One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure: Part 1: Generic formulation

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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): “More recently, a theory with (stable) strain gradients and acceleration gradients was derived from a discrete lattice, and the simultaneous appearance of the two types of gradients was denoted dynamic consistency (Metrikine and Askes, 2002; Askes and Metrikine, 2002; Metrikine and Askes, 2006).”
A new formulation and 𝒞0‐implementation of dynamically consistent gradient elasticity (2007, methodology): “Implementational aspects Physically realistic results have been obtained with the model of Equation (2) using one-dimensional dispersion analysis [10] and integral transformation methods [11, 12, 24].”