Analysis of the elastostatic specific stiffness of 2D stretching-dominated lattice materials

作者：Elsayed Mostafa S A; Pasini Damiano^*

来源：Mechanics of Materials, 2010, 42(7): 709-725.

DOI：10.1016/j.mechmat.2010.05.003

• Lattice material
• Micro-truss
• Bloch's theorem
• Dummy Node Scheme
• Stretching-dominated lattice material

This paper presents a matrix-based procedure to characterize the specific stiffness properties of 20 lattice materials with any arbitrary cell topology. Unlike previous works, the current study automates the analysis process to include lattice materials whose unit cell has elements extending between adjacent cells and thus intersecting their envelopes. The main challenge in the analysis of this periodic lattice structures is that the unit cell does not have the full information concerning its nodal kinematic and static periodicity. For this reason, we introduce the Dummy Node Scheme, which enables the analysis of lattice material with any cell topology.
The lattice material is modelled here as a pin-jointed infinite micro-truss structure. The results of the determinacy analysis are used to distinguish between the bending-dominated and the stretching-dominated behaviours of the material. The Cauchy Born hypothesis is used to homogenize the lattice material properties by formulating the microscopic lattice nodal deformations in terms of the material macroscopic strain field. This formulation, in turn, is used to express the microscopic element deformations in terms of the macroscopic strain field, from which the material macroscopic stiffness properties are derived. In this process, the Dummy Node Scheme is a necessary step to construct the nodal periodicity within the unit cell, which is used to apply the Cauchy Born kinematic boundary condition to the nodal deformation wave functions. The procedure introduced in this paper is applied to 10 lattice topologies, five of which have unit cells with a square Bravais lattice symmetry and the other five have unit cells with a hexagonal Bravais lattice symmetry. Finally, charts representing the relative elastic moduli of the lattice material versus its relative density are developed. These charts assist the selection of the best topology of a stretching-dominated lattice material for a given application that requires a material with specific stiffness properties.

• 出版日期2010-7