Eat away at
Definition 1 of 2
Pro Tip 1/3Gradual Impact
The phrase implies a slow process, not immediate damage. 
Years of pollution began to eat away at the coral reef.
Pro Tip 2/3Physical Damage
Commonly used to describe deterioration of tangible things. 
Acid rain can eat away at marble statues over time.
Pro Tip 3/3Not Literal
Sometimes used metaphorically for non-physical processes. 
Inflation is eating away at my savings.