An explicit, direct approach to obtaining multiaxial elastic potentials that exactly match data of four benchmark tests for rubbery materials—part 1: incompressible deformations
Abstract An explicit, direct approach is proposed to obtain multiaxial elastic potentials that exactly match finite strain data of four benchmark tests for incompressible rubberlike materials, including uniaxial, biaxial, plane-strain compression and simple shear tests. This approach is composed of...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Xiao, Heng [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2012 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2012 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mechanica - Springer Vienna, 1965, 223(2012), 9 vom: 24. Juni, Seite 2039-2063 |
|---|---|
| Übergeordnetes Werk: |
volume:223 ; year:2012 ; number:9 ; day:24 ; month:06 ; pages:2039-2063 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00707-012-0684-2 |
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| Katalog-ID: |
OLC2030137197 |
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| 520 | |a Abstract An explicit, direct approach is proposed to obtain multiaxial elastic potentials that exactly match finite strain data of four benchmark tests for incompressible rubberlike materials, including uniaxial, biaxial, plane-strain compression and simple shear tests. This approach is composed of three direct procedures. At first, we utilize a usual interpolating method for single-variable functions to obtain one-dimensional stress–strain relations matching data of uniaxial test and simple shear test, separately, and then obtain two one-dimensional elastic potentials via directly integrating the stress power. After that, we introduce a multiaxial bridging method based on certain invariants of Hencky strain and extend the foregoing two one-dimensional potentials to two potentials for multiaxial cases. Then, we further introduce a multiaxial matching method based also on Hencky invariants and combine the just-mentioned two independent multiaxial potentials to obtain a unified form of multiaxial potential. With two universal relations first disclosed here between the four tests, eventually we demonstrate that each such unified multiaxial potential exactly matches data of four benchmark tests. In particular, we apply the proposed explicit approach with a simple form of rational interpolating function for uniaxial stress–strain relation with two poles and directly from uniaxial stress–strain relation to obtain a new, simple form of multiaxial elastic potential with a limit for strain. It is found that this limit for strain is just a counterpart of the well-known von Mises limit for stress in the theory of elastoplasticity. Also, it is shown that this simple potential accurately matches data of four benchmark tests over the whole range from small to large deformations. | ||
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10.1007/s00707-012-0684-2 doi (DE-627)OLC2030137197 (DE-He213)s00707-012-0684-2-p DE-627 ger DE-627 rakwb eng 530 VZ Xiao, Heng verfasserin aut An explicit, direct approach to obtaining multiaxial elastic potentials that exactly match data of four benchmark tests for rubbery materials—part 1: incompressible deformations 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2012 Abstract An explicit, direct approach is proposed to obtain multiaxial elastic potentials that exactly match finite strain data of four benchmark tests for incompressible rubberlike materials, including uniaxial, biaxial, plane-strain compression and simple shear tests. This approach is composed of three direct procedures. At first, we utilize a usual interpolating method for single-variable functions to obtain one-dimensional stress–strain relations matching data of uniaxial test and simple shear test, separately, and then obtain two one-dimensional elastic potentials via directly integrating the stress power. After that, we introduce a multiaxial bridging method based on certain invariants of Hencky strain and extend the foregoing two one-dimensional potentials to two potentials for multiaxial cases. Then, we further introduce a multiaxial matching method based also on Hencky invariants and combine the just-mentioned two independent multiaxial potentials to obtain a unified form of multiaxial potential. With two universal relations first disclosed here between the four tests, eventually we demonstrate that each such unified multiaxial potential exactly matches data of four benchmark tests. In particular, we apply the proposed explicit approach with a simple form of rational interpolating function for uniaxial stress–strain relation with two poles and directly from uniaxial stress–strain relation to obtain a new, simple form of multiaxial elastic potential with a limit for strain. It is found that this limit for strain is just a counterpart of the well-known von Mises limit for stress in the theory of elastoplasticity. Also, it is shown that this simple potential accurately matches data of four benchmark tests over the whole range from small to large deformations. Simple Shear Elastic Potential Rubber Elasticity Hencky Strain Simple Shear Test Enthalten in Acta mechanica Springer Vienna, 1965 223(2012), 9 vom: 24. Juni, Seite 2039-2063 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:223 year:2012 number:9 day:24 month:06 pages:2039-2063 https://doi.org/10.1007/s00707-012-0684-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2020 GBV_ILN_4700 AR 223 2012 9 24 06 2039-2063 |
