Crack tip field in functional gradient material with exponential variation of elastic constants for the case ν≠0

The present paper derives the solution of the crack tip field in functional gradient material with exponential variation of elastic constants for the case 0. The crack is located on the Oxis (Fig.1). From the result in the Appendix VIII, only the exponential term exp(ax) is discussed. On the basis of exact mathematical theory, it has been found that although the exponential term is exp(ax) in the constitutive equations, yet it becomes exp(ax/2+ak11/2y/2-kr/2) and exp(ax/2-ak11/2y/2-kr/2) in the exact relation. For some numerical solutions, considering the results of the exact relation, they become explained more easily. Further study must focus on the influence of the large deformation.