くなる(かたくなる) A kind of scientific word:coal hardens into diamonds. Water turns into ice.  Hardening of the arteries. Also used with food:whip the egg whites until they’re firm.
める(かためる) Unlike 硬くなる、固める is intentional:you purposely congeal something. (clay, paint, ) OTHER MEANING:to harden or fortify one’s defenses (or strengthen the unity of factions within the party).   $$$TTT
する(こうちょくする) Rigid – but not like a boner. Usually used about people who tense up under fear or surprise, so tense they can’t move. Less commonly, it can mean a rigid class system resistant to change. Like rigor mortis. Other meaning:to sit bolt upright, soldiers rigidly standing at attention.
(こうか) This is pretty rare, and almost always used only in science. However, sometimes you will see the phrase 態度が硬化, meaning someone’s attitude becomes more strict or hard-assed, or the cops do a crackdown.