I am modelling a very simple 2D contact problem between a rigid wedge indenter and a deformable squared-shape specimen (general steel material) in frictionless contact case. I used an implicit function f to describe the rigid indenter.

I implemented Lagrange multiplier method for this contact problem and the contact condition is: Inside the contact zone of the deformable specimen, the node set is active if f(node)<=0 and the Lagrange multiplier lambda<=0.

I also generated an exactly the same model on ABAQUS in order to make a code2code comparison of the ouputs. And these are the things I see:

a. Displacement: I must say it is 99% similar considering displacement distribution and value between my implementation and ABAQUS results. (There is only a little bit tolerance at the displacement value).

b. Load-Displacement curve: the ABAQUS curve is very reasonable with a linearly increasing. However, it is so strange in my implementation due to the fact that the load is equal to zero in 3 first steps of an increasing displacement u.

I attached my model, and the 2 load-displacement curve outputs: one is my implementation and the other is ABAQUS result, so that you can see how strange it is.

Have anybody had experience with this before? Could you please help me to explain about it?

Thank you very much,
Best regards,

Minh

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.

Hi everybody,

I am a beginner in doing research :-) and my topic is about "Micro Indentation Analysis using Continuum Dislocation Theory". I am applying high-order finite element method for this nonlinear problem.

My plan is first writing a subroutine for the element. However, when I intend to compute the internal force by using Gauss Integration, I see a problem with the integrand function of some components of the internal force vector. This integrand is discontious function. It is therefore, I cannot get a good approximation with the standard Gauss integration.

Does anybody have idea on how to deal with this problem? I attached two images: one of the integrand function before and one of the integrand function after using standard Gauss integration in order to clarify my question. Thank you very much.

Best Regards,

Minh