Elastic wave scattering

This is a seed project. It depends on understanding the attached two documents. I have a working Matlab program that implements both. I need to simulate the interface between fiber and medium as a de-bonded or with an angular crack. I have also the theoretical derivations for a spring interface. The interface condition will be implemented as a boundary condition. The task are: derive independently the interface then compare it with mine. change this into a boundary value problem so it can be solved using existing Matlab programs. i.e. instead of having a partial de-bonded problem...the problem will be changed to boundary value