Hierarchy of beam models for lattice core sandwich structures Anssi T. Karttunen a,* , J.N. Reddy b a Aalto University, Department of Mechanical Engineering, Espoo, Finland b Texas A&M University, Department of Mechanical Engineering, College Station, Texas, USA Abstract A discrete-to-continuum transformation to model 2-D discrete lattices as energetically equivalent 1-D continuum beams is developed. The study is initiated in a classical setting but results in a non- classical two-scale micropolar beam model via a novel link within a unit cell between the second- order macrorotation-gradient and the micropolar antisymmetric shear deformation. The shear deformable micropolar beam is reduced to a couple-stress and two classical lattice beam models by successive approximations. The stiffness parameters for all models are given by the micropolar constitutive matrix. The four models are compared by studying stretching- and bending-dominated lattice core sandwich beams under various loads and boundary conditions. A classical 4th-order Timoshenko beam is an apt first choice for stretching-dominated beams, whereas the 6th-order micropolar model works for bending-dominated beams as well. The 6th-order couple-stress beam is often too stiff near point loads and boundaries. It is shown that the 1-D micropolar model leads to the exact 2-D lattice response in the absence of boundary effects even when the length of the 1-D beam (macrostructure) equals that of the 2-D unit cell (microstructure), that is, when L = l. Keywords: lattice material, constitutive modeling, sandwich beam, micropolar, couple-stress 1. Introduction Lattice materials are a class of lightweight structures that integrate concepts from materials science and structural mechanics. The dual nature of a lattice material is determined by a base material and a lattice structure driven by architected design (Greer and Deshpande, 2019). Increasing interest in creating intricate lattice materials has triggered fresh thinking and new developments in the domain of manufacturing. Traditional manufacturing processes such as weld- ing, investment casting or perforated metal sheet forming can be used to produce lattices visible to the naked eye (Wadley, 2006). As a specific example, laser welding has been used to manufacture all-steel sandwich panels with lattice cores for large structures such as ship and bridge decks (Teas- dale, 1988; Roland and Metschkow, 1997; Romanoff et al., 2007; Bright and Smith, 2007; Nilsson et al., 2017, 2020). The production of man-made small-scale lattice materials from a variety of base materials at reasonable cost has been enabled in recent years by advances in additive manufacturing processes (Schaedler and Carter, 2016; Valdevit et al., 2018; Mines, 2019). The different families of additive manufacturing are used to produce lattices in the areas of micro-electro-mechanical systems, metamaterials and biomechanics, to name a few (Phani and Hussein, 2017). Recompiled, unedited accepted manuscript. ©2020. Made available under CC-BY-NC-ND 4.0 * Corresponding author. anssi.karttunen@iki.fi. Cite as: Int. J. Solids Struct. 2020;121:103423 doi link 1 arXiv:2010.06271v3 [physics.app-ph] 18 Oct 2020
Hierarchy of beam models for lattice core sandwich structures
Jun 24, 2023
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