Digitangular numbers
Husk, 6 bytes

U¡(ṁΣd


Try it online!

Explanation

U¡(ṁΣd
 ¡(       Iterate the following function on the input:
     d       Split the number into digits
   ṁΣ        Map each digit to its triangular number, then sum the results
U         Take the results of iteration until before the first repeated one