On the Commutability of Homogenization and Linearization in Finite Elasticity
Abstract We consider a family of non-convex integral functionals %$\frac{1}{h^2}\int_\Omega W(x/\varepsilon,{\rm Id}+h\nabla g(x))\,\,{\rm d}x,\quad g\in W^{1,p}({\Omega};{\mathbb R}^n)%$ where W is a Carathéodory function periodic in its first variable, and non-degenerate in its second. We prove un...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Müller, Stefan [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2011 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2011 |
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| Übergeordnetes Werk: |
Enthalten in: Archive for rational mechanics and analysis - Berlin : Springer, 1957, 201(2011), 2 vom: 08. Juli, Seite 465-500 |
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| Übergeordnetes Werk: |
volume:201 ; year:2011 ; number:2 ; day:08 ; month:07 ; pages:465-500 |
| Links: |
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| DOI / URN: |
10.1007/s00205-011-0438-7 |
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| Katalog-ID: |
SPR001858947 |
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| 100 | 1 | |a Müller, Stefan |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a On the Commutability of Homogenization and Linearization in Finite Elasticity |
| 264 | 1 | |c 2011 | |
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| 520 | |a Abstract We consider a family of non-convex integral functionals %$\frac{1}{h^2}\int_\Omega W(x/\varepsilon,{\rm Id}+h\nabla g(x))\,\,{\rm d}x,\quad g\in W^{1,p}({\Omega};{\mathbb R}^n)%$ where W is a Carathéodory function periodic in its first variable, and non-degenerate in its second. We prove under suitable conditions that the Γ-limits corresponding to linearization (h → 0) and homogenization (%${\varepsilon\rightarrow 0}%$) commute, provided W is minimal at the identity and admits a quadratic Taylor expansion at the identity. Moreover, we show that the homogenized integrand, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the second variation of W. | ||
| 650 | 4 | |a Strong Convergence |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Strong Topology |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Quadratic Domain |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Bound Lipschitz Domain |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Quadratic Expansion |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Neukamm, Stefan |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Archive for rational mechanics and analysis |d Berlin : Springer, 1957 |g 201(2011), 2 vom: 08. Juli, Seite 465-500 |w (DE-627)253390036 |w (DE-600)1458447-5 |x 1432-0673 |7 nnns |
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10.1007/s00205-011-0438-7 doi (DE-627)SPR001858947 (SPR)s00205-011-0438-7-e DE-627 ger DE-627 rakwb eng Müller, Stefan verfasserin aut On the Commutability of Homogenization and Linearization in Finite Elasticity 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2011 Abstract We consider a family of non-convex integral functionals %$\frac{1}{h^2}\int_\Omega W(x/\varepsilon,{\rm Id}+h\nabla g(x))\,\,{\rm d}x,\quad g\in W^{1,p}({\Omega};{\mathbb R}^n)%$ where W is a Carathéodory function periodic in its first variable, and non-degenerate in its second. We prove under suitable conditions that the Γ-limits corresponding to linearization (h → 0) and homogenization (%${\varepsilon\rightarrow 0}%$) commute, provided W is minimal at the identity and admits a quadratic Taylor expansion at the identity. Moreover, we show that the homogenized integrand, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the second variation of W. Strong Convergence (dpeaa)DE-He213 Strong Topology (dpeaa)DE-He213 Quadratic Domain (dpeaa)DE-He213 Bound Lipschitz Domain (dpeaa)DE-He213 Quadratic Expansion (dpeaa)DE-He213 Neukamm, Stefan aut Enthalten in Archive for rational mechanics and analysis Berlin : Springer, 1957 201(2011), 2 vom: 08. Juli, Seite 465-500 (DE-627)253390036 (DE-600)1458447-5 1432-0673 nnns volume:201 year:2011 number:2 day:08 month:07 pages:465-500 https://dx.doi.org/10.1007/s00205-011-0438-7 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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 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 201 2011 2 08 07 465-500 |
| spelling |
10.1007/s00205-011-0438-7 doi (DE-627)SPR001858947 (SPR)s00205-011-0438-7-e DE-627 ger DE-627 rakwb eng Müller, Stefan verfasserin aut On the Commutability of Homogenization and Linearization in Finite Elasticity 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2011 Abstract We consider a family of non-convex integral functionals %$\frac{1}{h^2}\int_\Omega W(x/\varepsilon,{\rm Id}+h\nabla g(x))\,\,{\rm d}x,\quad g\in W^{1,p}({\Omega};{\mathbb R}^n)%$ where W is a Carathéodory function periodic in its first variable, and non-degenerate in its second. We prove under suitable conditions that the Γ-limits corresponding to linearization (h → 0) and homogenization (%${\varepsilon\rightarrow 0}%$) commute, provided W is minimal at the identity and admits a quadratic Taylor expansion at the identity. Moreover, we show that the homogenized integrand, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the second variation of W. Strong Convergence (dpeaa)DE-He213 Strong Topology (dpeaa)DE-He213 Quadratic Domain (dpeaa)DE-He213 Bound Lipschitz Domain (dpeaa)DE-He213 Quadratic Expansion (dpeaa)DE-He213 Neukamm, Stefan aut Enthalten in Archive for rational mechanics and analysis Berlin : Springer, 1957 201(2011), 2 vom: 08. Juli, Seite 465-500 (DE-627)253390036 (DE-600)1458447-5 1432-0673 nnns volume:201 year:2011 number:2 day:08 month:07 pages:465-500 https://dx.doi.org/10.1007/s00205-011-0438-7 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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 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 201 2011 2 08 07 465-500 |
