We present an extension of a discrete, geometrically exact beam formulation originally introduced in the computer graphics community, as well as an implementation that fits naturally in existing finite element programs. This numerical method is variational, fully 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 is well suited to engineering applications, and can e ciently and accurately simulate the nonlinear deformation of slender beams featuring complex material behavior, such as those found in the topical design of truss metamaterials.