The overall behavior of carbon fiber reinforced concrete (CFRC) heavily depends on the morphology and physico-chemical interphase properties between the fiber and the matrix. To improve the toughness of the overall composite, ideas are adapted from nature, such as the structure of the nacre or the glass sponge. Built up from hard brittle inorganic and soft organic components, nacre and glass sponge form structures that give them a specific fracture toughness. Similar structures are applied in the interphase between fiber and matrix with the aim to transfer their beneficial mechanical properties to the CFRC. The failure behavior of single-fiber composites as a function of different interphase properties is investigated using the single-fiber-pull-out (SFPO) test. Capturing the fiber-matrix interaction properly within the Finite Element Method is an important part of modeling CFRC accurately. In this contribution, the simulation of the SFPO is realized using the membrane mode enhanced cohesive zone elements (MMECZE) formulation. These cohesive zone elements take into account membrane damage coupled with the classical traction-separation laws used in standard cohesive zone elements and therefore allow for an improved representation of the fiber-matrix interface behavior.