The cap yield surface and the Coulomb yield surface intersect. In order to determine the mapping zone, the intersection point of the cap and Coulomb yield surfaces must be identified.
This formulation is required in terms of the stress invariants 𝑝–𝑞, rather than the 𝜎–𝜏 representation. Therefore, the Coulomb yield surface must first be expressed in 𝑝–𝑞 space.
The procedure is as follows:
- Derive the Coulomb yield surface in 𝑝–𝑞 form (already provided in the documentation).
- Obtain an analytical solution for the intersection point between the Coulomb and cap yield surfaces.
- Implement the analytical solution in the numerical code.
- Defining two new regions related to the cap.
- Add unit tests.
- Documentation
The cap yield surface and the Coulomb yield surface intersect. In order to determine the mapping zone, the intersection point of the cap and Coulomb yield surfaces must be identified.
This formulation is required in terms of the stress invariants 𝑝–𝑞, rather than the 𝜎–𝜏 representation. Therefore, the Coulomb yield surface must first be expressed in 𝑝–𝑞 space.
The procedure is as follows: