Reprint of: Wave momentum in models of generalized continua

•Notions of wave momentum and quasi-particles in generalized continua.•Application to the case of strain-gradient elasticity (weak nonlocality).•Application to Cosserat–micropolar materials (rigid microstructure).•Application to models with long-range interactions (nonlocal elasticity).

The possibility of associating the notion of quasi-particles with elastic wave modes is explored for three basic models of generalized continua: strain-gradient model (weak nonlocality), elasticity with a microstructure such as in Cosserat/micropolar materials, and a true nonlocal model involving the long-range interactions in the underlying crystal lattice. In each case a simplified one-dimensional model is considered. Approximate solutions involving small parameters and exhibiting scale effects are obtained for the Newtonian-like motion of associated quasi-particles. Interpretation for alternate wave-like and quasi-particle-like behaviors is given.