Ogden-type constitutive equations in finite elasticity of elastomers
Summary An explicit expression is derived for the strain energy of a chain under three-dimensional deformation with finite strains. For a Gaussian chain, this relation implies the Mooney–Rivlin constitutive law, while for non-Gaussian chains it results in novel constitutive equations. Based on a thr...
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Gespeichert in:
| Autor*in: |
Drozdov, A. D. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2006 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Wien 2006 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mechanica - Springer-Verlag, 1965, 183(2006), 3-4 vom: 19. Mai, Seite 231-252 |
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| Übergeordnetes Werk: |
volume:183 ; year:2006 ; number:3-4 ; day:19 ; month:05 ; pages:231-252 |
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| DOI / URN: |
10.1007/s00707-005-0292-5 |
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OLC2030128872 |
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| 520 | |a Summary An explicit expression is derived for the strain energy of a chain under three-dimensional deformation with finite strains. For a Gaussian chain, this relation implies the Mooney–Rivlin constitutive law, while for non-Gaussian chains it results in novel constitutive equations. Based on a three-chain approximation, a formula is derived for the strain energy of a chain with excluded-volume interactions between segments. It is demonstrated that for self-avoiding chains with a stretched exponential distribution function of end-to-end vectors, the strain energy density of a network is described by the Ogden law with two material constants. For the des Cloizeaux distribution function, a constitutive equation is derived that involves three adjustable parameters. The governing equations are verified by fitting observations at uniaxial tension–compression and biaxial tension of elastomers. Good agreement is demonstrated between the experimental data and the results of numerical analysis. | ||
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10.1007/s00707-005-0292-5 doi (DE-627)OLC2030128872 (DE-He213)s00707-005-0292-5-p DE-627 ger DE-627 rakwb eng 530 VZ Drozdov, A. D. verfasserin aut Ogden-type constitutive equations in finite elasticity of elastomers 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2006 Summary An explicit expression is derived for the strain energy of a chain under three-dimensional deformation with finite strains. For a Gaussian chain, this relation implies the Mooney–Rivlin constitutive law, while for non-Gaussian chains it results in novel constitutive equations. Based on a three-chain approximation, a formula is derived for the strain energy of a chain with excluded-volume interactions between segments. It is demonstrated that for self-avoiding chains with a stretched exponential distribution function of end-to-end vectors, the strain energy density of a network is described by the Ogden law with two material constants. For the des Cloizeaux distribution function, a constitutive equation is derived that involves three adjustable parameters. The governing equations are verified by fitting observations at uniaxial tension–compression and biaxial tension of elastomers. Good agreement is demonstrated between the experimental data and the results of numerical analysis. Energy Density Governing Equation Constitutive Equation Exponential Distribution Adjustable Parameter Gottlieb, M. aut Enthalten in Acta mechanica Springer-Verlag, 1965 183(2006), 3-4 vom: 19. Mai, Seite 231-252 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:183 year:2006 number:3-4 day:19 month:05 pages:231-252 https://doi.org/10.1007/s00707-005-0292-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_21 GBV_ILN_22 GBV_ILN_59 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2020 GBV_ILN_2409 GBV_ILN_4700 AR 183 2006 3-4 19 05 231-252 |
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10.1007/s00707-005-0292-5 doi (DE-627)OLC2030128872 (DE-He213)s00707-005-0292-5-p DE-627 ger DE-627 rakwb eng 530 VZ Drozdov, A. D. verfasserin aut Ogden-type constitutive equations in finite elasticity of elastomers 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2006 Summary An explicit expression is derived for the strain energy of a chain under three-dimensional deformation with finite strains. For a Gaussian chain, this relation implies the Mooney–Rivlin constitutive law, while for non-Gaussian chains it results in novel constitutive equations. Based on a three-chain approximation, a formula is derived for the strain energy of a chain with excluded-volume interactions between segments. It is demonstrated that for self-avoiding chains with a stretched exponential distribution function of end-to-end vectors, the strain energy density of a network is described by the Ogden law with two material constants. For the des Cloizeaux distribution function, a constitutive equation is derived that involves three adjustable parameters. The