Smooth snake game turning animation - Bring me on the rigth track

Hello, I'm (trying) to develop a 2D Snake-Like game.

Unlike the original game the movement of my snake are smooth; For that reason I'm not usig the classic "move the last piece in front of the head" and instead I'm using transform.MoveTowards to move every piece to the position of the previous piece of the snake in a smooth way. This is the best idea so far, but of course I'm open to new ideas.

Now the problem that I have is this: I have NO idea on how to create the turning animation when the snake make a turn.

I'm not asking for a complete solution, I just need someone to put me on the rigth track. Thanks.