Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories
Abstract This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material poi...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Surana, K. S. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Continuum mechanics and thermodynamics - Berlin : Springer, 1989, 29(2017), 2 vom: 25. Jan., Seite 665-698 |
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| Übergeordnetes Werk: |
volume:29 ; year:2017 ; number:2 ; day:25 ; month:01 ; pages:665-698 |
| Links: |
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| DOI / URN: |
10.1007/s00161-017-0554-1 |
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| Katalog-ID: |
SPR001339486 |
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| 100 | 1 | |a Surana, K. S. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories |
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| 520 | |a Abstract This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements %$( \pmb {\varvec{u }})%$ and (ii) three internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$ about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations %$({}_e \pmb {\varvec{{\varTheta } }})%$ about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to %$ \pmb {\varvec{u }}%$ and %${}_e \pmb {\varvec{{\varTheta } }}%$ as six degrees of freedom at a material point. The internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$, often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations %${}_i \pmb {\varvec{{\varTheta } }}%$ are resisted by the deforming matter, conjugate moment tensor arises that together with %${}_i \pmb {\varvec{{\varTheta } }}%$ may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations %${}_e \pmb {\varvec{{\varTheta } }}%$ also result in conjugate moment tensor which, together with %${}_e \pmb {\varvec{{\varTheta } }}%$, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the entropy inequality. Material coefficients introduced in the constitutive theories are clearly defined and discussed. | ||
| 650 | 4 | |a Non-classical continua |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Polar continua |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Lagrangian description |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Internal rotations |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Cosserat rotations |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Joy, A. D. |4 aut | |
| 700 | 1 | |a Reddy, J. N. |4 aut | |
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10.1007/s00161-017-0554-1 doi (DE-627)SPR001339486 (SPR)s00161-017-0554-1-e DE-627 ger DE-627 rakwb eng Surana, K. S. verfasserin aut Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2017 Abstract This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements %$( \pmb {\varvec{u }})%$ and (ii) three internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$ about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations %$({}_e \pmb {\varvec{{\varTheta } }})%$ about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to %$ \pmb {\varvec{u }}%$ and %${}_e \pmb {\varvec{{\varTheta } }}%$ as six degrees of freedom at a material point. The internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$, often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations %${}_i \pmb {\varvec{{\varTheta } }}%$ are resisted by the deforming matter, conjugate moment tensor arises that together with %${}_i \pmb {\varvec{{\varTheta } }}%$ may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations %${}_e \pmb {\varvec{{\varTheta } }}%$ also result in conjugate moment tensor which, together with %${}_e \pmb {\varvec{{\varTheta } }}%$, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the entropy inequality. Material coefficients introduced in the constitutive theories are clearly defined and discussed. Non-classical continua (dpeaa)DE-He213 Polar continua (dpeaa)DE-He213 Lagrangian description (dpeaa)DE-He213 Internal rotations (dpeaa)DE-He213 Cosserat rotations (dpeaa)DE-He213 Joy, A. D. aut Reddy, J. N. aut Enthalten in Continuum mechanics and thermodynamics Berlin : Springer, 1989 29(2017), 2 vom: 25. Jan., Seite 665-698 (DE-627)270937617 (DE-600)1478722-2 1432-0959 nnns volume:29 year:2017 number:2 day:25 month:01 pages:665-698 https://dx.doi.org/10.1007/s00161-017-0554-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 29 2017 2 25 01 665-698 |
