# Structural mechanics traction boundary condition question

In structural mechanics, are the boundary conditions "free surface," "Traction free", "stress free" all equivalent Neumann boundary conditions?

• Yes, your understanding is correct. – Bill Greene Jan 1 '18 at 23:43
• Thanks. When applying a traction boundary condition, is the problem no longer unique? – David Jan 1 '18 at 23:52
• I'm not sure I understand your question. The classical stress analysis problem must have displacement constraints (i.e. Dirichlet BC) over part of the boundary. If stresses are specified at all points on the boundary, the solution is no longer unique. – Bill Greene Jan 2 '18 at 0:41
• Sorry, I'll clarify. I'm trying to compute displacement on a mesh. I have a mixture of Dirichlet&Neumann BCs. I use a layer of ghost cells, where I specify the Dirichlet BC. For Neumann BCs, I specify at the face of the ghost and real cell. I need to compute the corresponding ghost cell displacement given the face stress BC. Before computing the displacement, I compute the face gradient using Hooke's law and strain-displacement relationship. However this does NOT give a unique displacement gradient as I have 9 unknowns (9 displacement gradients) but only 6 knowns (6 distinct stress values). – David Jan 2 '18 at 2:14
• I can write out the equations if the above description is ambiguous. – David Jan 2 '18 at 2:15