In this article, the nonlinear constitutive behavior is considered in the geometrically nonlinear formulation for beams proposed by Simo and Vu-Quoc. The displacement based method is employed in solving the resulting nonlinear problem in the static case. Thermodynamically consistent three-dimensional constitutive laws are used in describing the material behavior, leading to a more precise estimation of the energy dissipated by the structures. The simple mixing rule is also applied in modeling materials which are composed by several simple components. An appropriated cross sectional analysis is implemented under the assumption and limitations of the planarity of the beam cross sections. Special attention is paid to the development of a method for defining the global damage state of a structure based on a scalar damage index capable of describing the residual strength and the load carrying capacity. Several numerical examples,including composite materials and strain localization, are presented and discussed.