We present an extension of a discrete, geometrically exact beam formulation based on discrete framed curves and discrete parallel transport originally introduced in the computer graphics community. In combination with variational constitutive updates, our numerical scheme decouples the kinematics from the material behavior, and can handle finite rotations as well as a wide class of constitutive laws depending on the stretching, flexural and torsional strain and strain rates. We demonstrate its capabilities through a suite of benchmark problems involving elastic, viscous and visco-elastic beams. The method fits naturally in existing finite element frameworks and is well suited to engineering applications. It can efficiently and accurately simulate the nonlinear deformation of slender beams featuring complex material behavior, such as those found in the topical design of flexible structural metamaterials.