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10.1007/s00707-012-0684-2 doi (DE-627)OLC2030137197 (DE-He213)s00707-012-0684-2-p DE-627 ger DE-627 rakwb eng 530 VZ Xiao, Heng verfasserin aut An explicit, direct approach to obtaining multiaxial elastic potentials that exactly match data of four benchmark tests for rubbery materials—part 1: incompressible deformations 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2012 Abstract An explicit, direct approach is proposed to obtain multiaxial elastic potentials that exactly match finite strain data of four benchmark tests for incompressible rubberlike materials, including uniaxial, biaxial, plane-strain compression and simple shear tests. This approach is composed of three direct procedures. At first, we utilize a usual interpolating method for single-variable functions to obtain one-dimensional stress–strain relations matching data of uniaxial test and simple shear test, separately, and then obtain two one-dimensional elastic potentials via directly integrating the stress power. After that, we introduce a multiaxial bridging method based on certain invariants of Hencky strain and extend the foregoing two one-dimensional potentials to two potentials for multiaxial cases. Then, we further introduce a multiaxial matching method based also on Hencky invariants and combine the just-mentioned two independent multiaxial potentials to obtain a unified form of multiaxial potential. With two universal relations first disclosed here between the four tests, eventually we demonstrate that each such unified multiaxial potential exactly matches data of four benchmark tests. In particular, we apply the proposed explicit approach with a simple form of rational interpolating function for uniaxial stress–strain relation with two poles and directly from uniaxial stress–strain relation to obtain a new, simple form of multiaxial elastic potential with a limit for strain. It is found that this limit for strain is just a counterpart of the well-known von Mises limit for stress in the theory of elastoplasticity. Also, it is shown that this simple potential accurately matches data of four benchmark tests over the whole range from small to large deformations. Simple Shear Elastic Potential Rubber Elasticity Hencky Strain Simple Shear Test Enthalten in Acta mechanica Springer Vienna, 1965 223(2012), 9 vom: 24. Juni, Seite 2039-2063 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:223 year:2012 number:9 day:24 month:06 pages:2039-2063 https://doi.org/10.1007/s00707-012-0684-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2020 GBV_ILN_4700 AR 223 2012 9 24 06 2039-2063 |
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10.1007/s00707-012-0684-2 doi (DE-627)OLC2030137197 (DE-He213)s00707-012-0684-2-p DE-627 ger DE-627 rakwb eng 530 VZ Xiao, Heng verfasserin aut An explicit, direct approach to obtaining multiaxial elastic potentials that exactly match data of four benchmark tests for rubbery materials—part 1: incompressible deformations 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2012 Abstract An explicit, direct approach is proposed to obtain multiaxial elastic potentials that exactly match finite strain data of four benchmark tests for incompressible rubberlike materials, including uniaxial, biaxial, plane-strain compression and simple shear tests. This approach is composed of three direct procedures. At first, we utilize a usual interpolating method for single-variable functions to obtain one-dimensional stress–strain relations matching data of uniaxial test and simple shear test, separately, and then obtain two one-dimensional elastic potentials via directly integrating the stress power. After that, we introduce a multiaxial bridging method based on certain invariants of Hencky strain and extend the foregoing two one-dimensional potentials to two potentials for multiaxial cases. Then, we further introduce a multiaxial matching method based also on Hencky invariants and combine the just-mentioned two independent multiaxial potentials to obtain a unified form of multiaxial potential. With two universal relations first disclosed here between the four tests, eventually we demonstrate that each such unified multiaxial potential exactly matches data of four benchmark tests. In particular, we apply the proposed explicit approach with a simple form of rational interpolating function for uniaxial stress–strain relation with two poles and directly from uniaxial stress–strain relation to obtain a new, simple form of multiaxial elastic potential with a limit for strain. It is found that this limit for strain is just a counterpart of the well-known von Mises limit for stress in the theory of elastoplasticity. Also, it is shown that this simple potential accurately matches data of four benchmark tests over the whole range from small to large deformations. Simple Shear Elastic Potential Rubber Elasticity Hencky Strain Simple Shear Test Enthalten in Acta mechanica Springer Vienna, 1965 223(2012), 9 vom: 24. Juni, Seite 2039-2063 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:223 year:2012 number:9 day:24 month:06 pages:2039-2063 https://doi.org/10.1007/s00707-012-0684-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2020 GBV_ILN_4700 AR 223 2012 9 24 06 2039-2063 |
