FEM modeling of fiber reinforced composites

Abstract

Recently several studies have been performed at the TUDelft on the use of the generalized finite element method (GFEM) to model fiber reinforced composite materials in a two dimensional space. The GFEM model allows a large number of arbitrarily placed fibers to be taken into account. The fibers are placed on top of the ordinary mesh and therefore do not require aligned meshing to be done. Matrix material, fiber material and the interface between them each have their own material parameters. The discontinuous displacement field on the fiber, also known as the "fiber slip" is taken into account by the use of extra degrees of freedom. These extra degrees of freedom are placed on the original nodes of the elements crossed by fibers. Fibers are in essence one dimensional objects. The main degree of freedom they should have is the slip in direction of the fiber. It is therefore computationally expensive to use extra degrees of freedom on top of regular element nodes to describe the displacement field of the fiber. Why not inserting the extra degrees of freedom in direction of the fiber on top of the fiber itself? In this thesis a search is done to an efficient element with extra degrees of freedom on the fiber. A first unsuccessful try is the use of a so called "Interface-enriched GFEM" element (IGFEM). The second successful approach is the slightly different "embedded reinforcement approach including bond slip" (ERS). This is an element that has been used before in calculating reinforced concrete in several publications. This element is used here for calculating elastic material reinforced with many fibers. In its mathematical derivations, a small extension is made to allow for an arbitrary enrichment function to be inserted on the fiber displacement field analogous to the GFEM derivations. This enrichment function inserts a priori knowledg into the solution allowing it to converge faster. However, enrichments in this research are kept simple. Next to a two dimensional implementation of the GFEM and ERS approach, a three dimensional implementation is presented. Encountered problems and numerical examples for both models are discussed. Both approaches produce very similar numerical results. The ERS approach is more efficient as the current GFEM approach.