Wei-Jin Zheng, UT-Austin

"Numerical Studies of Complex Materials"

Abstract: My research contains two inter-related studies: three-dimensional hydraulic fractures and static cracks in rubber, using the molecular dynamics method for numerical simulations.

Hydraulic fracturing is widely used to extract shale gas from shale formations. Pressurized water is injected into the horizontal wells in the shale formations to create fracture networks. If a network contains many fractures, the shale gas is easier to transport to the surface via this network. However, what the networks look like in the shale formations is still not precisely known so far. This research is to numerically simulate and analyze three-dimensional hydrofractures by using a simulation method, molecular dynamics, which integrates the physics of linear elasticity and fracture mechanics as well as the discrete channel and fluid variables to dynamically see the propagation of hydrofractures. This approach allows an arbitrary number of cracks and arbitrary crack paths and have successfully simulated tilted and twisted fractures growing in response to various loading condtions.

Static cracks in latex rubber sheet have two unusual features: cusped crack tips and a sharp boundary between two phases with distinct deformations. When a latex rubber sheet is stretched beyond a critical stretch ratio, a slit that is cut in the middle will not cause this sheet to break apart but forms a static crack due to the crystallization of rubber. The cusped tip cannot be explained by the existing theories in fracture mechanics, and the sharp change of deformation is puzzling. This research is to explain the phenomena with the aid of the numerical simulation method molecular dynamics for us to use different hyperelastic energy functionals to seek the particular crack shape in rubber. Based on the different symmetries of the regular and crystalline phases of rubber, I have formulated an energy functional and have successfully numerically created the static cracks with the two unusual features.