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10.1007/s00161-017-0554-1 doi (DE-627)SPR001339486 (SPR)s00161-017-0554-1-e DE-627 ger DE-627 rakwb eng Surana, K. S. verfasserin aut Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2017 Abstract This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements %$( \pmb {\varvec{u }})%$ and (ii) three internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$ about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations %$({}_e \pmb {\varvec{{\varTheta } }})%$ about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to %$ \pmb {\varvec{u }}%$ and %${}_e \pmb {\varvec{{\varTheta } }}%$ as six degrees of freedom at a material point. The internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$, often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations %${}_i \pmb {\varvec{{\varTheta } }}%$ are resisted by the deforming matter, conjugate moment tensor arises that together with %${}_i \pmb {\varvec{{\varTheta } }}%$ may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations %${}_e \pmb {\varvec{{\varTheta } }}%$ also result in conjugate moment tensor which, together with %${}_e \pmb {\varvec{{\varTheta } }}%$, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the entropy inequality. Material coefficients introduced in the constitutive theories are clearly defined and discussed. Non-classical continua (dpeaa)DE-He213 Polar continua (dpeaa)DE-He213 Lagrangian description (dpeaa)DE-He213 Internal rotations (dpeaa)DE-He213 Cosserat rotations (dpeaa)DE-He213 Joy, A. D. aut Reddy, J. N. aut Enthalten in Continuum mechanics and thermodynamics Berlin : Springer, 1989 29(2017), 2 vom: 25. Jan., Seite 665-698 (DE-627)270937617 (DE-600)1478722-2 1432-0959 nnns volume:29 year:2017 number:2 day:25 month:01 pages:665-698 https://dx.doi.org/10.1007/s00161-017-0554-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 29 2017 2 25 01 665-698 |
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10.1007/s00161-017-0554-1 doi (DE-627)SPR001339486 (SPR)s00161-017-0554-1-e DE-627 ger DE-627 rakwb eng Surana, K. S. verfasserin aut Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2017 Abstract This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements %$( \pmb {\varvec{u }})%$ and (ii) three internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$ about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations %$({}_e \pmb {\varvec{{\varTheta } }})%$ about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to %$ \pmb {\varvec{u }}%$ and %${}_e \pmb {\varvec{{\varTheta } }}%$ as six degrees of freedom at a material point. The internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$, often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations %${}_i \pmb {\varvec{{\varTheta } }}%$ are resisted by the deforming matter, conjugate moment tensor arises that together with %${}_i \pmb {\varvec{{\varTheta } }}%$ may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations %${}_e \pmb {\varvec{{\varTheta } }}%$ also result in conjugate moment tensor which, together with %${}_e \pmb {\varvec{{\varTheta } }}%$, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the entropy inequality. Material coefficients introduced in the constitutive theories are clearly defined and discussed. Non-classical continua (dpeaa)DE-He213 Polar continua (dpeaa)DE-He213 Lagrangian description (dpeaa)DE-He213 Internal rotations (dpeaa)DE-He213 Cosserat rotations (dpeaa)DE-He213 Joy, A. D. aut Reddy, J. N. aut Enthalten in Continuum mechanics and thermodynamics Berlin : Springer, 1989 29(2017), 2 vom: 25. Jan., Seite 665-698 (DE-627)270937617 (DE-600)1478722-2 1432-0959 nnns volume:29 year:2017 number:2 day:25 month:01 pages:665-698 https://dx.doi.org/10.1007/s00161-017-0554-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 29 2017 2 25 01 665-698 |
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10.1007/s00161-017-0554-1 doi (DE-627)SPR001339486 (SPR)s00161-017-0554-1-e DE-627 ger DE-627 rakwb eng Surana, K. S. verfasserin aut Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2017 Abstract This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements %$( \pmb {\varvec{u }})%$ and (ii) three internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$ about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations %$({}_e \pmb {\varvec{{\varTheta } }})%$ about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to %$ \pmb {\varvec{u }}%$ and %${}_e \pmb {\varvec{{\varTheta } }}%$ as six degrees of freedom at a material point. The internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$, often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations %${}_i \pmb {\varvec{{\varTheta } }}%$ are resisted by the deforming matter, conjugate moment tensor arises that together with %${}_i \pmb {\varvec{{\varTheta } }}%$ may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations %${}_e \pmb {\varvec{{\varTheta } }}%$ also result in conjugate moment tensor which, together with %${}_e \pmb {\varvec{{\varTheta } }}%$, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the entropy inequality. Material coefficients introduced in the constitutive theories are clearly defined and discussed. Non-classical continua (dpeaa)DE-He213 Polar continua (dpeaa)DE-He213 Lagrangian description (dpeaa)DE-He213 Internal rotations (dpeaa)DE-He213 Cosserat rotations (dpeaa)DE-He213 Joy, A. D. aut Reddy, J. N. aut Enthalten in Continuum mechanics and thermodynamics Berlin : Springer, 1989 29(2017), 2 vom: 25. Jan., Seite 665-698 (DE-627)270937617 (DE-600)1478722-2 1432-0959 nnns volume:29 year:2017 number:2 day:25 month:01 pages:665-698 https://dx.doi.org/10.1007/s00161-017-0554-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 29 2017 2 25 01 665-698 |
