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On the Symmetric Lamination Convex and Quasiconvex Hull for the Coplanar n-Well Problem in Two Dimensions.

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Title: On the Symmetric Lamination Convex and Quasiconvex Hull for the Coplanar n-Well Problem in Two Dimensions.
Authors: Capella, A.1 (AUTHOR), Morales, L.1 (AUTHOR) lmm@ciencias.unam.mx
Source: Journal of Elasticity. Jan2022, Vol. 148 Issue 1, p27-54. 28p.
Subjects: Elasticity, Cones, Convex sets
Abstract: We study some particular cases of the n -well problem in two-dimensional linear elasticity. Assuming that every well in U ⊂ R sym 2 × 2 belong to the same two-dimensional affine subspace, we characterize the symmetric lamination convex hull L e (U) for any number of wells in terms of the symmetric lamination convex hull of all three-well subsets contained in U . For a family of four-well sets where two pairs of wells are rank-one compatible, we show that the symmetric lamination convex and quasiconvex hulls coincide, but are strictly contained in its convex hull C (U) . We extend this result to some particular configurations of n wells. Most of the proofs are constructive, and we also present explicit examples. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Elasticity is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 155548991
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: On the Symmetric Lamination Convex and Quasiconvex Hull for the Coplanar n-Well Problem in Two Dimensions.
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  Data: <searchLink fieldCode="AR" term="%22Capella%2C+A%2E%22">Capella, A.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Morales%2C+L%2E%22">Morales, L.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lmm@ciencias.unam.mx</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Elasticity%22">Journal of Elasticity</searchLink>. Jan2022, Vol. 148 Issue 1, p27-54. 28p.
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  Data: We study some particular cases of the n -well problem in two-dimensional linear elasticity. Assuming that every well in U ⊂ R sym 2 × 2 belong to the same two-dimensional affine subspace, we characterize the symmetric lamination convex hull L e (U) for any number of wells in terms of the symmetric lamination convex hull of all three-well subsets contained in U . For a family of four-well sets where two pairs of wells are rank-one compatible, we show that the symmetric lamination convex and quasiconvex hulls coincide, but are strictly contained in its convex hull C (U) . We extend this result to some particular configurations of n wells. Most of the proofs are constructive, and we also present explicit examples. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Journal of Elasticity is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1007/s10659-021-09878-w
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      – Code: eng
        Text: English
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        PageCount: 28
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      – SubjectFull: Elasticity
        Type: general
      – SubjectFull: Cones
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      – SubjectFull: Convex sets
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      – TitleFull: On the Symmetric Lamination Convex and Quasiconvex Hull for the Coplanar n-Well Problem in Two Dimensions.
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            NameFull: Capella, A.
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              Text: Jan2022
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