Basic PHP contact form issue

Im trying to setup a basic PHP contact form and despite my best efforts I can't seem to make it work:

on contact.php my code looks like this:

include_once('form_record.php');
$obj = new formRECORD(); 
if ( $_POST )
     $obj->send_mail($_POST);
echo $obj->display_form();

And then form_record.php looks like this:

class formRECORD {

    public function display_form() {
    $entry_display .= <<<ENTRY_DISPLAY
               <form >
               <label>Name</label><br/>
               <input id="form_name"><br/>
               <label>Email</label><br/>
               <input id="form_email"><br/>
               <label>Phone:</label><br/>
               <input id="form_phone"><br/>
               <label>Name</label><br/>
               <textarea id="body"></textarea><br/>
               <input type="submit" value="Send" />
               </form>
ENTRY_DISPLAY;

  return $entry_display;

}
    public function send_mail($p) {
        $to = "example@gmail.com"; 
        $subject = "Contact Us"; 
        $email = $_POST['form_email'] ; 
        $message = $_POS开发者_如何学GoT['body'] ; 
        $headers = "From: $email"; $sent = mail($to, $subject, $message, $headers) ; 
        if($sent) {return "Your mail was sent successfully"; } else {return "We encountered an error sending your mail"; }
    }

}

The contact form shows up OK and there aren't any php errors when the user hits submit. However the email never appears in my inbox. Any ideas?

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You have to set the name-attributes of the form-fields, otherwise the fields cannot be submitted. The IDs have no meaning for PHP.