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10.1007/s00161-017-0554-1 doi (DE-627)SPR001339486 (SPR)s00161-017-0554-1-e DE-627 ger DE-627 rakwb eng Surana, K. S. verfasserin aut Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2017 Abstract This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements %$( \pmb {\varvec{u }})%$ and (ii) three internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$ about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations %$({}_e \pmb {\varvec{{\varTheta } }})%$ about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to %$ \pmb {\varvec{u }}%$ and %${}_e \pmb {\varvec{{\varTheta } }}%$ as six degrees of freedom at a material point. The internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$, often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations %${}_i \pmb {\varvec{{\varTheta } }}%$ are resisted by the deforming matter, conjugate moment tensor arises that together with %${}_i \pmb {\varvec{{\varTheta } }}%$ may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations %${}_e \pmb {\varvec{{\varTheta } }}%$ also result in conjugate moment tensor which, together with %${}_e \pmb {\varvec{{\varTheta } }}%$, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the entropy inequality. Material coefficients introduced in the constitutive theories are clearly defined and discussed. Non-classical continua (dpeaa)DE-He213 Polar continua (dpeaa)DE-He213 Lagrangian description (dpeaa)DE-He213 Internal rotations (dpeaa)DE-He213 Cosserat rotations (dpeaa)DE-He213 Joy, A. D. aut Reddy, J. N. aut Enthalten in Continuum mechanics and thermodynamics Berlin : Springer, 1989 29(2017), 2 vom: 25. Jan., Seite 665-698 (DE-627)270937617 (DE-600)1478722-2 1432-0959 nnns volume:29 year:2017 number:2 day:25 month:01 pages:665-698 https://dx.doi.org/10.1007/s00161-017-0554-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 29 2017 2 25 01 665-698 |
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Enthalten in Continuum mechanics and thermodynamics 29(2017), 2 vom: 25. Jan., Seite 665-698 volume:29 year:2017 number:2 day:25 month:01 pages:665-698 |
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Enthalten in Continuum mechanics and thermodynamics 29(2017), 2 vom: 25. Jan., Seite 665-698 volume:29 year:2017 number:2 day:25 month:01 pages:665-698 |
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Surana, K. S. @@aut@@ Joy, A. D. @@aut@@ Reddy, J. N. @@aut@@ |
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S.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</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">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag Berlin Heidelberg 2017</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements %$( \pmb {\varvec{u }})%$ and (ii) three internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$ about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations %$({}_e \pmb {\varvec{{\varTheta } }})%$ about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to %$ \pmb {\varvec{u }}%$ and %${}_e \pmb {\varvec{{\varTheta } }}%$ as six degrees of freedom at a material point. The internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$, often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations %${}_i \pmb {\varvec{{\varTheta } }}%$ are resisted by the deforming matter, conjugate moment tensor arises that together with %${}_i \pmb {\varvec{{\varTheta } }}%$ may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations %${}_e \pmb {\varvec{{\varTheta } }}%$ also result in conjugate moment tensor which, together with %${}_e \pmb {\varvec{{\varTheta } }}%$, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the entropy inequality. Material coefficients introduced in the constitutive theories are clearly defined and discussed.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Non-classical continua</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polar continua</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lagrangian description</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Internal rotations</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cosserat rotations</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Joy, A. 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Surana, K. S. |
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Surana, K. S. misc Non-classical continua misc Polar continua misc Lagrangian description misc Internal rotations misc Cosserat rotations Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories |
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Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories Non-classical continua (dpeaa)DE-He213 Polar continua (dpeaa)DE-He213 Lagrangian description (dpeaa)DE-He213 Internal rotations (dpeaa)DE-He213 Cosserat rotations (dpeaa)DE-He213 |
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misc Non-classical continua misc Polar continua misc Lagrangian description misc Internal rotations misc Cosserat rotations |
