I am working on a finite element modelling problem in MATLAB. I had a code which did not take contacts between elements into account and the elements just went through each other. But I modified my code so that it just detects the contacts between two elements and stops solving for further displacement increments. This does not include the contact mechanics when the elements touch each other. I want to formulate a friction-less contact and make the elements just slide over each other without penetration assuming the elements form a rigid body.I have read many references for going about including the contact model and I can understand those models but can't determine how to integrate them with the existing code.I am kind of sure that it should be added into the part of the code that updates the displacement vector but don't know how.

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