On the directional approach in constitutive modelling: A general thermomechanical framework and exact solutions for Mooney–Rivlin type elasticity in each direction
In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere a...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Lion, Alexander [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013transfer abstract |
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| Schlagwörter: |
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| Umfang: |
9 |
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| Übergeordnetes Werk: |
Enthalten in: One pot synthesis of poly(5-hydroxyl-1,4-naphthoquinone) stabilized gold nanoparticles using the monomer as the reducing agent for nonenzymatic electrochemical detection of glucose - Cooray, M.C. Dilusha ELSEVIER, 2015, New York, NY [u.a.] |
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| Übergeordnetes Werk: |
volume:50 ; year:2013 ; number:14 ; pages:2518-2526 ; extent:9 |
| Links: |
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| DOI / URN: |
10.1016/j.ijsolstr.2013.04.002 |
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| 245 | 1 | 0 | |a On the directional approach in constitutive modelling: A general thermomechanical framework and exact solutions for Mooney–Rivlin type elasticity in each direction |
| 264 | 1 | |c 2013transfer abstract | |
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| 520 | |a In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. | ||
| 520 | |a In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. | ||
| 650 | 7 | |a Mooney–Rivlin |2 Elsevier | |
| 650 | 7 | |a Generalization of uniaxial models |2 Elsevier | |
| 650 | 7 | |a Microsphere |2 Elsevier | |
| 650 | 7 | |a Exact solutions |2 Elsevier | |
| 650 | 7 | |a Directional approach |2 Elsevier | |
| 700 | 1 | |a Diercks, Nico |4 oth | |
| 700 | 1 | |a Caillard, Julien |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier |a Cooray, M.C. Dilusha ELSEVIER |t One pot synthesis of poly(5-hydroxyl-1,4-naphthoquinone) stabilized gold nanoparticles using the monomer as the reducing agent for nonenzymatic electrochemical detection of glucose |d 2015 |g New York, NY [u.a.] |w (DE-627)ELV023913754 |
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10.1016/j.ijsolstr.2013.04.002 doi GBVA2013021000018.pica (DE-627)ELV039106527 (ELSEVIER)S0020-7683(13)00150-9 DE-627 ger DE-627 rakwb eng 530 530 DE-600 540 VZ 610 VZ 540 VZ 35.10 bkl Lion, Alexander verfasserin aut On the directional approach in constitutive modelling: A general thermomechanical framework and exact solutions for Mooney–Rivlin type elasticity in each direction 2013transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. Mooney–Rivlin Elsevier Generalization of uniaxial models Elsevier Microsphere Elsevier Exact solutions Elsevier Directional approach Elsevier Diercks, Nico oth Caillard, Julien oth Enthalten in Elsevier Cooray, M.C. Dilusha ELSEVIER One pot synthesis of poly(5-hydroxyl-1,4-naphthoquinone) stabilized gold nanoparticles using the monomer as the reducing agent for nonenzymatic electrochemical detection of glucose 2015 New York, NY [u.a.] (DE-627)ELV023913754 volume:50 year:2013 number:14 pages:2518-2526 extent:9 https://doi.org/10.1016/j.ijsolstr.2013.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_70 35.10 Physikalische Chemie: Allgemeines VZ AR 50 2013 14 2518-2526 9 045F 530 |
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10.1016/j.ijsolstr.2013.04.002 doi GBVA2013021000018.pica (DE-627)ELV039106527 (ELSEVIER)S0020-7683(13)00150-9 DE-627 ger DE-627 rakwb eng 530 530 DE-600 540 VZ 610 VZ 540 VZ 35.10 bkl Lion, Alexander verfasserin aut On the directional approach in constitutive modelling: A general thermomechanical framework and exact solutions for Mooney–Rivlin type elasticity in each direction 2013transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. Mooney–Rivlin Elsevier Generalization of uniaxial models Elsevier Microsphere Elsevier Exact solutions Elsevier Directional approach Elsevier Diercks, Nico oth Caillard, Julien oth Enthalten in Elsevier Cooray, M.C. Dilusha ELSEVIER One pot synthesis of poly(5-hydroxyl-1,4-naphthoquinone) stabilized gold nanoparticles using the monomer as the reducing agent for nonenzymatic electrochemical detection of glucose 2015 New York, NY [u.a.] (DE-627)ELV023913754 volume:50 year:2013 number:14 pages:2518-2526 extent:9 https://doi.org/10.1016/j.ijsolstr.2013.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_70 35.10 Physikalische Chemie: Allgemeines VZ AR 50 2013 14 2518-2526 9 045F 530 |
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10.1016/j.ijsolstr.2013.04.002 doi GBVA2013021000018.pica (DE-627)ELV039106527 (ELSEVIER)S0020-7683(13)00150-9 DE-627 ger DE-627 rakwb eng 530 530 DE-600 540 VZ 610 VZ 540 VZ 35.10 bkl Lion, Alexander verfasserin aut On the directional approach in constitutive modelling: A general thermomechanical framework and exact solutions for Mooney–Rivlin type elasticity in each direction 2013transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. Mooney–Rivlin Elsevier Generalization of uniaxial models Elsevier Microsphere Elsevier Exact solutions Elsevier Directional approach Elsevier Diercks, Nico oth Caillard, Julien oth Enthalten in Elsevier Cooray, M.C. Dilusha ELSEVIER One pot synthesis of poly(5-hydroxyl-1,4-naphthoquinone) stabilized gold nanoparticles using the monomer as the reducing agent for nonenzymatic electrochemical detection of glucose 2015 New York, NY [u.a.] (DE-627)ELV023913754 volume:50 year:2013 number:14 pages:2518-2526 extent:9 https://doi.org/10.1016/j.ijsolstr.2013.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_70 35.10 Physikalische Chemie: Allgemeines VZ AR 50 2013 14 2518-2526 9 045F 530 |
