Asymptotics for 1d string/beam immersed into a 2d/3d media

Dear iMechanicians,

Could someone suggest me the references regarding the following topics:

Consider  a 2d or 3d elastic body with an immersed 1d inclusion.

I am looking  for asymptotics at the inclusion's tips for the following cases:

1. Inclusion is an absolutely rigid beam or string.

2. Inclusion is an elastic string (i.e., there is no bending stiffness).

3. Inclusion is an elatic beam. 

Many thanks in advance,

Evgeny Savenkov