(also engrain) [with object] firmly fix or establish (a habit, belief, or attitude) in a person:they trivialize the struggle and further ingrain the long-standing attitudes
(of a textile) composed of fibres which have been dyed different colours before being woven.
late Middle English (originally as engrain in the sense 'dye with cochineal or in fast colours'): from en-1, in-2 (as an intensifier) + the verb grain. The adjective is from in grain 'fast-dyed', from the old use of grain meaning 'kermes, cochineal'
ingrain in other Oxford dictionaries
Definition of ingrain in the US English dictionary