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10.1016/j.ijsolstr.2013.04.002 doi GBVA2013021000018.pica (DE-627)ELV039106527 (ELSEVIER)S0020-7683(13)00150-9 DE-627 ger DE-627 rakwb eng 530 530 DE-600 540 VZ 610 VZ 540 VZ 35.10 bkl Lion, Alexander verfasserin aut On the directional approach in constitutive modelling: A general thermomechanical framework and exact solutions for Mooney–Rivlin type elasticity in each direction 2013transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. Mooney–Rivlin Elsevier Generalization of uniaxial models Elsevier Microsphere Elsevier Exact solutions Elsevier Directional approach Elsevier Diercks, Nico oth Caillard, Julien oth Enthalten in Elsevier Cooray, M.C. Dilusha ELSEVIER One pot synthesis of poly(5-hydroxyl-1,4-naphthoquinone) stabilized gold nanoparticles using the monomer as the reducing agent for nonenzymatic electrochemical detection of glucose 2015 New York, NY [u.a.] (DE-627)ELV023913754 volume:50 year:2013 number:14 pages:2518-2526 extent:9 https://doi.org/10.1016/j.ijsolstr.2013.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_70 35.10 Physikalische Chemie: Allgemeines VZ AR 50 2013 14 2518-2526 9 045F 530 |
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10.1016/j.ijsolstr.2013.04.002 doi GBVA2013021000018.pica (DE-627)ELV039106527 (ELSEVIER)S0020-7683(13)00150-9 DE-627 ger DE-627 rakwb eng 530 530 DE-600 540 VZ 610 VZ 540 VZ 35.10 bkl Lion, Alexander verfasserin aut On the directional approach in constitutive modelling: A general thermomechanical framework and exact solutions for Mooney–Rivlin type elasticity in each direction 2013transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. Mooney–Rivlin Elsevier Generalization of uniaxial models Elsevier Microsphere Elsevier Exact solutions Elsevier Directional approach Elsevier Diercks, Nico oth Caillard, Julien oth Enthalten in Elsevier Cooray, M.C. Dilusha ELSEVIER One pot synthesis of poly(5-hydroxyl-1,4-naphthoquinone) stabilized gold nanoparticles using the monomer as the reducing agent for nonenzymatic electrochemical detection of glucose 2015 New York, NY [u.a.] (DE-627)ELV023913754 volume:50 year:2013 number:14 pages:2518-2526 extent:9 https://doi.org/10.1016/j.ijsolstr.2013.04.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_70 35.10 Physikalische Chemie: Allgemeines VZ AR 50 2013 14 2518-2526 9 045F 530 |
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English |
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Enthalten in One pot synthesis of poly(5-hydroxyl-1,4-naphthoquinone) stabilized gold nanoparticles using the monomer as the reducing agent for nonenzymatic electrochemical detection of glucose New York, NY [u.a.] volume:50 year:2013 number:14 pages:2518-2526 extent:9 |
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Enthalten in One pot synthesis of poly(5-hydroxyl-1,4-naphthoquinone) stabilized gold nanoparticles using the monomer as the reducing agent for nonenzymatic electrochemical detection of glucose New York, NY [u.a.] volume:50 year:2013 number:14 pages:2518-2526 extent:9 |
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One pot synthesis of poly(5-hydroxyl-1,4-naphthoquinone) stabilized gold nanoparticles using the monomer as the reducing agent for nonenzymatic electrochemical detection of glucose |
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on the directional approach in constitutive modelling: a general thermomechanical framework and exact solutions for mooney–rivlin type elasticity in each direction |
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On the directional approach in constitutive modelling: A general thermomechanical framework and exact solutions for Mooney–Rivlin type elasticity in each direction |
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In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. |
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In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. |
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In order to represent process-induced anisotropies in continuum mechanics or to transfer one-dimensional material models to three spatial dimensions the directional approach is a helpful technique. Since the essential equations are defined in the orientation space it is also denoted as microsphere approach. In the current article, the relation for the directional stress tensor of the second Piola–Kirchhoff type is motivated using the volumetric/isochoric split of the deformation gradient and the Clausius–Duhem inequality. Owing to inherent nonlinearities, numerical discretisation techniques are usually applied to calculate the total stress by averaging the directional stress tensors over the unit sphere. In order to investigate the accuracy of such simulations, the availability of exact solutions in closed form is essential. To this end, the tension/compression behaviour which belongs to a certain direction in the orientation space is modelled by an elasticity relation of the Mooney Rivlin type. The exact solutions are calculated, visualized and discussed for uniaxial tension and compression as well as for equibiaxial tension. |
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