Determination of stress intensity factor of FGM materials

It is important to note that the determination of Stress intensity Factors lead to major problem for researchers, some of them have proposed an analytical method based on linear fracture mechanic by using the theorem de Giffth and also Paris, other have proposed numerical method using finite elememt analysis codes such as Ansys or Abaqus, other researcher have used experimental method.
  However, these methods still need an improvement for given accurate results.
How to develop an analytical method and adopted to FGM structure.
as you know in the case of FGM beam ,Young's  modulus vary along the thikness of beam