The physical heterogeneity and the geometrical periodicity of several bundle architectures found in biological materials play a key role in determining their superior mechanical performances. The underlying mechanism is based on the shear stress transfer between hard fibers and soft matrix. This process yields a size-dependent behavior characterized by specific lengths scales. Here, we elaborate a Floquet-based homogenization valid for arbitrary periodically heterogeneous fiber bundles with fibers subject to mutual interactions. This approach allows us to separately evaluate the energy distribution within the fibers and the matrix, and to define an efficiency function able to optimize the mechanical response of the bundle. We show the existence of a characteristic length scale that maximizes the transfer of the elastic energy from the fibers to the matrix, thus reducing the fibers solicitation and enhancing the overall mechanical response. This theory is able to describe the geometrical features of several biomaterials, such as nacre shell, muscle sarcomere, collagen fibril, and spider silk, in excellent agreement with experimental data. Moreover, it can be used to design bioinspired artificial structures with optimal response.