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Have someone met a strange behavior of Load-Displacement curve in a simple 2D indentation problem

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.

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.

Problems with numerical integration of discontinuous functions

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.

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