I am trying to simulate the compression of a rectangular block of material by applying a displacement BC on a rigid plate (the dimension of which is larger than the block. The material is soft but elastic (constant elastic modulus from a linear stress-strain graph). 

Since the plate is larger than the block, and the block squishes out as it is being compressed, obviously new elements come into contact with the plate. However, it does not converge, and aborts after a few steps, due to exceeding the number of max increments, and showing warnings "The system has 3 negative eigenvalues".

I gave it some thought, and I think what is happening is that since the material is soft and being compressed, this would mean that the element at the extreme corner undergoes excessive deformation, to the point that the two adjacent sides of the corner element become a straight line, exhibiting a terrible aspect ratio (images attached, progressing over time - focus on the corner-most element). Is this what might be causing this? If yes, how can I tackle issues like this where new elements are coming into contact and the deformation is so much that a quad element ultimately looks like a tri element?

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