Non‐local dispersive model for wave propagation in heterogeneous media: one‐dimensional case

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Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results (2011, background): “Fish et al. (2002a) have also suggested multi-dimensional extensions of Eq.”
Multiscale enrichment based on partition of unity (2005, methodology): “Existing methodologies (see for example [55,56, 57 ]) are based on continuum (or quasi-continuum) enrichment.”
Update on a class of gradient theories (2003, methodology): “Such expressions can be deduced, for example, from the work of Triantafyllidis and Aifantis (1986) based on atomistic considerations or the more recent work of Fish and Belsky (1995), and Fish et al. (2002) based on homogeneization techniques.”
Bridging the scales in nano engineering and science (2006, background): “Higher order GMH theory incorporating slow time scales leads to the nonlocal continuum description (Fish et al., 2002a, b; Fish & Schwob, 2003).”