Effective elastic properties of 3D lattice materials with intrinsic stresses: bottom-up spectral characterization and constitutive programming

Abstract

Analytical investigations to characterize the effective mechanical properties of lattice materials allow an in-depth exploration of the parameter space efficiently following an insightful, yet elegant framework. 2D lattice materials, which have been extensively dealt with in the literature following analytical as well as numerical and experimental approaches, have limitations concerning multi-directional stiffness and Poisson's ratio tunability. The primary objective of this paper is to develop mechanics-based formulations for a more complex analysis of 3D lattices, leading to a physically insightful analytical approach capable of accounting the beam-level mechanics of pre-existing intrinsic stresses along with their interaction with 3D unit cell architecture. We have investigated the in-plane and out-of-plane effective elastic properties to portray the physics behind the deformation of 3D lattices under externally applied far-field normal and shear stresses. The considered effect of beam-level intrinsic stresses therein can be regarded as a consequence of inevitable temperature variation, pre-stress during fabrication, inelastic and non-uniform deformation, manufacturing irregularities etc. Such effects can notably impact the effective elastic properties of lattice materials, quantifying which for 3D honeycombs is the central focus of this work. Further, from the material innovation viewpoint, the intrinsic stresses can be deliberately introduced to expand the microstructural design space for effective elastic property modulation of 3D lattices. This will lead to programming of effective properties as a function of intrinsic stresses without altering the microstructural geometry and lattice density. We have proposed a generic spectral framework of analyzing 3D lattices analytically, wherein the beam-level stiffness matrix including the effect of bending, axial, shear and twisting deformations along with intrinsic stresses can be coupled with the unit cell mechanics for obtaining the effective elastic properties.

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ORCID for S. Naskar: orcid.org/0000-0003-3294-8333

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