An Overview of Theories of Continuum Mechanics With Nonlocal Elastic Response and a General Framework for Conservative and Dissipative Systems

Abstract

The aim of this review is to classify and provide a summary of the most widely used theories of continuum mechanics with nonlocal 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 nonlocal dissipative systems can also be unified by extending this methodology to a wide (but special) class of nonlocal dissipative continua. We hope that the paper may serve as a starting point for researchers for the development of novel nonlocal models.