An introduction to computational nanomechanics and materials

W. K. Liu, E. G. Karpov, S. Zhang, H. S. Park

Research output: Contribution to journalArticlepeer-review

396 Scopus citations


Many arenas of research are rapidly advancing due to a combined effort between engineering and science. In some cases, fields of research that were stagnating under the exclusive domain of one discipline have been imbued with new discoveries through collaboration with practitioners from the second discipline. In computational mechanics, we are particularly concerned about the technological engineering interest by combining engineering technology and basic sciences through modeling and simulations. These goals have become particularly relevant due to the emergence of the field of nanotechnology, and the related burst of interest in nanoscale research. In this introductory article, we first briefly review the essential tools used by nanoscale researchers. These simulation methods include the broad areas of quantum mechanics, molecular dynamics and multiple-scale approaches, based on coupling the atomistic and continuum models. Upon completing this review, we shall conclusively demonstrate that the atomistic simulation tools themselves are not sufficient for many of the interesting and fundamental problems that arise in computational mechanics, and that these deficiencies lead to the thrust of multiple-scale methods. We summarize the strengths and limitations of currently available multiple-scale techniques, where the emphasis is made on the latest perspective approaches, such as the bridging scale method, multi-scale boundary conditions, and multi-scale fluidics. Example problems, in which multiple-scale simulation methods yield equivalent results to full atomistic simulations at fractions of the computational cost, are shown. We conclude by discussing future research directions and needs in multiple-scale analysis, and also discuss the ramifications of the integration of current nanoscale research into education.

Original languageEnglish (US)
Pages (from-to)1529-1578
Number of pages50
JournalComputer Methods in Applied Mechanics and Engineering
Issue number17-20
StatePublished - May 7 2004

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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