Problem with SmoothDamp when applied to each child of a gameObject

Hello, I'm new to unity and, with friends, we want to make a Slither.io like game. We made a Player Controller for our snake and we have a problem with the last 2/3 spheres composing our snake wihch don't follow the trajectory of the rest of the body, whereas the rest of the body works fine. Our snake is made like follows : an empty GameObject composed of a head (ball in the code below) and the body parts.

 public class PlayerControler : MonoBehaviour {
     private Rigidbody rb;
     public float speed;
     Transform ball;
     private Vector3 movementVelocity;
     
     void FixedUpdate () {
         
         ball = transform.GetChild(0).transform;
         if(Input.GetKey(KeyCode.Mouse0)){
             speed = 20;
         } else {
             speed = 10;
         }
         
         if(Input.GetKey(KeyCode.Q)) {
             ball.transform.Rotate(0, Time.deltaTime * (-180), 0);
         }
         if(Input.GetKey(KeyCode.D)) {
             ball.transform.Rotate(0, Time.deltaTime * 180, 0);
         }
         
         Move();
     }
     
     void Move(){
         for (int i = transform.childCount-1; i>=0; i--){
             Transform t=transform.GetChild(i);
             
             if (i == 0){
                 t.position += ball.transform.forward * speed * Time.fixedDeltaTime;
             } else {
                 t.position = Vector3.SmoothDamp(t.position, transform.GetChild(i-1).transform.position, ref movementVelocity, 1.9f*Time.fixedDeltaTime, Mathf.Infinity, Time.fixedDeltaTime);
             }
         }
     }
 }

We think it's related to the SmoothDamp but we can't figure out why. Thanks for your help.