The Verification of Computing J-Integral in Functionally Graded Material

We present a verification method for the finite element computation of the J-integrals in functionally graded material. An interval is obtained for the J-integral by an output bound procedure for the quantity of interest. The difference between homogeneous material and functionally graded material is that the parameter before the quadratic term in the error equation is a function of coordinates, not a constant in the homogeneous material. An optimal value for of the parameter is calculated for obtaining efficient bounds on the J-integral.