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10.1007/s00707-012-0684-2 doi (DE-627)OLC2030137197 (DE-He213)s00707-012-0684-2-p DE-627 ger DE-627 rakwb eng 530 VZ Xiao, Heng verfasserin aut An explicit, direct approach to obtaining multiaxial elastic potentials that exactly match data of four benchmark tests for rubbery materials—part 1: incompressible deformations 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2012 Abstract An explicit, direct approach is proposed to obtain multiaxial elastic potentials that exactly match finite strain data of four benchmark tests for incompressible rubberlike materials, including uniaxial, biaxial, plane-strain compression and simple shear tests. This approach is composed of three direct procedures. At first, we utilize a usual interpolating method for single-variable functions to obtain one-dimensional stress–strain relations matching data of uniaxial test and simple shear test, separately, and then obtain two one-dimensional elastic potentials via directly integrating the stress power. After that, we introduce a multiaxial bridging method based on certain invariants of Hencky strain and extend the foregoing two one-dimensional potentials to two potentials for multiaxial cases. Then, we further introduce a multiaxial matching method based also on Hencky invariants and combine the just-mentioned two independent multiaxial potentials to obtain a unified form of multiaxial potential. With two universal relations first disclosed here between the four tests, eventually we demonstrate that each such unified multiaxial potential exactly matches data of four benchmark tests. In particular, we apply the proposed explicit approach with a simple form of rational interpolating function for uniaxial stress–strain relation with two poles and directly from uniaxial stress–strain relation to obtain a new, simple form of multiaxial elastic potential with a limit for strain. It is found that this limit for strain is just a counterpart of the well-known von Mises limit for stress in the theory of elastoplasticity. Also, it is shown that this simple potential accurately matches data of four benchmark tests over the whole range from small to large deformations. Simple Shear Elastic Potential Rubber Elasticity Hencky Strain Simple Shear Test Enthalten in Acta mechanica Springer Vienna, 1965 223(2012), 9 vom: 24. Juni, Seite 2039-2063 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:223 year:2012 number:9 day:24 month:06 pages:2039-2063 https://doi.org/10.1007/s00707-012-0684-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2020 GBV_ILN_4700 AR 223 2012 9 24 06 2039-2063 |
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10.1007/s00707-012-0684-2 doi (DE-627)OLC2030137197 (DE-He213)s00707-012-0684-2-p DE-627 ger DE-627 rakwb eng 530 VZ Xiao, Heng verfasserin aut An explicit, direct approach to obtaining multiaxial elastic potentials that exactly match data of four benchmark tests for rubbery materials—part 1: incompressible deformations 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2012 Abstract An explicit, direct approach is proposed to obtain multiaxial elastic potentials that exactly match finite strain data of four benchmark tests for incompressible rubberlike materials, including uniaxial, biaxial, plane-strain compression and simple shear tests. This approach is composed of three direct procedures. At first, we utilize a usual interpolating method for single-variable functions to obtain one-dimensional stress–strain relations matching data of uniaxial test and simple shear test, separately, and then obtain two one-dimensional elastic potentials via directly integrating the stress power. After that, we introduce a multiaxial bridging method based on certain invariants of Hencky strain and extend the foregoing two one-dimensional potentials to two potentials for multiaxial cases. Then, we further introduce a multiaxial matching method based also on Hencky invariants and combine the just-mentioned two independent multiaxial potentials to obtain a unified form of multiaxial potential. With two universal relations first disclosed here between the four tests, eventually we demonstrate that each such unified multiaxial potential exactly matches data of four benchmark tests. In particular, we apply the proposed explicit approach with a simple form of rational interpolating function for uniaxial stress–strain relation with two poles and directly from uniaxial stress–strain relation to obtain a new, simple form of multiaxial elastic potential with a limit for strain. It is found that this limit for strain is just a counterpart of the well-known von Mises limit for stress in the theory of elastoplasticity. Also, it is shown that this simple potential accurately matches data of four benchmark tests over the whole range from small to large deformations. Simple Shear Elastic Potential Rubber Elasticity Hencky Strain Simple Shear Test Enthalten in Acta mechanica Springer Vienna, 1965 223(2012), 9 vom: 24. Juni, Seite 2039-2063 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:223 year:2012 number:9 day:24 month:06 pages:2039-2063 https://doi.org/10.1007/s00707-012-0684-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2020 GBV_ILN_4700 AR 223 2012 9 24 06 2039-2063 |
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An explicit, direct approach to obtaining multiaxial elastic potentials that exactly match data of four benchmark tests for rubbery materials—part 1: incompressible deformations |
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An explicit, direct approach to obtaining multiaxial elastic potentials that exactly match data of four benchmark tests for rubbery materials—part 1: incompressible deformations |
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Xiao, Heng |
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Acta mechanica |
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Xiao, Heng |
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10.1007/s00707-012-0684-2 |
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an explicit, direct approach to obtaining multiaxial elastic potentials that exactly match data of four benchmark tests for rubbery materials—part 1: incompressible deformations |
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An explicit, direct approach to obtaining multiaxial elastic potentials that exactly match data of four benchmark tests for rubbery materials—part 1: incompressible deformations |
| abstract |
