A novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory
Abstract Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Rogers, C. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2007 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, Inc. 2007 |
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| Übergeordnetes Werk: |
Enthalten in: Theoretical and mathematical physics - Springer US, 1969, 152(2007), 1 vom: Juli, Seite 1030-1042 |
|---|---|
| Übergeordnetes Werk: |
volume:152 ; year:2007 ; number:1 ; month:07 ; pages:1030-1042 |
| Links: |
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| DOI / URN: |
10.1007/s11232-007-0087-z |
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OLC205423088X |
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| 520 | |a Abstract Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and soft nonlinear elastic responses. A natural extension of the latter leads to a novel class of model constitutive laws where the stress and strain are given parametrically in terms of elliptic functions. Such models allow a change in the concavity of the stress-strain law. Such behavior can be observed in the compression of polycrystalline materials or in the unloading regimes of superelastic nickel-titanium. | ||
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10.1007/s11232-007-0087-z doi (DE-627)OLC205423088X (DE-He213)s11232-007-0087-z-p DE-627 ger DE-627 rakwb eng 530 VZ Rogers, C. verfasserin aut A novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and soft nonlinear elastic responses. A natural extension of the latter leads to a novel class of model constitutive laws where the stress and strain are given parametrically in terms of elliptic functions. Such models allow a change in the concavity of the stress-strain law. Such behavior can be observed in the compression of polycrystalline materials or in the unloading regimes of superelastic nickel-titanium. nonlinearity elasticity Loewner theory Schief, W. K. aut Chow, K. W. aut Enthalten in Theoretical and mathematical physics Springer US, 1969 152(2007), 1 vom: Juli, Seite 1030-1042 (DE-627)130017507 (DE-600)420246-6 (DE-576)01556018X 0040-5779 nnns volume:152 year:2007 number:1 month:07 pages:1030-1042 https://doi.org/10.1007/s11232-007-0087-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2003 GBV_ILN_2088 AR 152 2007 1 07 1030-1042 |
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10.1007/s11232-007-0087-z doi (DE-627)OLC205423088X (DE-He213)s11232-007-0087-z-p DE-627 ger DE-627 rakwb eng 530 VZ Rogers, C. verfasserin aut A novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and soft nonlinear elastic responses. A natural extension of the latter leads to a novel class of model constitutive laws where the stress and strain are given parametrically in terms of elliptic functions. Such models allow a change in the concavity of the stress-strain law. Such behavior can be observed in the compression of polycrystalline materials or in the unloading regimes of superelastic nickel-titanium. nonlinearity elasticity Loewner theory Schief, W. K. aut Chow, K. W. aut Enthalten in Theoretical and mathematical physics Springer US, 1969 152(2007), 1 vom: Juli, Seite 1030-1042 (DE-627)130017507 (DE-600)420246-6 (DE-576)01556018X 0040-5779 nnns volume:152 year:2007 number:1 month:07 pages:1030-1042 https://doi.org/10.1007/s11232-007-0087-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2003 GBV_ILN_2088 AR 152 2007 1 07 1030-1042 |
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10.1007/s11232-007-0087-z doi (DE-627)OLC205423088X (DE-He213)s11232-007-0087-z-p DE-627 ger DE-627 rakwb eng 530 VZ Rogers, C. verfasserin aut A novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and soft nonlinear elastic responses. A natural extension of the latter leads to a novel class of model constitutive laws where the stress and strain are given parametrically in terms of elliptic functions. Such models allow a change in the concavity of the stress-strain law. Such behavior can be observed in the compression of polycrystalline materials or in the unloading regimes of superelastic nickel-titanium. nonlinearity elasticity Loewner theory Schief, W. K. aut Chow, K. W. aut Enthalten in Theoretical and mathematical physics Springer US, 1969 152(2007), 1 vom: Juli, Seite 1030-1042 (DE-627)130017507 (DE-600)420246-6 (DE-576)01556018X 0040-5779 nnns volume:152 year:2007 number:1 month:07 pages:1030-1042 https://doi.org/10.1007/s11232-007-0087-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2003 GBV_ILN_2088 AR 152 2007 1 07 1030-1042 |
