Nonlinear elasticity tailoring and failure mode manipulation of functionally graded honeycombs under large deformation

Abstract

Design of lattice metamaterials with tailored mechanical properties at a relatively higher (macro) length scale by architecting lower (micro) length scale geometric and material configurations leads to achieving unprecedented mechanical properties for fulfilling advanced multi-functional structural demands. In the design space of innovative microstructural configurations, we propose a novel class of lattice metamaterials with cell walls made of optimally designed functionally graded intrinsic materials. Under different modes of remotely applied mechanical stresses, two different intuitive architectures of functional gradations for the intrinsic cell wall materials are proposed. The large-deformation nonlinear lattices result in broadband modulation of effective stiffness, and an unprecedented manipulation capability of failure modes and corresponding strengths covering ductile and brittle types depending on architected material gradation. For estimating the nonlinear elasticity and microstructural stresses as a measure of failure mode for the proposed functionally graded lattices undergoing large deformation, a multi-scale mechanics-based semi-analytical framework is developed. Geometrically nonlinear functionally graded beams with generalized material gradation, integrated with unit cell architectures, are analyzed through iterative variational energy principle-based Ritz approach. Based on the developed physically insightful computational framework, effective nonlinear elastic properties and failure modes of the functionally graded honeycomb lattices are tailored as a function of the intrinsic material gradation at the lower length scale. The proposed novel class of lattices with optimally designed functionally graded intrinsic materials and coupled unit cell architectures would open up innovative avenues for designing advanced multi-functional engineering structures and mechanical systems.