Conservation Laws and Energy-Release Rates

1973 ◽  
Vol 40 (1) ◽  
pp. 201-203 ◽  
Author(s):  
B. Budiansky ◽  
J. R. Rice
Keyword(s):  
Conservation Laws ◽  
Energy Release ◽  
Complex Variable ◽  
Plane Elasticity ◽  
Special Point ◽  
Stress Distributions ◽  
Isotropic Plane ◽  
Release Rates ◽  
Energy Release Rates ◽  
Plastic Stress

New path-independent integrals recently discovered by Knowles and Sternberg are related to energy-release rates associated with cavity or crack rotation and expansion. Complex-variable forms are presented for the conservation laws in the cases of linear, isotropic, plane elasticity. A special point concerning plastic stress distributions around cracks is discussed briefly.

Energy Release Rates and Related Balance Laws in Linear Elastic Defect Mechanics

1987 ◽  
Vol 54 (2) ◽  
pp. 388-392 ◽  
Author(s):  
J. W. Eischen ◽  
G. Herrmann
Keyword(s):  
Conservation Laws ◽  
Energy Release ◽  
Thermal Effects ◽  
Balance Laws ◽  
Release Rates ◽  
Direct Derivation ◽  
Linear Elastic ◽  
Linear Dynamic ◽  
Dynamic Elasticity ◽  
Energy Release Rates

A simple and direct derivation of certain balance (or conservation) laws for linear dynamic elasticity is presented including nonhomogeneities, thermal effects, anisotropy, and body forces. Additionally, the connection between the balance laws and energy release rates for defect motions is established.

scholarly journals Computation of Energy Release Rates for a Nearly Circular Crack

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Nik Mohd Asri Nik Long ◽  
Lee Feng Koo ◽  
Zainidin K. Eshkuvatov
Keyword(s):  
Integral Equation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Linear Equations ◽  
Circular Crack ◽  
Plane Elasticity ◽  
Hypersingular Integral Equation ◽  
Hypersingular Integral ◽  
Energy Release Rates

This paper deals with a nearly circular crack, in the plane elasticity. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over a considered domain, and it is then transformed into a similar equation over a circular region, , using conformal mapping. Appropriate collocation points are chosen on the region to reduce the hypersingular integral equation into a system of linear equations with unknown coefficients, which will later be used in the determination of energy release rate. Numerical results for energy release rate are compared with the existing asymptotic solution and are displayed graphically.

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