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The J-integral represents a way to calculate the strain energy release rate, or work per unit fracture surface area, in a material. [1] The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov [2] and independently in 1968 by James R. Rice, [3] who showed that an energetic contour path integral (called J) was independent of the path around a crack.
A path independent integral and the approximate analysis of strain concentration by notches and cracks. Department of Defense Advanced Research Projects Agency. Contract SD-86, Material Research Program, May 1967. Rice, James R. "Mathematical analysis in the mechanics of fracture." Fracture: an advanced treatise 2 (1968): 191–311.
95 characters; the 52 alphabet characters belong to the Latin script. The remaining 43 belong to the common script. The 33 characters classified as ASCII Punctuation & Symbols are also sometimes referred to as ASCII special characters. Often only these characters (and not other Unicode punctuation) are what is meant when an organization says a ...
1 Latin characters. 2 Greek characters. 3 Other characters. ... (J⋅K −1) constant of integration ... integral the inverse of the derivative. unitless
First, J does not give the energy release rate in small-scale yielding except under certain special cases. Those cases include monotonic loading in mode III or of pure power-law hardening materials. J is not path-independent for monotonic mode I and mode II loading of elastic-plastic materials, so only a contour very close to the crack tip ...
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the Skorokhod integral in Malliavin calculus, a subfield of stochastic analysis; the minimum degree of any vertex in a given graph; a partial charge. δ− represents a negative partial charge, and δ+ represents a positive partial charge chemistry (See also: Solvation) the chemical shift of an atomic nucleus in NMR spectroscopy.
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