Laravel attach() method not working to hasMany side

See the Laravel documentation here: http://laravel.com/docs/eloquent#inserting-related-models

Basically you have set up two different types of relationships for the same two tables - you've set up a many-to-many and a one-to-many. It looks as though you probably wanted a many-to-many, so you'll need to change this line:

return $this->hasMany('Atividade');

To this:

return $this->belongsToMany('Atividade');

This will set the relationship up as a many-to-many relationship, which will then support the attach() method.

The attach() method is only for many-to-many, for other relationships there's save() or saveMany() and associate() (see the docs linked above).

See the documentation Laravel 5.7

A Comment belongTo an unique Post

class Comment extends Model
{
    /**
     * Get the post that owns the comment.
     */
    public function post()
    {
        return $this->belongsTo('App\Post');
    }
}

A Post can Have multiple Comments

class Post extends Model
{
    /**
     * Get the comments for the blog post.
     */
    public function comments()
    {
        return $this->hasMany('App\Comment');
    }

When you want to update/delete a belongsTo relationship, you may use the associate/dissociate method.

$post= App\Post::find(10);
$comment= App\Comment::find(3);
$comment->post()->associate($post); //update the model

$comment->save(); //you have to call save() method

//delete operation
$comment->post()->dissociate(); 

$comment->save(); //save() method

attach() is for many-to-many relationships. It seems your relationship is supposed to be a many-to-many but you have not set it up correctly for that.

class Intervencao extends Eloquent {
    public function atividades() {
        return $this->belongsToMany('Atividade');
    }
}

Then the attach() should work