On the Plane Elastostatic Problem of a Loaded Crack Terminating at a Material Interface

1971 ◽  
Vol 38 (4) ◽  
pp. 911-918 ◽  
Author(s):  
D. B. Bogy
Keyword(s):  
Stress Field ◽  
Plane Problem ◽  
Stress Singularity ◽  
Two Dimensional ◽  
Severe Stress ◽  
Dimensional Theory ◽  
Material Interface ◽  
Material Parameters ◽  
Loaded Crack ◽  
Elastostatic Problem

The plane problem of a crack that terminates at the interface of a bimaterial composite and is loaded on its faces is treated within the two-dimensional theory of elastostatics. The emphasis is placed on determining how the order of the singularity in the stress field at the crack tip depends on the material constants and the angle at which the crack meets the interface. Numerical results are presented through figures showing this dependence on the material parameters for several fixed angles. It is then shown by way of examples how to use these figures to obtain the dependence on the angle for any desired composite. For the two examples chosen, it is found that when the crack is in the weaker constituent the stress singularity is most severe if the crack is tangent to (lies in) the interface; whereas, when the crack is in the stronger constituent a particular angle is associated with the most severe stress singularity for each composite.

Stress Singularity in Three-Phase Bonded Structure

1996 ◽  
Vol 63 (2) ◽  
pp. 252-258 ◽  
Author(s):  
Hideo Koguchi ◽  
Tadanobu Inoue ◽  
Toshio Yada
Keyword(s):  
Stress Field ◽  
Plane Problem ◽  
Stress Singularity ◽  
Theory Of Elasticity ◽  
Intermediate Region ◽  
Free Surfaces ◽  
Three Phase

The plane problem of three-phase materials consisting of three isotropic homogeneous wedges with arbitrary angles, which are with two interfaces and two free surfaces, is analyzed under arbitrary normal and shearing tractions by the theory of elasticity. An eigenequation to examine the order of stress singularity at the apex in the three-phase bonded structure is analytically derived. In particular, this paper emphasizes to investigate the order of singularity in the stress field at the apex when materials of both side regions against intermediate region in three regions are identical. For several bonded wedge geometries, it is demonstrated how the order of stress singularity varies with material pairs. Finally, it is shown that the bonding order of materials also influences on the order of stress singularity in the three-phase bonded structure.

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

scholarly journals Existence and uniqueness in the theory of bending of elastic plates

1986 ◽  
Vol 29 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Neumann Problems ◽  
Image Position

Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

The Elastostatic Axisymmetric Problem of a Cracked Sphere Embedded in a Dissimilar Matrix

1980 ◽  
Vol 47 (3) ◽  
pp. 545-550 ◽  
Author(s):  
R. Kant ◽  
D. B. Bogy
Keyword(s):  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Companion Paper ◽  
Infinite Medium ◽  
Applied Mechanics ◽  
Axisymmetric Solution ◽  
Material Parameters ◽  
The Difference ◽  
Elastostatic Problem

The axisymmetric elastostatic problem of a cracked sphere embedded in a dissimilar matrix is solved by using the solution for a spherical cavity in an infinite medium together with the axisymmetric solution for a cracked sphere given in the companion paper in this issue of the Journal of Applied Mechanics, Pages 538-544. Numerical results are presented for (a) interface stress for various composites (b) dependence of the stress-intensity factor on the material parameters and ratios of crack to sphere radii, (c) the difference in the elastic strain energy for a cracked and uncracked composite.

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