Fiber reinforced materials (FRMs) constitute a typical example of inhomogeneous materials. Their study needs suitable mathematical models since their properties are strongly dependent on their internal geometry.

In this talk, I shall briefly touch on the classical methods used to study FRMs. After pointing out in which conditions these methods fall short, I shall propose a possible solution. Using a distributed Lagrange multiplier approach, I will prove how to reduce the domain’s complexity while utilizing independent meshes for the fibers and the material’s domain. After analyzing the 3d-3d coupled model, I shall propose a reduced order model, where some additional hypotheses allow to describe the fibers with their one-dimensional center-line. After showing well posedness, existence, and uniqueness for both the continuous and the discrete models, I shall conclude with some numerical results.