Dear all:
I am confused by the "traction free boundry condition". Does that mean the stress on the boundry is zero? But the stress on the boundry is definitly not zero. I don't know how to use this condition. I hope someone can help me. Thanks very much.
Best wishes,
What does "traction-free boundary condition" mean?
Hi zhouyuer
Traction free boundary condition means that the the surface is free from external stress. We can mathematically express this as > t = σ.n = 0
where, t is the surface traction in the current configuration; σ = Cauchy stress tensor; n = vector normal to the deformed surface.
If you prefer Lagrangian description > s = P.N = 0
where, t is the surface traction in the reference configuration; P = 1st Piola Kirchoff stress tensor; N = vector normal to the refernce surface.
Therefore, if you divide the external force vector F by deformed surface area you will get t and by dividing F with undeformed surface area you will get s.
You may refer to the following online references:
1. http://en.wikiversity.org/wiki/Continuum_mechanics/Stress_measures
2. http://solidmechanics.org/Text/Chapter2_2/Chapter2_2.php