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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.
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Jade Mirror of the Four Unknowns-- Jaffard ring-- Jahrbuch über die Fortschritte der Mathematik-- Jaina seven-valued logic-- Jameh Mosque of Qazvin-- Jameh Mosque of Yazd-- James Anderson (computer scientist)-- James B. Anderson-- James embedding-- James H. Wilkinson Prize in Numerical Analysis and Scientific Computing-- James reduced product-- James–Stein estimator-- James' space-- James ...
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Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.
Gradshteyn and Ryzhik (GR) is the informal name of a comprehensive table of integrals originally compiled by the Russian mathematicians I. S. Gradshteyn and I. M. Ryzhik. . Its full title today is Table of Integrals, Series, and Produ