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10.1007/s00205-011-0438-7 doi (DE-627)SPR001858947 (SPR)s00205-011-0438-7-e DE-627 ger DE-627 rakwb eng Müller, Stefan verfasserin aut On the Commutability of Homogenization and Linearization in Finite Elasticity 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2011 Abstract We consider a family of non-convex integral functionals %$\frac{1}{h^2}\int_\Omega W(x/\varepsilon,{\rm Id}+h\nabla g(x))\,\,{\rm d}x,\quad g\in W^{1,p}({\Omega};{\mathbb R}^n)%$ where W is a Carathéodory function periodic in its first variable, and non-degenerate in its second. We prove under suitable conditions that the Γ-limits corresponding to linearization (h → 0) and homogenization (%${\varepsilon\rightarrow 0}%$) commute, provided W is minimal at the identity and admits a quadratic Taylor expansion at the identity. Moreover, we show that the homogenized integrand, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the second variation of W. Strong Convergence (dpeaa)DE-He213 Strong Topology (dpeaa)DE-He213 Quadratic Domain (dpeaa)DE-He213 Bound Lipschitz Domain (dpeaa)DE-He213 Quadratic Expansion (dpeaa)DE-He213 Neukamm, Stefan aut Enthalten in Archive for rational mechanics and analysis Berlin : Springer, 1957 201(2011), 2 vom: 08. Juli, Seite 465-500 (DE-627)253390036 (DE-600)1458447-5 1432-0673 nnns volume:201 year:2011 number:2 day:08 month:07 pages:465-500 https://dx.doi.org/10.1007/s00205-011-0438-7 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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 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 201 2011 2 08 07 465-500 |
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10.1007/s00205-011-0438-7 doi (DE-627)SPR001858947 (SPR)s00205-011-0438-7-e DE-627 ger DE-627 rakwb eng Müller, Stefan verfasserin aut On the Commutability of Homogenization and Linearization in Finite Elasticity 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2011 Abstract We consider a family of non-convex integral functionals %$\frac{1}{h^2}\int_\Omega W(x/\varepsilon,{\rm Id}+h\nabla g(x))\,\,{\rm d}x,\quad g\in W^{1,p}({\Omega};{\mathbb R}^n)%$ where W is a Carathéodory function periodic in its first variable, and non-degenerate in its second. We prove under suitable conditions that the Γ-limits corresponding to linearization (h → 0) and homogenization (%${\varepsilon\rightarrow 0}%$) commute, provided W is minimal at the identity and admits a quadratic Taylor expansion at the identity. Moreover, we show that the homogenized integrand, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the second variation of W. Strong Convergence (dpeaa)DE-He213 Strong Topology (dpeaa)DE-He213 Quadratic Domain (dpeaa)DE-He213 Bound Lipschitz Domain (dpeaa)DE-He213 Quadratic Expansion (dpeaa)DE-He213 Neukamm, Stefan aut Enthalten in Archive for rational mechanics and analysis Berlin : Springer, 1957 201(2011), 2 vom: 08. Juli, Seite 465-500 (DE-627)253390036 (DE-600)1458447-5 1432-0673 nnns volume:201 year:2011 number:2 day:08 month:07 pages:465-500 https://dx.doi.org/10.1007/s00205-011-0438-7 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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 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 201 2011 2 08 07 465-500 |
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10.1007/s00205-011-0438-7 doi (DE-627)SPR001858947 (SPR)s00205-011-0438-7-e DE-627 ger DE-627 rakwb eng Müller, Stefan verfasserin aut On the Commutability of Homogenization and Linearization in Finite Elasticity 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2011 Abstract We consider a family of non-convex integral functionals %$\frac{1}{h^2}\int_\Omega W(x/\varepsilon,{\rm Id}+h\nabla g(x))\,\,{\rm d}x,\quad g\in W^{1,p}({\Omega};{\mathbb R}^n)%$ where W is a Carathéodory function periodic in its first variable, and non-degenerate in its second. We prove under suitable conditions that the Γ-limits corresponding to linearization (h → 0) and homogenization (%${\varepsilon\rightarrow 0}%$) commute, provided W is minimal at the identity and admits a quadratic Taylor expansion at the identity. Moreover, we show that the homogenized integrand, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the second variation of W. Strong Convergence (dpeaa)DE-He213 Strong Topology (dpeaa)DE-He213 Quadratic Domain (dpeaa)DE-He213 Bound Lipschitz Domain (dpeaa)DE-He213 Quadratic Expansion (dpeaa)DE-He213 Neukamm, Stefan aut Enthalten in Archive for rational mechanics and analysis Berlin : Springer, 1957 201(2011), 2 vom: 08. Juli, Seite 465-500 (DE-627)253390036 (DE-600)1458447-5 1432-0673 nnns volume:201 year:2011 number:2 day:08 month:07 pages:465-500 https://dx.doi.org/10.1007/s00205-011-0438-7 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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 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 201 2011 2 08 07 465-500 |
