PittsburghV1, Main, Exploration, bibRecord, 000037

Plates with incompatible prestrain of high order

Identifieur interne : 000037 ( Main/Exploration ); précédent : 000036; suivant : 000038

Plates with incompatible prestrain of high order

Auteurs : Marta Lewicka [États-Unis] ; Annie Raoult [France] ; Diego Ricciotti [États-Unis]

Source :

RBID : Hal:hal-01138338

Abstract

We study the effective elastic behaviour of the incompatibly prestrained thin plates, characterized by a Riemann metric G on the reference configuration. We assume that the prestrain is " weak " , i.e. it induces scaling of the incompatible elastic energy E^h of order less than h^2 in terms of the plate's thickness h. We essentially prove two results. First, we establish the Γ-limit of the scaled energies h^{−4} E^h and show that it consists of a von Kármán-like energy, given in terms of the first order infinitesimal isometries and of the admissible strains on the surface isometrically immersing G_{2×2} (i.e. the prestrain metric on the midplate) in R^3. Second, we prove that in the scaling regime E^h~ h^β with β > 2, there is no other limiting theory: if inf h^{−2} E^h → 0 then inf E^h ≤ Ch^4 , and if inf h^{−4} E^h → 0 then G is realizable and hence min E^h = 0 for every h.

Url:

https://hal.archives-ouvertes.fr/hal-01138338

DOI: 10.1016/j.anihpc.2017.01.003

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 000461
to stream Hal, to step Curation: 000461
to stream Hal, to step Checkpoint: 000038
to stream Main, to step Merge: 000035
to stream Main, to step Curation: 000037

Le document en format XML

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<front><div type="abstract" xml:lang="en">We study the effective elastic behaviour of the incompatibly prestrained thin plates, characterized by a Riemann metric G on the reference configuration. We assume that the prestrain is " weak " , i.e. it induces scaling of the incompatible elastic energy E^h of order less than h^2 in terms of the plate's thickness h. We essentially prove two results. First, we establish the Γ-limit of the scaled energies h^{−4} E^h and show that it consists of a von Kármán-like energy, given in terms of the first order infinitesimal isometries and of the admissible strains on the surface isometrically immersing G_{2×2} (i.e. the prestrain metric on the midplate) in R^3. Second, we prove that in the scaling regime E^h~ h^β with β > 2, there is no other limiting theory: if inf h^{−2} E^h → 0 then inf E^h ≤ Ch^4 , and if inf h^{−4} E^h → 0 then G is realizable and hence min E^h = 0 for every h.</div>
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Plates with incompatible prestrain of high order

Plates with incompatible prestrain of high order

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Abstract

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