Calculation of strain energy release rates using a complex variable finite element method

In the study of fracture mechanics, the Strain Energy Release Rate (SERR) is one of the most important variables needed to accurately predict when crack growth will occur. The multicomplex step derivative method was implemented into the commercial finite element software package ABAQUS through the use of a user element subroutine (UEL). The complex variable finite element method (ZFEM) gives users the capability to calculate accurate high order derivatives while conducting a finite element analysis. The primary focus of this thesis is to calculate the SERR for both two-dimensional and three-dimensional isotropic and anisotropic materials. In addition to calculating derivatives with respect to the change in crack size, ZFEM is able to simultaneously calculate derivatives with respect to material properties such as the Elastic Modulus, material orientation, and Shear Modulus. The results calculated using ZFEM were verified with analytical solutions and the J-integral technique.