Edwin Arroyave -- Teddi's husband of more than a decade -- shared a post-workout selfie outside hot yoga this morning with a message to supporters who aren't always inspired or motivated to train.

Arroyave says this is where habits and ritual come into play ... saying they help people stay motivated in the workout journeys.

EA says good habits will help people through the "dark days" ... and, pressure reveals the true character of a person. He doesn't specifically mention Teddi or the looming divorce -- but, the timing of the post is raising some eyebrows.

Mellencamp announced she was filing in an emotional Instagram post Saturday ... saying her main priority is her children, and she announced the news because she wants to avoid unfounded rumors about their split. She did not provide a reason for the divorce.

The two first met in 2008 and married in 2011 ... though Teddi later admitted they nearly divorced in 2017 during their first season on "The Real Housewives of Beverly Hills."

BTW ... looks like Edwin's got the kids this weekend -- sharing a pic with some of his four children on their way to church. Edwin and Teddi share three kids -- son Cruz and daughters Slate and Dove. He also has a daughter Isabella from a previous relationship.