Non-invariant elastic moduli of bi-level architected lattice materials through programmed domain discontinuity

Abstract

Effective elastic moduli of lattice-based materials are one of the most crucial parameters for the adoption of such artificial microstructures in advanced mechanical and structural systems as per various application-specific demands. In conventional naturally occurring materials, these elastic moduli remain invariant under tensile and compressive normal modes or clock-wise and anti-clock-wise shear modes. Here we introduce programmed domain discontinuities in the cell walls of the unit-cells of lattice metamaterials involving a bi-level microstructural design to achieve non-invariant elastic moduli under tensile and compressive normal modes or clock-wise and anti-clock-wise shear modes. More interestingly, such non-invariance can be realized in the linear small deformation regime and the elastic moduli can be tailored to have higher or lower value in any mode compared to the other depending on the placement and intensity of the discontinuities in a programmable paradigm. We have derived an efficient analytical framework for the effective elastic moduli of lattice materials taking into account the influence of domain discontinuity. The axial and shear deformations at the beam level are considered along with bending deformation in the proposed analytical expressions. The numerical results ascertain that the domain discontinuities, in conjunction with unit cell level geometric parameters, can impact the effective elastic constants significantly under different modes of far-field stresses. It is further revealed that the degree of auxeticity of such lattices can be programmed to have target values (including non-invariance under different modes of deformation) as a function of the intensity and location of domain discontinuity when axial and shear deformations are included at the beam level. Realization of the unusual non-invariant elastic moduli of bi-level architected lattice materials would lead to a range of technologically demanding niche applications where one mode of deformation requires more or less force to deform compared to the opposite mode. Besides being able to perform as a load-bearing component, the proposed metamaterial can be used as an integrated sensor for measuring the level of stress or strain in structures.

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