My current research is focused on using the extended finite element method (XFEM) to simulate complex fracture problems. I have implemented several XFEM enrichments into a MATLAB code including cracks in homogeneous material, cracks at bi-material interface, voids and inclusions. In addition crack propagation can be modeled with the code. The discontinuities are represented using level set functions. Crack propagation is modeled using a combination of the maximum circumferential stress criterion for growth direction and either a fixed value or Paris law for the growth increment. For more information about the details of crack growth modeling, level set method, and XFEM, please refer to the pages with a general overview and references on the various topics.

The particular areas of interest with respect to my research in order of current activity include:
1. Modeling quasi-static crack growth with reduced computational time and/or increased number of iterations by taking advantage of the XFEM formulation
    a. Reanalysis of the extended finite element method
    b. Surrogates for more accurate integration of fatigue growth laws
2. Modeling the initiation of cracks from an initial body which is defect free

Please visit my publications page for up to date details on my research as well as MATLAB codes in one-dimension as well as two-dimensions.