We develop a model for predicting the mechanical behavior of a system of slender one-dimensional bodies (fibers or beams) interacting via frictional contact. Relying on an integral penalty-based formulation, it can robustly capture the behavior in the case of conforming contact occurring over regions of finite size. Two formulations of the model are presented and validated against fully resolved continuum finite element simulations. Overall, the proposed framework is an effective tool in exploring the mechanical behavior of fabrics, textiles as well as three-dimensional frictional architected solids, as demonstrated by the simulation of the effective response of a periodic intertwined metamaterial.