Optimizing multifunctional materials: Design of microstructures for maximized stiffness and fluid permeability

James K. Guest, Jean H. Prévost

Research output: Contribution to journalArticlepeer-review

270 Scopus citations


Topology optimization is used to systematically design periodic materials that are optimized for multiple properties and prescribed symmetries. In particular, mechanical stiffness and fluid transport are considered. The base cell of the periodic material serves as the design domain and the goal is to determine the optimal distribution of material phases within this domain. Effective properties of the material are computed from finite element analyses of the base cell using numerical homogenization techniques. The elasticity and fluid flow inverse homogenization design problems are formulated and existing techniques for overcoming associated numerical instabilities and difficulties are discussed. These modules are then combined and solved to maximize bulk modulus and permeability in periodic materials with cubic elastic and isotropic flow symmetries. The multiphysics problem is formulated such that the final design is dependent on the relative importance, or weights, assigned by the designer to the competing stiffness and flow terms in the objective function. This allows the designer to tailor the microstructure according to the materials' future application, a feature clearly demonstrated by the presented results. The methodology can be extended to incorporate other material properties of interest as well as the design of composite materials.

Original languageEnglish (US)
Pages (from-to)7028-7047
Number of pages20
JournalInternational Journal of Solids and Structures
Issue number22-23
StatePublished - Nov 2006

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


  • Finite element method
  • Inverse homogenization
  • Length scale
  • Multiphysics
  • Topology optimization


Dive into the research topics of 'Optimizing multifunctional materials: Design of microstructures for maximized stiffness and fluid permeability'. Together they form a unique fingerprint.

Cite this