Hyphens are used to connect words which are linked to form adjectives placed before nouns.
The report is up to date (no hyphens)
This is an
So in your sentence it would depend on which elements you thought were comprising the multi-word adjective in front of the noun.
They are used to distinguish elements which might otherwise cause confusion (grammar-monster.com):
a heavy-metal detector
a heavy metal detector
Both are correct, but they mean different things. The first device
detects heavy metals. The second device detects metal, and the device
It's hard to see how the words in your sentence would be misunderstood in this way. If they are simple adjectives you can just separate them with commas:
Simplified node-to-rigid, flat surface contact element was implemented
Does this make sense, in context? But it's a fairly horrible sentence, brief to the point of incomprehensibility.
Based on OP's comment and link below, it seems clear that the important compound elements are:
I think these elements should not be separated by other adjectives. Personally I would write:
Simplified node-to-surface (rigid flat) contact element was
implemented in Matlab
You could then insert any other criteria from the table in the same way, eg node-to-surface (thermal) contact element.