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EnglishWe describe multiscale geometrical changes via structured deformations (g, G) and the non-local energetic response at a point x via a function 9 of the weighted averages of the jumps [un](y) of microlevel deformations un at points y within a distance r of x. The deformations un are chosen so that limn→∞ un = g and limn→∞ ∇un = G. We provide conditions on 9 under which the upscaling “n → ∞” results in a macroscale energy that depends through 9 on (1) the jumps [g] of g and the “disarrangement field” ∇g − G, (2) the “horizon” r, and (3) the weighting function αr for microlevel averaging of [un](y). We also study the upscaling “n → ∞” followed by spatial localization “r → 0” and show that this succession of processes results in a purely local macroscale energy I(g, G) that depends through 9 upon the jumps [g] of g and the “disarrangement field” ∇g − G alone. In special settings, such macroscale energies I(g, G) have been shown to support the phenomena of yielding and hysteresis, and our results provide a broader setting for studying such yielding and hysteresis. As an illustration, we apply our results in the context of the plasticity of single crystals.
Upscaling and spatial localization of non-local energies with applications to crystal plasticity / Matias, José; Morandotti, Marco; Owen, David R.; Zappale, Elvira. - In: MATHEMATICS AND MECHANICS OF SOLIDS. - ISSN 1081-2865. - 26:7(2021), pp. 963-997. [10.1177/1081286520973245]
| Titolo: | Upscaling and spatial localization of non-local energies with applications to crystal plasticity | |
| Autori: | ||
| Data di pubblicazione: | 2021 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1177/1081286520973245 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| [027]-2020-Mat-Mor-Owe-Zap[MMS]1081286520973245.pdf | Articolo principale | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
| weighted-average-revised.pdf | Articolo principale | 2. Post-print / Author's Accepted Manuscript | PUBBLICO - Tutti i diritti riservati | Visibile a tuttiVisualizza/Apri |
http://hdl.handle.net/11583/2883352
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