Large-deformation mechanics of anti-curvature lattice materials for mode-dependent enhancement of non-linear shear modulus

Abstract

Shear modulus assumes an important role in characterizing the applicability of different materials in various multi-functional systems and devices, such as deformation under shear and torsional modes and vibrational behavior involving torsion, wrinkling, and rippling effects. 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. In general, the lattice materials can be conceptualized as a network of beams with different periodic architectures, wherein the common practice is to adopt initially straight beams. While shear modulus and multiple other 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. In this article, we propose a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing shear modulus in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating effective shear modulus of honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. We propose to consider the complementary deformed shapes of cell walls of honeycomb lattices under anti-clockwise or clockwise modes of shear stress as the initial beam-level elementary configuration. A substantially increased resistance against deformation can be realized when such a lattice is subjected to the opposite mode of shear stress, leading to increased effective shear modulus. Within the framework of a unit cell based approach, initially curved lattice cell walls are modeled as programmed curved beams under large deformation. The combined effect of bending, stretching, and shear deformation is considered in the framework of Reddy’s third order shear deformation theory in a body embedded curvilinear frame. Governing equation of the elementary beam problem is derived using variational energy principle based Ritz method. In addition to application-specific design and enhancement of shear modulus, unlike conventional materials, we demonstrate through numerical results that it is possible to achieve non-invariant shear modulus under anti-clockwise and clockwise modes of shear stress. The developed physically insightful semi-analytical model captures nonlinearity in shear modulus as a function of the degree of anti-curvature and applied shear stress along with conventional parameters related to unit cell geometry and intrinsic material property. The concept of anti-curvature in lattices would introduce novel exploitable dimensions in mode-dependent effective shear modulus modulation, leading to an expanded design space including more generic scopes of nonlinear large deformation analysis.