This work is devoted to the numerical modeling of contact problems in the context of multibody dynamics. Non-linearities including large deformation and frictional contact are modeled based on the finite element method. An improved approach by means of a semi-explicit calculation is applied to integrate the equation of motion. The frictional contact forces and the relative velocity establish an implicit relationship within the bi-potential framework. A hybrid methodology consisting of the Octree structure and the bounding volume hierarchy is proposed to reduce exhaustive contact inspections. Two numerical examples implemented in our in-house finite element software FER/Impact are given to illustrate the efficiency and accuracy of the resulting methods.