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Enthalten in Archive for rational mechanics and analysis 201(2011), 2 vom: 08. Juli, Seite 465-500 volume:201 year:2011 number:2 day:08 month:07 pages:465-500 |
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Enthalten in Archive for rational mechanics and analysis 201(2011), 2 vom: 08. Juli, Seite 465-500 volume:201 year:2011 number:2 day:08 month:07 pages:465-500 |
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Müller, Stefan @@aut@@ Neukamm, Stefan @@aut@@ |
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We prove under suitable conditions that the Γ-limits corresponding to linearization (h → 0) and homogenization (%${\varepsilon\rightarrow 0}%$) commute, provided W is minimal at the identity and admits a quadratic Taylor expansion at the identity. 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Müller, Stefan |
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Müller, Stefan misc Strong Convergence misc Strong Topology misc Quadratic Domain misc Bound Lipschitz Domain misc Quadratic Expansion On the Commutability of Homogenization and Linearization in Finite Elasticity |
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On the Commutability of Homogenization and Linearization in Finite Elasticity Strong Convergence (dpeaa)DE-He213 Strong Topology (dpeaa)DE-He213 Quadratic Domain (dpeaa)DE-He213 Bound Lipschitz Domain (dpeaa)DE-He213 Quadratic Expansion (dpeaa)DE-He213 |
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On the Commutability of Homogenization and Linearization in Finite Elasticity |
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On the Commutability of Homogenization and Linearization in Finite Elasticity |
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Müller, Stefan |
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Müller, Stefan |
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10.1007/s00205-011-0438-7 |
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on the commutability of homogenization and linearization in finite elasticity |
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On the Commutability of Homogenization and Linearization in Finite Elasticity |
| abstract |
Abstract We consider a family of non-convex integral functionals %$\frac{1}{h^2}\int_\Omega W(x/\varepsilon,{\rm Id}+h\nabla g(x))\,\,{\rm d}x,\quad g\in W^{1,p}({\Omega};{\mathbb R}^n)%$ where W is a Carathéodory function periodic in its first variable, and non-degenerate in its second. We prove under suitable conditions that the Γ-limits corresponding to linearization (h → 0) and homogenization (%${\varepsilon\rightarrow 0}%$) commute, provided W is minimal at the identity and admits a quadratic Taylor expansion at the identity. Moreover, we show that the homogenized integrand, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the second variation of W. © Springer-Verlag 2011 |
| abstractGer |
Abstract We consider a family of non-convex integral functionals %$\frac{1}{h^2}\int_\Omega W(x/\varepsilon,{\rm Id}+h\nabla g(x))\,\,{\rm d}x,\quad g\in W^{1,p}({\Omega};{\mathbb R}^n)%$ where W is a Carathéodory function periodic in its first variable, and non-degenerate in its second. We prove under suitable conditions that the Γ-limits corresponding to linearization (h → 0) and homogenization (%${\varepsilon\rightarrow 0}%$) commute, provided W is minimal at the identity and admits a quadratic Taylor expansion at the identity. Moreover, we show that the homogenized integrand, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the second variation of W. © Springer-Verlag 2011 |
| abstract_unstemmed |
Abstract We consider a family of non-convex integral functionals %$\frac{1}{h^2}\int_\Omega W(x/\varepsilon,{\rm Id}+h\nabla g(x))\,\,{\rm d}x,\quad g\in W^{1,p}({\Omega};{\mathbb R}^n)%$ where W is a Carathéodory function periodic in its first variable, and non-degenerate in its second. We prove under suitable conditions that the Γ-limits corresponding to linearization (h → 0) and homogenization (%${\varepsilon\rightarrow 0}%$) commute, provided W is minimal at the identity and admits a quadratic Taylor expansion at the identity. Moreover, we show that the homogenized integrand, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the second variation of W. © Springer-Verlag 2011 |
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On the Commutability of Homogenization and Linearization in Finite Elasticity |
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https://dx.doi.org/10.1007/s00205-011-0438-7 |
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Neukamm, Stefan |
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| score |
7.400199 |