UBC Theses and Dissertations
Effective mechanical properties of lattice materials Chopra, Prateek
Lattice materials possess a spatially repeating porous microstructure or unit cell. Their usefulness lies in their multi-functionality in terms of providing high specific stiffness, thermal conductivity, energy absorption and vibration control by attenuating forcing frequencies falling within the band gap region. Analytical expressions have been proposed in the past to predict cell geometry dependent effective material properties by considering a lattice as a network of beams in the high porosity limit. Applying these analytical techniques to complex cell geometries is cumbersome. This precludes the use of analytical methods in conducting a comparative study involving complex lattice topologies. A numerical method based on the method of long wavelengths and Bloch theory is developed here and applied to a chosen set of lattice geometries in order to compare effective material properties of infinite lattices. The proposed method requires implementation of Floquet-bloch transformation in conjunction with a Finite Element (FE) scheme. Elastic boundary layers emerge from surfaces and interfaces in a finite lattice, or an infinite lattice with defects such as cracks. Boundary layers can degrade effective material properties. A semi-analytical formulation is developed and applied to a chosen set of topologies and the topologies with deep boundary layers are identified. The methods developed in this dissertation facilitate rapid design calculation and selection of appropriate core topologies in multifunctional design of sandwich structures employing a lattice core.
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