An overview of non-local theories of continuum mechanics and a general framework for conservative and dissipative systems

[+] Author and Article Information
Arun R. Srinivasa

Holdredge/Paul Professor, Fellow of ASME Department of Mechanical Engineering Texas A&M University College Station, Texas 77843-3123

J. N. Reddy

Oscar S. Wyatt Jr. Chair Regents Professor Distinguished Professor, Life Fellow of ASME Member, U.S. National Academy of Engineering (NAE) Department of Mechanical Engineering Texas A&M University College Station, Texas 77843-3123

1Corresponding author.

ASME doi:10.1115/1.4036723 History: Received September 20, 2016; Revised April 22, 2017


The aim of this review is to classify and provide a summary of the most widely used theories of continuum mechanics with non-local elastic response ranging from generalized continua to peridynamics showing, in broad outlines, the similarities and differences between them. We then show that, for elastic materials, these disparate approaches can be unified using a total energy based methodology. While our primary focus is on elastic response, we show that a large class of local and non-local dissipative systems can also be unified by extending this methodology to a wide (but special) class of non-local dissipative continua. We hope that the paper may serve as a starting point for researchers for the development of novel non-local models.

Copyright (c) 2017 by ASME
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