governing equations are verified by fitting observations at uniaxial tension–compression and biaxial tension of elastomers. Good agreement is demonstrated between the experimental data and the results of numerical analysis. Energy Density Governing Equation Constitutive Equation Exponential Distribution Adjustable Parameter Gottlieb, M. aut Enthalten in Acta mechanica Springer-Verlag, 1965 183(2006), 3-4 vom: 19. Mai, Seite 231-252 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:183 year:2006 number:3-4 day:19 month:05 pages:231-252 https://doi.org/10.1007/s00707-005-0292-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_21 GBV_ILN_22 GBV_ILN_59 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2020 GBV_ILN_2409 GBV_ILN_4700 AR 183 2006 3-4 19 05 231-252 |
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10.1007/s00707-005-0292-5 doi (DE-627)OLC2030128872 (DE-He213)s00707-005-0292-5-p DE-627 ger DE-627 rakwb eng 530 VZ Drozdov, A. D. verfasserin aut Ogden-type constitutive equations in finite elasticity of elastomers 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2006 Summary An explicit expression is derived for the strain energy of a chain under three-dimensional deformation with finite strains. For a Gaussian chain, this relation implies the Mooney–Rivlin constitutive law, while for non-Gaussian chains it results in novel constitutive equations. Based on a three-chain approximation, a formula is derived for the strain energy of a chain with excluded-volume interactions between segments. It is demonstrated that for self-avoiding chains with a stretched exponential distribution function of end-to-end vectors, the strain energy density of a network is described by the Ogden law with two material constants. For the des Cloizeaux distribution function, a constitutive equation is derived that involves three adjustable parameters. The governing equations are verified by fitting observations at uniaxial tension–compression and biaxial tension of elastomers. Good agreement is demonstrated between the experimental data and the results of numerical analysis. Energy Density Governing Equation Constitutive Equation Exponential Distribution Adjustable Parameter Gottlieb, M. aut Enthalten in Acta mechanica Springer-Verlag, 1965 183(2006), 3-4 vom: 19. Mai, Seite 231-252 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:183 year:2006 number:3-4 day:19 month:05 pages:231-252 https://doi.org/10.1007/s00707-005-0292-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_21 GBV_ILN_22 GBV_ILN_59 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2020 GBV_ILN_2409 GBV_ILN_4700 AR 183 2006 3-4 19 05 231-252 |
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10.1007/s00707-005-0292-5 doi (DE-627)OLC2030128872 (DE-He213)s00707-005-0292-5-p DE-627 ger DE-627 rakwb eng 530 VZ Drozdov, A. D. verfasserin aut Ogden-type constitutive equations in finite elasticity of elastomers 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2006 Summary An explicit expression is derived for the strain energy of a chain under three-dimensional deformation with finite strains. For a Gaussian chain, this relation implies the Mooney–Rivlin constitutive law, while for non-Gaussian chains it results in novel constitutive equations. Based on a three-chain approximation, a formula is derived for the strain energy of a chain with excluded-volume interactions between segments. It is demonstrated that for self-avoiding chains with a stretched exponential distribution function of end-to-end vectors, the strain energy density of a network is described by the Ogden law with two material constants. For the des Cloizeaux distribution function, a constitutive equation is derived that involves three adjustable parameters. The governing equations are verified by fitting observations at uniaxial tension–compression and biaxial tension of elastomers. Good agreement is demonstrated between the experimental data and the results of numerical analysis. Energy Density Governing Equation Constitutive Equation Exponential Distribution Adjustable Parameter Gottlieb, M. aut Enthalten in Acta mechanica Springer-Verlag, 1965 183(2006), 3-4 vom: 19. Mai, Seite 231-252 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:183 year:2006 number:3-4 day:19 month:05 pages:231-252 https://doi.org/10.1007/s00707-005-0292-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_21 GBV_ILN_22 GBV_ILN_59 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2020 GBV_ILN_2409 GBV_ILN_4700 AR 183 2006 3-4 19 05 231-252 |
