Elliptical hole enlarged by a rigid elliptical inclusion

1986 ◽  
Vol 62 (1-4) ◽  
pp. 185-188
Author(s):  
C. Perdikis
Keyword(s):  
Elliptical Hole ◽  
Elliptical Inclusion ◽  
Rigid Elliptical Inclusion

Two-Dimensional Crack Inclusion Interaction Effects: Analysis and Experiments

1991 ◽  
Vol 113 (3) ◽  
pp. 392-397 ◽  
Author(s):  
M. H. Santare ◽  
B. J. O’Toole ◽  
E. M. Patton
Keyword(s):  
Stress Intensity ◽  
Crack Problem ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Quadratic Polynomials ◽  
Elliptical Inclusion ◽  
Inclusion Interaction ◽  
Plane Interaction ◽  
Fringe Patterns ◽  
Rigid Elliptical Inclusion

The plane interaction between a crack and a rigid elliptical inclusion is investigated. In particular, the effects of the orientation and aspect ratio of the inclusion are considered. Analytically, the solution for the interaction of a dislocation with an inclusion is used as Green’s function for the problem. The crack problem is then cast in the form of a set of integral equations with Cauchy singularities. These are solved numerically by the use of piecewise quadratic polynomials to approximate the unknown dislocation density along the crack. From this density the stress intensity at the crack tip can be determined. To model the situation experimentally photoelastic specimens with various elliptical inclusions are tested in uniaxial tension. The stress intensity factors are evaluated from the isochromatic fringe patterns and compared to those predicted numerically.

scholarly journals The study of nonlinear deformation of a plane with an elliptical inclusion for harmonic materials

2020 ◽  
Vol 16 (4) ◽  
pp. 375-390
Author(s):  
Venyamin M. Malkov ◽  
◽  
Yulia V. Malkova ◽  
Keyword(s):  
Boundary Conditions ◽  
Complex Variable ◽  
Nonlinear Deformation ◽  
Elliptical Hole ◽  
Nonlinear Problems ◽  
Elliptical Inclusion ◽  
Elastic Bodies ◽  
Analytical Functions ◽  
Nonlinear Plane ◽  
Linear Material

Analytical methods are used to study nonlinear deformation of a plane with an elliptical inclusion. The elastic properties of a material of the plane and inclusion are described with a semi-linear material. The external load is constant nominal (Piola) stresses at infinity. At the inclusion boundary, the conditions of the continuity for stresses and displacements are satisfied. Semi-linear material belongs to the class of harmonic, the methods of the theory of functions of a complex variable are applicable to solving nonlinear plane problems. Stresses and displacements are expressed in terms of two analytical functions of a complex variable, determined by the boundary conditions on the inclusion contour. It is assumed that the stress state of an inclusion is uniform (the tensor of nominal stresses is constant). This hypothesis made it possible to reduce the difficult nonlinear problem of conjugation of two elastic bodies to the solution of two more simpler problems for a plane with an elliptical hole. The validity of this hypothesis is justified by the fact that the constructed solution exactly satisfies all the equations and boundary conditions of the problem. The same hypothesis was used earlier by other authors to solve linear and nonlinear problems of an elliptical inclusion. In the article, a comparative analysis of the stresses and strains is carried out for two models of harmonic materials — semi-linear and John’s. Various variants of values of elasticity parameters of the inclusion and matrix have been considered.

Interaction Between an Edge Dislocation and a Rigid Elliptical Inclusion

1986 ◽  
Vol 53 (2) ◽  
pp. 382-385 ◽  
Author(s):  
M. H. Santare ◽  
L. M. Keer
Keyword(s):  
Rigid Body ◽  
Edge Dislocation ◽  
Complex Potential ◽  
Closed Form Solution ◽  
Elastic Field ◽  
Form Solution ◽  
Two Dimensional ◽  
Elliptical Inclusion ◽  
Contour Plots ◽  
Rigid Elliptical Inclusion

A solution is presented for the two-dimensional elastic field created by the interaction of an edge dislocation with a rigid elliptical inclusion. The complex potential approach by Muskhelishvili is used and a closed-form solution is obtained. Contour plots for the glide component of the Peach–Koehler forces are presented. Particular attention is paid to the rigid body of the inclusion with respect to the dislocation.

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