Smoothed FEM based verification method for computation of strain energy release rate in functionally graded materials

A verification method for the finite element computation of the strain energy release rate in functionally graded materials is presented based on the node based smoothed finite element method, both the finite element solution and the smoothed finite element solution of the functionally graded materials are used as the ingredients for computing the lower and upper bounds on the exact strain energy release rate, this results in an interval, in which the exact strain energy release rate exists, and it can acts as a quantitative verification of the computational results. An example of the functionally graded material with open mode crack is solved to verify the method.