Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives

By Francesco dell'Isola, A. Della Corte, Ivan Giorgio. 2017

257 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/1742e1f12bcebbc39ff383cbb847688d1b288126

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Linear pantographic sheets: Asymptotic micro-macro models identification (2017, background): “[33, 42]) is not sufficient to describe, at a macro-level, all conceivable physical systems.”
Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions (2017, background): “For some reasons (initially studied in [20, 21, 29], but surely further investigations are needed!) this kind of boundary conditions has been considered, sometimes and by some schools of mechanicians, unphysical: the reader is referred to the beautiful paper by Sedov, Leonid Ivanovich, [57] for a lu”
Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”** by E. Hellinger (2017, background): “The historical stage in mechanical sciences which is very well described by Hellinger’s article, suffered a “ricorso” where the variational ansatz was rejected as logically inconsistent and not physically well-grounded (see [26] for a detailed discussion of this point).”
Strain gradient and generalized continua obtained by homogenizing frame lattices (2018, methodology): “Their most distinctive feature is that they do not enter the framework of Cauchy stress theory (the internal mechanical interactions are not described by a Cauchy stress tensor) [37], [35], [33].”
Pantographic metamaterials: an example of mathematically driven design and of its technological challenges (2018, background): “It is possible to state that some of these theories were already known at least two centuries ago [7,8].”