Journal
MECHANICS RESEARCH COMMUNICATIONS
Volume 33, Issue 6, Pages 753-757Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.mechrescom.2006.05.001
Keywords
elasticity; fractional calculus; non-local strain energy density; coexistence of phases
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The present work introduces fractional calculus into the continuum mechanics area describing non-local constitutive relations. Considering a one-dimensional body and assuming total stored energy depending not only upon the local strain but also upon a fractional derivative of the stain, an elastic model with non-local stress-strain behavior is introduced. Fractional calculus provides a natural framework for describing non-local constitutive relations and requires no assumptions for the interval of non-local influence. Furthermore, the proposed method works in finite intervals contrary to the existing theories requiring infinite domains. (C) 2006 Elsevier Ltd. All rights reserved.
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