The Westergaard approach is derived for a crack that propagates in Mode I, therefore
Using this condition and employing (A.29) we can write
![]() | (B.1) |
which can be satisfied only if
![]() | (B.2) |
where
As it is possible to express the stresses and displacements by a single analytic function we write
![]() | (B.3) |
which can be plugged into (A.27) using (A.37). Solving the resulting equation leads to the stresses
![]() | (B.4) |
and the displacements
![]() | (B.5) |
If we define
![]() | (B.6) |
where the hat in
![]() | (B.7) |
where
Therefore, the stresses and displacements (B.7) can be derived by choosing the following Airy stress function
![]() | (B.8) |
where the derivatives of the function are defined as
![]() | (B.9) |