Can someone explain the strange physical behavior in contact problem using Lagrange method in modeling a simple 2D indentation?

I am modelling a very simple 2D contact problem between a rigid indenter and a deformable squared-shape specimen. I used a implicit function f to describe the rigid indenter. 
The contact condition is: Inside the contact zone of the deformable specimen, a node n is outside of rigid indenter for f(n)>0, and inside for f(n)<0. In case f(n)=0, the contacting node lies on the surface of the rigid body.
Then, I implemented the above contact condition for both Penalty and Lagrange method and make a comparison between two outputs: the deformed configuration of the Penalty method looks very reasonable in physical behavior but the Lagrange method seems to stick more strongly than enough to the indenter.

Does someone have idea or experience about this before? Could you please explain it to me? I attached the 2 deformed configuration of the 2 methods in order to depict my outputs.