Anti-curvature honeycomb lattices for mode-dependent enhancement of nonlinear elastic properties under large deformation

Abstract

Lattice-based artificial microstructures have been receiving significant attention from the scientific community over the past decade due to the possibility of developing materials with tailored multifunctional capabilities that are not achievable in naturally occurring materials. Such lattice materials can be conceptualized as a network of beams with different periodic architectures, wherein the common practice is to adopt straight beams. While a large set of mechanical properties can be simultaneously modulated by adopting an appropriate network architecture in the conventional periodic lattices, the prospect of on-demand global specific stiffness and flexibility modulation has become rather saturated lately due to intense investigation in this field. Thus there exists a strong rationale for innovative design at a more elementary level in order to break the conventional bounds of specific stiffness that can be obtained only by lattice-level geometries. Here we propose a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing the effective elastic moduli in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating effective elastic moduli of honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. We propose to consider the deformed shapes corresponding to compressive or tensile modes of the honeycomb cell walls as the initial beam-level configuration. A substantially increased resistance against deformation can be realized when such a lattice is subjected to the opposite mode, leading to increased effective elastic moduli. Moreover, unlike conventional materials, we demonstrate that it is possible to achieve non-invariant elastic moduli under tension and compression. Within the framework of a unit cell based approach, the cell walls with initial curvature are modeled as curved beams including nonlinear bending and axial deformation, wherein the governing equation is derived using variational energy principle through the Ritz method. The developed physically insightful semi-analytical model captures nonlinearity in elastic moduli as a function of the degree of anti-curvature and applied stress along with conventional parameters related to unit cell geometry and intrinsic material property. The concept of anti-curvature in lattice materials proposed in the present article introduces novel exploitable dimensions in mode-dependent effective elastic property modulation, leading to an expanded design space including more generic scopes of nonlinear large deformation analysis.