complex crack problems in infinite/finite plate are examined to test further the accuracy and robustness of the boundary element method.

A Crack Model of a Bone Cement Interface

1984 ◽  
Vol 106 (3) ◽  
pp. 235-243 ◽  
Author(s):  
J. P. Clech ◽  
L. M. Keer ◽  
J. L. Lewis
Keyword(s):  
Bone Cement ◽  
Cohesive Zone ◽  
Edge Crack ◽  
Crack Problem ◽  
Bimaterial Interface ◽  
Fracture Mechanisms ◽  
Homogeneous Material ◽  
Crack Model ◽  
Cement Interface ◽  
Crack Faces

This paper is concerned with the fracture mechanics of a bone-cement interface that includes a cohesive zone effect on the crack faces. This accounts for the experimentally observed strengthening mechanism due to the mechanical interlock between the crack faces. Edge crack models are developed where the cohesive zone is simulated by a continuous or a discrete distribution of linear or nonlinear springs. It is shown that the solution obtained by assuming a homogeneous material is fairly close to the exact solution for the bimaterial interface edge crack problem. On the basis of that approximation, the analysis is conducted for the problem of two interacting edge cracks, one at the interface, and the other one in the cement. The small crack that was observed to initiate in the cement, close to the bone-cement interface, does not affect much the mode I stress-intensity factor at the tip of the interface crack. However it may grow, leading to a catastrophic breakdown of the cement. The analysis and following discussion point out an interdependency between bone-cement interface strength and cement strength not previously appreciated. The suggested crack models provide a framework for quantifying the fracture mechanisms at the bone-cement interface.

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