What is the physical meaning of the term: \grad{d}.n=0 ? This is the boundary condition of the phase field equation for fracture.
And, how would you enforce it in your solution?
This is a natural boundary condition, so you do not need to enforce it. This is similar to zero traction condition in the displacement problem.
Thanks Professor Nguyen. As you said, it is similar to zero traction on the surface of displacement problem. But is there any "physical" meaning to it? In displacement problem, it means no traction is applied on the surface of the solid, is there a similar physical meaning here?
Also for traction free surfaces, we kind of enforce them by having external force vector with zero value entries on the external nodes. Then, when we calculate the internal forces, we naturally get the value zero on the traction free external nodes and the applied tractions value on the external nodes with applied traction, am I totally wrong?
Perhaps one can think about the thermodynamic force conjugated to the vector \grad{d}. It is also not so clear to me how one can "physically" interpret this type of force. For example, in the case of the damage variable "d" the conjugate force is "damage driving force" and in the case of \grad{u}, it is similar to stress (or its projection traction).
Forcing \grad{d}.n=0 may let the crack normal to the free boundary. In FEM, it can be automaticlly satisfied on the free boundary. However, I am also wondering if it is appropriate for a realistic case.
I think one can consider a cantilever beam fixed on the left side, and want to apply a certain value of d on the boundary exactly. with this condition, we will end up with a horizontal tangent for d (nabla d for 1D here in this case d,x) near the boundary which is similar to the displacement near the boundary for this case by forcing this condition here for a 2D example.
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