If a conventional material is compressed in one direction, it tries to expand in the other two perpendicular directions and vice versa, indicating a positive Poisson's ratio. Recently auxetic materials with negative Poisson's ratios, which can be realized through artificial microstructuring, are attracting increasing attention due to enhanced mechanical performances in multiple applications. Most of the proposed auxetic materials show different degrees of in‐plane auxeticity depending on their microstructural configurations. However, this restricts harnessing the advantages of auxeticity in 3D systems and devices where multidirectional functionalities are warranted. Thus, there exists a strong rationale to develop microstructures that can exhibit auxeticity both in the in‐plane and out‐of‐plane directions. Herein, generic 3D connected double loop (3DCDL) type periodic microstructures are proposed for multi‐directional modulation of Poisson's ratios. Based on the bending dominated behavior of elementary beams with variable curvature, mixed‐mode auxeticity following the framework of multimaterial unit cells is demonstrated. The proposed 3DCDL unit cell and expanded unit cells formed based on their clusters are capable of achieving partially auxetic, purely auxetic, purely nonauxetic and nullauxetic behavior. Comprehensive numerical results are presented for the entire spectrum of combinations concerning the auxetic behavior in the in‐plane and out‐of‐plane directions including their relative degrees.

Architected lattice materials, realized through artificial micro‐structuring, have drawn tremendous attention lately due to their enhanced mechanical performances in multifunctional applications. However, the research area on the design of artificial microstructures for the modulation of mechanical properties is increasingly becoming saturated due to extensive investigations considering different possibilities of lattice geometry and beam‐like network design. Thus, there exists a strong rationale for innovative design at a more elementary level. It can enhance and grow the microstructural space laterally for exploiting the potential of geometries and patterns in multiple length scales, and the mutual interactions thereof. A bi‐level design is proposed, where besides having the architected cellular networks at an upper scale, the constituting beam‐like members at a lower scale are further topology‐engineered for most optimum material utilization. The coupled interaction of beam‐level and lattice‐level architectures can enhance the specific elastic properties to an extreme extent (up to ≈25 and 20 times, depending on normal and shear modes, respectively), leading to ultra‐lightweight multifunctional materials for critical applications under static and dynamic environments.