I don't think it's a popular concept. Naruto has a well - established image in the anime and manga world. The idea of him being a 'barbarian' in fanfiction is quite a deviation from the norm. Fans usually enjoy fanfictions that expand on the original story's themes and characters in a more in - line way, rather than completely changing Naruto into a 'barbarian' which might seem too extreme for many.
Well, it could imply that the fanfiction portrays Naruto in a very rough or uncivilized way. Maybe in this fanfic, Naruto's character is given traits that are more savage or brute - like compared to his original character in the official Naruto series.
The concept of 'barbarian' can be incorporated by changing Naruto's setting. Instead of the normal ninja villages, he could be in a more primitive land. For instance, he might be in a place where there are no advanced ninja tools, so he has to rely on his raw skills and strength like a barbarian would.
One good 'barbarian Naruto fanfiction' could be one where Naruto is thrust into a barbarian - like land and has to adapt his ninja skills. For example, he might use his shadow clone jutsu in creative ways to hunt for food or defend against the wild beasts in this new and savage environment.
In a Naruto barbarian fanfiction, perhaps Naruto discovers a hidden tribe of barbarians who have a special connection to chakra. He tries to understand their way of using chakra which is very different from what he knows. This could lead to him having to adapt and find new ways to use his own chakra, all while building relationships with the barbarians.
You can try fanfiction websites like FanFiction.net or Archive of Our Own. They have a wide range of fanfictions, and you can search specifically for 'Naruto barbarian' to find relevant stories.
Often, a common element is the portrayal of Edward's physical strength. Since he's a barbarian, he's usually depicted as being very strong. Another element could be his primitive lifestyle, like living in a tribal setting, wearing animal skins, etc.
Strength is a common theme. Female barbarians are often depicted as physically strong and capable fighters. For example, in many stories, they can take on male opponents with ease.
The Legend of a Barbarian was a novel about a mountain child who yearned for a better life. This child was forced to embark on the path of cultivation and becoming an immortal. Even though he was ridiculed by others for being like a raging bull that only knew how to rampage, he used his brute force to shatter everyone's prejudice and constructed a legend that only belonged to barbarians. The latest chapter of the novel was chapter 286, and the story took place at the place where the Soul Society encountered a Dao intercept.
The barbarian may develop through combat experiences. Each battle he or she faces could teach new combat techniques or ways to better use their existing strength.