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10.1007/s00707-005-0292-5 doi (DE-627)OLC2030128872 (DE-He213)s00707-005-0292-5-p DE-627 ger DE-627 rakwb eng 530 VZ Drozdov, A. D. verfasserin aut Ogden-type constitutive equations in finite elasticity of elastomers 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2006 Summary An explicit expression is derived for the strain energy of a chain under three-dimensional deformation with finite strains. For a Gaussian chain, this relation implies the Mooney–Rivlin constitutive law, while for non-Gaussian chains it results in novel constitutive equations. Based on a three-chain approximation, a formula is derived for the strain energy of a chain with excluded-volume interactions between segments. It is demonstrated that for self-avoiding chains with a stretched exponential distribution function of end-to-end vectors, the strain energy density of a network is described by the Ogden law with two material constants. For the des Cloizeaux distribution function, a constitutive equation is derived that involves three adjustable parameters. The governing equations are verified by fitting observations at uniaxial tension–compression and biaxial tension of elastomers. Good agreement is demonstrated between the experimental data and the results of numerical analysis. Energy Density Governing Equation Constitutive Equation Exponential Distribution Adjustable Parameter Gottlieb, M. aut Enthalten in Acta mechanica Springer-Verlag, 1965 183(2006), 3-4 vom: 19. Mai, Seite 231-252 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:183 year:2006 number:3-4 day:19 month:05 pages:231-252 https://doi.org/10.1007/s00707-005-0292-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_21 GBV_ILN_22 GBV_ILN_59 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2020 GBV_ILN_2409 GBV_ILN_4700 AR 183 2006 3-4 19 05 231-252 |
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ogden-type constitutive equations in finite elasticity of elastomers |
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Ogden-type constitutive equations in finite elasticity of elastomers |
| abstract |
Summary An explicit expression is derived for the strain energy of a chain under three-dimensional deformation with finite strains. For a Gaussian chain, this relation implies the Mooney–Rivlin constitutive law, while for non-Gaussian chains it results in novel constitutive equations. Based on a three-chain approximation, a formula is derived for the strain energy of a chain with excluded-volume interactions between segments. It is demonstrated that for self-avoiding chains with a stretched exponential distribution function of end-to-end vectors, the strain energy density of a network is described by the Ogden law with two material constants. For the des Cloizeaux distribution function, a constitutive equation is derived that involves three adjustable parameters. The governing equations are verified by fitting observations at uniaxial tension–compression and biaxial tension of elastomers. Good agreement is demonstrated between the experimental data and the results of numerical analysis. © Springer-Verlag Wien 2006 |
| abstractGer |
Summary An explicit expression is derived for the strain energy of a chain under three-dimensional deformation with finite strains. For a Gaussian chain, this relation implies the Mooney–Rivlin constitutive law, while for non-Gaussian chains it results in novel constitutive equations. Based on a three-chain approximation, a formula is derived for the strain energy of a chain with excluded-volume interactions between segments. It is demonstrated that for self-avoiding chains with a stretched exponential distribution function of end-to-end vectors, the strain energy density of a network is described by the Ogden law with two material constants. For the des Cloizeaux distribution function, a constitutive equation is derived that involves three adjustable parameters. The governing equations are verified by fitting observations at uniaxial tension–compression and biaxial tension of elastomers. Good agreement is demonstrated between the experimental data and the results of numerical analysis. © Springer-Verlag Wien 2006 |
| abstract_unstemmed |
Summary An explicit expression is derived for the strain energy of a chain under three-dimensional deformation with finite strains. For a Gaussian chain, this relation implies the Mooney–Rivlin constitutive law, while for non-Gaussian chains it results in novel constitutive equations. Based on a three-chain approximation, a formula is derived for the strain energy of a chain with excluded-volume interactions between segments. It is demonstrated that for self-avoiding chains with a stretched exponential distribution function of end-to-end vectors, the strain energy density of a network is described by the Ogden law with two material constants. For the des Cloizeaux distribution function, a constitutive equation is derived that involves three adjustable parameters. The governing equations are verified by fitting observations at uniaxial tension–compression and biaxial tension of elastomers. Good agreement is demonstrated between the experimental data and the results of numerical analysis. © Springer-Verlag Wien 2006 |
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| title_short |
Ogden-type constitutive equations in finite elasticity of elastomers |
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https://doi.org/10.1007/s00707-005-0292-5 |
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Gottlieb, M. |
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