Some Properties of J-Integral in Plane Elasticity

Abstract

Some properties of the J-integral in plane elasticity are analyzed. An infinite plate with any number of inclusions, cracks, and any loading conditions is considered. In addition to the physical field, a derivative field is defined and introduced. Using the Betti’s reciprocal theorem for the physical and derivative fields, two new path-independent D1 and D2 are obtained. It is found that the values of Jk(k=1,2) on a large circle are equal to the values of Dk(k=1,2) on the same circle. Using this property and the complex variable function method, the values of Jk(k=1,2) on a large circle is obtained. It is proved that the vector Jk(k=1,2) is a gradient of a scalar function P(x,y).