  Designing anisotropic structured materials by reducing symmetry results in
unique behaviors, such as shearing under uniaxial compression or tension. This
direction-dependent coupled mechanical phenomenon is crucial for applications
such as energy redirection. While rank-deficient materials such as hierarchical
laminates have been shown to exhibit extreme elastic anisotropy, there is
limited knowledge about the fully anisotropic elasticity tensors achievable
with single-scale fabrication techniques. No established upper and lower bounds
on anisotropic moduli achieving extreme elastic anisotropy exist, similar to
Hashin-Shtrikman bounds in isotropic composites. In this paper, we estimate the
range of anisotropic stiffness tensors achieved by single-scale two-dimensional
structured materials. To achieve this, we first develop a database of periodic
anisotropic single-scale unit cell geometries using linear combinations of
periodic cosine functions. The database covers a wide range of anisotropic
elasticity tensors, which are then compared with the elasticity tensors of
hierarchical laminates. Through this comparison, we identify the regions in the
property space where hierarchical design is necessary to achieve extremal
properties. We demonstrate a method to construct various 2D functionally graded
structures using this cosine function representation for the unit cells. These
graded structures seamlessly interpolate between unit cells with distinct
patterns, allowing for independent control of several functional gradients,
such as porosity, anisotropic moduli, and symmetry. The graded structures
exhibit unique mechanical behaviors when designed with unit cells positioned at
extreme parts of the property space. Specific graded designs are numerically
studied to observe behaviors such as selective strain energy localization,
compressive strains under tension, and localized rotations.
