Non-local solutions to direct and inverse problems in mechanics: A fractional calculus approach

C. S. Drapaca, S. Sivaloganathan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

In this paper we present a new non-local model of continuum mechanics based on fractional calculus. The model encompasses in a single unified framework both classical continuum mechanics and non-local theories for continua with discontinuities and long range forces. Our theoretical framework can be used to solve both direct and inverse problems of importance in practical applications. We present results to two direct mechanical problems: (1) the deformation of an infinite bar subjected to a self-equilibrated load distribution, and (2) the propagation of longitudinal waves in a thin finite bar. We also show results to the inverse problem of magnetic resonance elastography using our proposed model.

Original languageEnglish (US)
Title of host publicationMechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials - Proceedings of the 2011 Annual Conference on Experimental and Applied Mechanics
PublisherSpringer New York LLC
Pages267-274
Number of pages8
ISBN (Print)9781461402121
DOIs
StatePublished - 2011
Event2011 SEM Annual Conference on Experimental and Applied Mechanics - Uncasville, CT, United States
Duration: Jun 13 2011Jun 16 2011

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
Volume3
ISSN (Print)2191-5644
ISSN (Electronic)2191-5652

Other

Other2011 SEM Annual Conference on Experimental and Applied Mechanics
CountryUnited States
CityUncasville, CT
Period6/13/116/16/11

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Computational Mechanics
  • Mechanical Engineering

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    Drapaca, C. S., & Sivaloganathan, S. (2011). Non-local solutions to direct and inverse problems in mechanics: A fractional calculus approach. In Mechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials - Proceedings of the 2011 Annual Conference on Experimental and Applied Mechanics (pp. 267-274). (Conference Proceedings of the Society for Experimental Mechanics Series; Vol. 3). Springer New York LLC. https://doi.org/10.1007/978-1-4614-0213-8_38