Abstract An explicit, direct approach is proposed to obtain multiaxial elastic potentials that exactly match finite strain data of four benchmark tests for incompressible rubberlike materials, including uniaxial, biaxial, plane-strain compression and simple shear tests. This approach is composed of three direct procedures. At first, we utilize a usual interpolating method for single-variable functions to obtain one-dimensional stress–strain relations matching data of uniaxial test and simple shear test, separately, and then obtain two one-dimensional elastic potentials via directly integrating the stress power. After that, we introduce a multiaxial bridging method based on certain invariants of Hencky strain and extend the foregoing two one-dimensional potentials to two potentials for multiaxial cases. Then, we further introduce a multiaxial matching method based also on Hencky invariants and combine the just-mentioned two independent multiaxial potentials to obtain a unified form of multiaxial potential. With two universal relations first disclosed here between the four tests, eventually we demonstrate that each such unified multiaxial potential exactly matches data of four benchmark tests. In particular, we apply the proposed explicit approach with a simple form of rational interpolating function for uniaxial stress–strain relation with two poles and directly from uniaxial stress–strain relation to obtain a new, simple form of multiaxial elastic potential with a limit for strain. It is found that this limit for strain is just a counterpart of the well-known von Mises limit for stress in the theory of elastoplasticity. Also, it is shown that this simple potential accurately matches data of four benchmark tests over the whole range from small to large deformations. © Springer-Verlag 2012 |
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Abstract An explicit, direct approach is proposed to obtain multiaxial elastic potentials that exactly match finite strain data of four benchmark tests for incompressible rubberlike materials, including uniaxial, biaxial, plane-strain compression and simple shear tests. This approach is composed of three direct procedures. At first, we utilize a usual interpolating method for single-variable functions to obtain one-dimensional stress–strain relations matching data of uniaxial test and simple shear test, separately, and then obtain two one-dimensional elastic potentials via directly integrating the stress power. After that, we introduce a multiaxial bridging method based on certain invariants of Hencky strain and extend the foregoing two one-dimensional potentials to two potentials for multiaxial cases. Then, we further introduce a multiaxial matching method based also on Hencky invariants and combine the just-mentioned two independent multiaxial potentials to obtain a unified form of multiaxial potential. With two universal relations first disclosed here between the four tests, eventually we demonstrate that each such unified multiaxial potential exactly matches data of four benchmark tests. In particular, we apply the proposed explicit approach with a simple form of rational interpolating function for uniaxial stress–strain relation with two poles and directly from uniaxial stress–strain relation to obtain a new, simple form of multiaxial elastic potential with a limit for strain. It is found that this limit for strain is just a counterpart of the well-known von Mises limit for stress in the theory of elastoplasticity. Also, it is shown that this simple potential accurately matches data of four benchmark tests over the whole range from small to large deformations. © Springer-Verlag 2012 |
| abstract_unstemmed |
Abstract An explicit, direct approach is proposed to obtain multiaxial elastic potentials that exactly match finite strain data of four benchmark tests for incompressible rubberlike materials, including uniaxial, biaxial, plane-strain compression and simple shear tests. This approach is composed of three direct procedures. At first, we utilize a usual interpolating method for single-variable functions to obtain one-dimensional stress–strain relations matching data of uniaxial test and simple shear test, separately, and then obtain two one-dimensional elastic potentials via directly integrating the stress power. After that, we introduce a multiaxial bridging method based on certain invariants of Hencky strain and extend the foregoing two one-dimensional potentials to two potentials for multiaxial cases. Then, we further introduce a multiaxial matching method based also on Hencky invariants and combine the just-mentioned two independent multiaxial potentials to obtain a unified form of multiaxial potential. With two universal relations first disclosed here between the four tests, eventually we demonstrate that each such unified multiaxial potential exactly matches data of four benchmark tests. In particular, we apply the proposed explicit approach with a simple form of rational interpolating function for uniaxial stress–strain relation with two poles and directly from uniaxial stress–strain relation to obtain a new, simple form of multiaxial elastic potential with a limit for strain. It is found that this limit for strain is just a counterpart of the well-known von Mises limit for stress in the theory of elastoplasticity. Also, it is shown that this simple potential accurately matches data of four benchmark tests over the whole range from small to large deformations. © Springer-Verlag 2012 |
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An explicit, direct approach to obtaining multiaxial elastic potentials that exactly match data of four benchmark tests for rubbery materials—part 1: incompressible deformations |
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