Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof

By J. Alibert, A. Della Corte. 2015

152 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7c97df3b6ddedb0bef65f16e34f3ec908c53d0d8

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Strain gradient and generalized continua obtained by homogenizing frame lattices (2018, methodology): “We recover the results obtained in [Seppecher et al. 2011; Alibert et al. 2003; Alibert and Della Corte 2015] where the exotic properties of this pantographic structure have been detailed.”
Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence (2015, unknown): “Of course this micro–macro procedure is needed, and following the ideas presented, for example, in [2,3,77], in [6–8,18,28,62,71,72] in [10] or in [48–50] will be the object of further investigations (see also [63] for a general overview on generalized continua).”
Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models (2016, background): “First of all, they supply a strong motivation to the study of several complex mathematical problems, especially in homogenization theory; indeed the methods presented in [81] need to be applied to the present context to prove that the correct homogenized model is indeed the second gradient model pre”
Linear pantographic sheets: Asymptotic micro-macro models identification (2017, background): “[13, 77, 11, 16, 9, 4, 2, 34, 35]) but it has not been applied too often to the case of multiscale materials in which a great contrast in physical properties appears at micro-level (see [88, 15]).”
Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices (2015, methodology): “…field models (and demonstrating their results using heuristic – as done in the present paper – or by more rigorous identification methods – see Alibert and Della Corte (2015) for a rigorous result in a similar context) has been limited to the “traditional” class of beam lattices, which…”