Strange iteration behavior when using higher order elements

Dear all,

I’m a newbie in finite element simulations. I have been studying this tutorial on a gradient damage model

The tutorial is excellent, and the code works perfectly. I’m able to reproduce all the results.

Out of curiosity, I tried to increase the degree of all elements used in the model by one. In the original tutorial, P1 element is used for both displacement and damage. When I switched to P2 element for both fields, I observed a strange phenomena. The first 5 iterations are exactly the same as before, but from the 6th iteration, both displacement and damage fields reverted back to zero (i.e. the initial fields), and the same 5 iterations repeat over again. I attached a screenshot of the first 7 iterations below.

Since the code already works well with P1 element, I’m not seeking help in debugging this specific case. I’m rather interested to know whether this is a general issue with higher order elements, and if there is any advice on how to investigate and prevent it.

There are some discussions on the internet talking about second order elements causing problems in contact problem. It appears that increasing element order does not always leads to better results.

Have any of you encountered similar issues when solving things iteratively? How did you resolve your issue? Any references/guidelines in choosing elements for a specific problem in general?