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Organizing Cells Within Non-Periodic Microarchitectured Materials That Achieve Graded Thermal Expansions

[+] Author Affiliations
Jonathan B. Hopkins, Lucas A. Shaw

University of California, Los Angeles, Los Angeles, CA

Todd H. Weisgraber, George R. Farquar, Christopher D. Harvey, Christopher M. Spadaccini

Lawrence Livermore National Laboratory, Livermore, CA

Paper No. DETC2015-46638, pp. V02BT03A005; 11 pages
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2B: 41st Design Automation Conference
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5708-3
  • Copyright © 2015 by ASME


The aim of this paper is to introduce an approach for optimally organizing a variety of different unit cell designs within a large lattice such that the bulk behavior of the lattice exhibits a desired Young’s modulus with a graded change in thermal expansion over its geometry. This lattice, called a graded microarchitectured material, can be sandwiched between two other materials with different thermal expansion coefficients to accommodate their different expansions or contractions caused by changing temperature while achieving a desired uniform stiffness. First, this paper provides the theory necessary to calculate the thermal expansion and Young’s modulus of large multi-material lattices that consist of periodic (i.e., repeating) unit cells of the same design. Then it introduces the theory for calculating the graded thermal expansions of a large multimaterial lattice that consists of non-periodic unit cells of different designs. An approach is then provided for optimally designing and organizing different unit cells within a lattice such that both of its ends achieve the same thermal expansion as the two materials between which the lattice is sandwiched. A MATLAB tool is used to generate images of the undeformed and deformed lattices to verify their behavior and various examples are provided as case studies. The theory provided is also verified and validated using finite element analysis and experimentation.

Copyright © 2015 by ASME



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