Hierarchy of beam models for lattice core sandwich structures

• Published in: International journal of solids and structures Vol. 204-205; pp. 172 - 186
• Main Authors: Karttunen, Anssi T., Reddy, J.N.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01-11-2020; Elsevier BV
• Subjects: Beams (structural); Bending; Boundary conditions; Constitutive modeling; Couple-stress; Formability; Lattice material; Lattices; Macrostructure; Micropolar; Sandwich beam; Sandwich structures; Shear deformation; Stiffness; Stretching; Timoshenko beams; Two dimensional models; Unit cell; Sandwich beam; Micropolar; Lattice material; Couple-stress; Constitutive modeling
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2020.08.020

•2-D discrete lattices are modeled as classical and non-classical 1-D continuum beams.•Link is derived between the macrorotation and the micropolar antisymmetric shear.•Micropolar beam is reduced to a couple-stress and two classical lattice beam models.•Classical Timoshenko beam is an apt first choice for stretching-dominated cores.•The micropolar Timoshenko beam model works also for bending-dominated cores.
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.