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10.1007/s11232-007-0087-z doi (DE-627)OLC205423088X (DE-He213)s11232-007-0087-z-p DE-627 ger DE-627 rakwb eng 530 VZ Rogers, C. verfasserin aut A novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and soft nonlinear elastic responses. A natural extension of the latter leads to a novel class of model constitutive laws where the stress and strain are given parametrically in terms of elliptic functions. Such models allow a change in the concavity of the stress-strain law. Such behavior can be observed in the compression of polycrystalline materials or in the unloading regimes of superelastic nickel-titanium. nonlinearity elasticity Loewner theory Schief, W. K. aut Chow, K. W. aut Enthalten in Theoretical and mathematical physics Springer US, 1969 152(2007), 1 vom: Juli, Seite 1030-1042 (DE-627)130017507 (DE-600)420246-6 (DE-576)01556018X 0040-5779 nnns volume:152 year:2007 number:1 month:07 pages:1030-1042 https://doi.org/10.1007/s11232-007-0087-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2003 GBV_ILN_2088 AR 152 2007 1 07 1030-1042 |
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10.1007/s11232-007-0087-z doi (DE-627)OLC205423088X (DE-He213)s11232-007-0087-z-p DE-627 ger DE-627 rakwb eng 530 VZ Rogers, C. verfasserin aut A novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and soft nonlinear elastic responses. A natural extension of the latter leads to a novel class of model constitutive laws where the stress and strain are given parametrically in terms of elliptic functions. Such models allow a change in the concavity of the stress-strain law. Such behavior can be observed in the compression of polycrystalline materials or in the unloading regimes of superelastic nickel-titanium. nonlinearity elasticity Loewner theory Schief, W. K. aut Chow, K. W. aut Enthalten in Theoretical and mathematical physics Springer US, 1969 152(2007), 1 vom: Juli, Seite 1030-1042 (DE-627)130017507 (DE-600)420246-6 (DE-576)01556018X 0040-5779 nnns volume:152 year:2007 number:1 month:07 pages:1030-1042 https://doi.org/10.1007/s11232-007-0087-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2003 GBV_ILN_2088 AR 152 2007 1 07 1030-1042 |
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Abstract Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and soft nonlinear elastic responses. A natural extension of the latter leads to a novel class of model constitutive laws where the stress and strain are given parametrically in terms of elliptic functions. Such models allow a change in the concavity of the stress-strain law. Such behavior can be observed in the compression of polycrystalline materials or in the unloading regimes of superelastic nickel-titanium. © Springer Science+Business Media, Inc. 2007 |
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Abstract Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and soft nonlinear elastic responses. A natural extension of the latter leads to a novel class of model constitutive laws where the stress and strain are given parametrically in terms of elliptic functions. Such models allow a change in the concavity of the stress-strain law. Such behavior can be observed in the compression of polycrystalline materials or in the unloading regimes of superelastic nickel-titanium. © Springer Science+Business Media, Inc. 2007 |
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Abstract Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and soft nonlinear elastic responses. A natural extension of the latter leads to a novel class of model constitutive laws where the stress and strain are given parametrically in terms of elliptic functions. Such models allow a change in the concavity of the stress-strain law. Such behavior can be observed in the compression of polycrystalline materials or in the unloading regimes of superelastic nickel-titanium. © Springer Science+Business Media, Inc. 2007 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC205423088X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230504055526.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2007 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11232-007-0087-z</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC205423088X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11232-007-0087-z-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rogers, C.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2007</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media, Inc. 2007</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and soft nonlinear elastic responses. A natural extension of the latter leads to a novel class of model constitutive laws where the stress and strain are given parametrically in terms of elliptic functions. Such models allow a change in the concavity of the stress-strain law. Such behavior can be observed in the compression of polycrystalline materials or in the unloading regimes of superelastic nickel-titanium.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">nonlinearity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">elasticity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Loewner theory</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Schief, W. K.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Chow, K. 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