md-datepicker input format

The complete solution base it's:

$mdDateLocaleProvider.formatDate = function(date) {
 return date ? moment(date).format('DD-MM-YYYY') : '';
};

$mdDateLocaleProvider.parseDate = function(dateString) {
 var m = moment(dateString, 'DD-MM-YYYY', true);
 return m.isValid() ? m.toDate() : new Date(NaN);
};

Format date event is not enough. You should also configure parse date event.

$mdDateLocaleProvider.parseDate = function(dateString) {
  var m = moment(dateString, 'DD-MM-YYYY', true);
  return m.isValid() ? m.toDate() : new Date(NaN);
};

See updated pen: http://codepen.io/anon/pen/GpBpwZ?editors=101