How to make the effect in this image with illustrator? I want to make this effect where the shadow just appears half-way the rectangle and then bend and grow gradually till the end. It gives a realistic feel to the shape. Also, what is the conventional name of this effect?
The trick is not to use a shadow, but to create a separate shape (probably a duplicate of the shape that you want to have the shadow effect), colour it the colour that you want the shadow to be and then apply a blur to that shape. You can then use envelope > distort to bend it and twist it anyway that you want (or any other distortions that you can apply to shapes for that matter).
I don't think that this effect has an 'official' name, but I've heard it called 'peel off' and 'page curl' because of the effect that it gives.
Because you supplied such a small image, it is very difficult to see exactly what you were looking to achieve. I think this may be what you're looking for.
In illustrator go to menu item Effect/Stylize/Feather
And because it's only an effect.. It is nondestructive. You can re edit the amount of feather or toggle visibility or remove the effect at anytime
You could also achieve similar results and have a little more control with adding opacity masks