In Borderlands 2 Non Elemental Weapons are the most common Weapons. The Common Rarity will always be non elemental, except Maliwan and Torgue Weapons.
Non Elemental Damage deals full damage to Flesh and Shielded enemies, only Armored targets take 20% less damage. Melee Attacks also count as Non-Elemental.
Manufacturer Jakobs primarily produces Non Elemental Weapons with a few exceptions: Stinkpot, Greed, Twister, Cobra, Hot Mama
Rocket Launchers and Grenade Mods, that do not have an element, deal Explosive damage.
Non Elemental Weapons have 10-20% more base damage than elemental Weapons.
Non-Elemental Damage is now called Physical Damage. Includes all non-elemental Explosive Damage and melee damage.
Non Elemental Damage deals full damage to Flesh and Shielded enemies, only Armored targets take 20% less damage.