# Linear elasticity modeling load using traction vs. mixed BC

In classical linear elasticity, when modeling a force/load boundary condition, it appears that we could either:

1. Use a pure Neumann boundary condition, where the 3 traction components are specified. In 3-D the 2 tangential traction components would be zero, with the non-zero component being the normal component.

2. Use a mixed boundary condition. Here, the 2 tangential traction components would be zero. The normal traction component is unknown. However, the normal displacement is now known, and the 2 tangential displacements are unknown.

Questions:

• Is it correct to say that 1 and 2 are both accurate methods of modeling this force boundary condition?

• Is there an actual analytical expression for converting the 1 to 2?

• If we know the normal traction component, could we actually uniquely convert this to a normal displacement value?

• I was reading this PPT presentation on how a 3pt bend test was modeled. There was a load in mid point, and 2 points on the bottom of the beam are supported. There was some device that measured the reaction force, $R_f$ at these 2 bottom supports. They modeled this experiment by applying a normal displacement BC at the mid point until the simulation generated the force at the 2 bottom supports that matched $R_f$. I was confused why they would do this instead of applying a force BC at the mid pt. I think they could have simply just applied a force BC where the force is equal to $2R_f$. – doubleD Mar 16 at 18:05