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Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories |
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Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories |
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Surana, K. S. |
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Continuum mechanics and thermodynamics |
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Surana, K. S. |
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10.1007/s00161-017-0554-1 |
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non-classical continuum theory for solids incorporating internal rotations and rotations of cosserat theories |
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Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories |
| abstract |
Abstract This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements %$( \pmb {\varvec{u }})%$ and (ii) three internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$ about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations %$({}_e \pmb {\varvec{{\varTheta } }})%$ about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to %$ \pmb {\varvec{u }}%$ and %${}_e \pmb {\varvec{{\varTheta } }}%$ as six degrees of freedom at a material point. The internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$, often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations %${}_i \pmb {\varvec{{\varTheta } }}%$ are resisted by the deforming matter, conjugate moment tensor arises that together with %${}_i \pmb {\varvec{{\varTheta } }}%$ may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations %${}_e \pmb {\varvec{{\varTheta } }}%$ also result in conjugate moment tensor which, together with %${}_e \pmb {\varvec{{\varTheta } }}%$, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the entropy inequality. Material coefficients introduced in the constitutive theories are clearly defined and discussed. © Springer-Verlag Berlin Heidelberg 2017 |
| abstractGer |
Abstract This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements %$( \pmb {\varvec{u }})%$ and (ii) three internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$ about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations %$({}_e \pmb {\varvec{{\varTheta } }})%$ about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to %$ \pmb {\varvec{u }}%$ and %${}_e \pmb {\varvec{{\varTheta } }}%$ as six degrees of freedom at a material point. The internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$, often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations %${}_i \pmb {\varvec{{\varTheta } }}%$ are resisted by the deforming matter, conjugate moment tensor arises that together with %${}_i \pmb {\varvec{{\varTheta } }}%$ may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations %${}_e \pmb {\varvec{{\varTheta } }}%$ also result in conjugate moment tensor which, together with %${}_e \pmb {\varvec{{\varTheta } }}%$, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the entropy inequality. Material coefficients introduced in the constitutive theories are clearly defined and discussed. © Springer-Verlag Berlin Heidelberg 2017 |
| abstract_unstemmed |
Abstract This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements %$( \pmb {\varvec{u }})%$ and (ii) three internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$ about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations %$({}_e \pmb {\varvec{{\varTheta } }})%$ about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to %$ \pmb {\varvec{u }}%$ and %${}_e \pmb {\varvec{{\varTheta } }}%$ as six degrees of freedom at a material point. The internal rotations %$({}_i \pmb {\varvec{{\varTheta } }})%$, often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations %${}_i \pmb {\varvec{{\varTheta } }}%$ are resisted by the deforming matter, conjugate moment tensor arises that together with %${}_i \pmb {\varvec{{\varTheta } }}%$ may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations %${}_e \pmb {\varvec{{\varTheta } }}%$ also result in conjugate moment tensor which, together with %${}_e \pmb {\varvec{{\varTheta } }}%$, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the entropy inequality. Material coefficients introduced in the constitutive theories are clearly defined and discussed. © Springer-Verlag Berlin Heidelberg 2017 |
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2 |
| title_short |
Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories |
| url |
https://dx.doi.org/10.1007/s00161-017-0554-1 |
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| author2 |
Joy, A. D. Reddy, J. N. |
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Joy, A. D. Reddy, J. N. |
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| doi_str |
10.1007/s00161-017-0554-1 |
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2024-07-03T21:54:16.679Z |
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| score |
7.400114 |