On enhancing mode-dependent failure strength under large deformation: The concept of anti-curvature in honeycomb lattices

Over the last decade, lattice-based artificial materials have demonstrated the possibility of tailoring multifunctional capabilities that are not achievable in traditional materials. 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 enhancing global specific stiffness and failure strength 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 and failure strength 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 elastic failure strength in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating the onset of failure in honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. The physically insightful semi-analytical model captures nonlinearity in elastic failure strength of anti-curvature lattices as a function of the degree of curvature and applied stress together with conventional microstructural and intrinsic material properties.