The Fracture Boundary Condition
The Fracture boundary condition relies on the linear slip interface theory proposed by Schoenberg in Ref. 2. The linear slip condition implements the concept of an imperfectly bonded interface between two elastic domains. Imperfect bonding means that:
•
The traction is continuous across the interface
•
The displacement is discontinuous across the interface
The traction at the interface is expressed as a function of the displacement jump, which up to the first order terms reads
,
where kA is the positive definite symmetric boundary stiffness matrix which has dimensions stress/length. For the velocity, which is the dependent variable in the velocity-strain formulation, the linear slip interface boundary condition reads
.
A fracture can represent a thin elastic layer, a fluid filled crack, or a discontinuity (open gap or free surface) in the elastic material. The free surface is approached when kA = 0. For the fluid filled crack, the tangential stiffness should vanish kT = 0.