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Advances in Mathematical Physics
Volume 2015, Article ID 828475, 11 pages
http://dx.doi.org/10.1155/2015/828475
Review Article

On Finsler Geometry and Applications in Mechanics: Review and New Perspectives

1Impact Physics, US ARL, Aberdeen, MD 21005-5066, USA
2A. James Clark School of Engineering (Adjunct Faculty), University of Maryland, College Park, MD 20742, USA

Received 21 November 2014; Accepted 18 January 2015

Academic Editor: Mahouton N. Hounkonnou

Copyright © 2015 J. D. Clayton. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [6 citations]

The following is the list of published articles that have cited the current article.

  • Elena S. Afanas’eva, “The boundary behavior of Q-homeomorphisms on the Finsler spaces,” Journal of Mathematical Sciences (United States), vol. 214, no. 2, pp. 161–171, 2016. View at Publisher · View at Google Scholar
  • J. D. Clayton, “Generalized Finsler geometric continuum physics with applications in fracture and phase transformations,” Zeitschrift für angewandte Mathematik und Physik, vol. 68, no. 1, 2016. View at Publisher · View at Google Scholar
  • J. D. Clayton, “Finsler-geometric continuum mechanics and the micromechanics of fracture in crystals,” Journal of Micromechanics and Molecular Physics, vol. 01, no. 03n04, pp. 1640003, 2016. View at Publisher · View at Google Scholar
  • J. D. Clayton, “Finsler-geometric continuum dynamics and shock compression,” International Journal of Fracture, 2017. View at Publisher · View at Google Scholar
  • J. D. Clayton, “Generalized pseudo-Finsler geometry applied to the nonlinear mechanics of torsion of crystalline solids,” International Journal of Geometric Methods in Modern Physics, pp. 1850113, 2018. View at Publisher · View at Google Scholar
  • John D. Clayton, and John D. Clayton, “Finsler-Geometric Modeling of Structural Changes in Solids,” Nonlinear Elastic and Inelastic Models for Shock Compression of Crystalline Solids, pp. 385–452, 2019. View at Publisher · View at Google Scholar