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.

In this expository article, a simple concise treatment of Lagrange's prescription for constraint forces and constraint moments in the dynamics of rigid bodies is presented. The treatment is suited to both Newton–Euler and Lagrangian treatments of rigid body dynamics and is illuminated with a range of examples from classical mechanics and orthopedic biomechanics.