Date of Completion


Embargo Period



Dr. Wei Sun, Dr. Eric Jordan, Dr. Alexander Staroselsky

Field of Study

Mechanical Engineering


Master of Engineering

Open Access

Open Access


Computationally handling cracks generally results in numerically unstable results. Specifically handling the infinite stresses at the crack tip as well as the abrupt change from virgin material to failed material creates numerical instabilities. This project seeks to determine if phase field physics theory, particularly the physics based modification developed by B. N. Cassenti, can be appropriately applied to cracks. Phase field theory introduces an additional state variable, the phase of the material. The phase represents the level of failure (by cracking), and diffuses the failure along a crack by specified equations. The modification, based on a variational principle, was tested in this project.

To test this theory, two test cases were modeled using finite difference approximations. Test 1 applied shear loading creating a mode II fracture. This test case allowed the accuracy of the crack propagation, particularly the kink angle, to be shown. Test 2 applied tension to a crack in a standard mode I fracture. This allowed for the stress intensity factor to be measured.

Both test cases provided results that were compared to calculations from fracture mechanics theory. In both test cases the results of the phase diffusion and stress distribution agreed with the results from fracture mechanics. From the results, it is clear that the particular physics based variational formulation can be appropriately applied to cracks.

This project has successfully proven that this theory is ready to be implemented into a finite element program using a custom user element that includes additional state variables.

Major Advisor

Dr. Brice N. Cassenti