Indentation due to a frictionless rigid flat punch[edit | edit source]
Indentation by a plat rigid punch
- Start with uneven surface profile .
- Unsymmetric load , but sufficient for complete contact over the area .
Displacement in direction is
where is a rigid body translation and is a rigid body rotation.
Rigid body motions can be determined using a statically equivalent
set of forces and moments
The displacement gradient is
Integral is a Cauchy Singular Integral that appears often and very naturally when the problem is solved using complex variable methods.
Note that the only thing we are interested in is the distribution of contact forces .If we change the variables so that
and , then
If we write and as
and do some algebra, we get
Flat punch with symmetric load : [edit | edit source]
In this case,
Also, (origin at the center of ), hence . Therefore,
At , the load is infinite, i.e. there is a singularity.