A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage

A new spectral representation of the strain energy function for linear anisotropic elasticity is proposed in the form of a sum of 6 scalar eigen-stiffnesses times the squares of their associated scalar eigen-strains. Since this new representation is general, it is no less or more general than the st...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Rubin, M.B. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Compliance tensor Anisotropic elasticity Invariants Spectral representation Stiffness tensor Damage

Übergeordnetes Werk:	Enthalten in: International journal of engineering science - New York, NY [u.a.] : Science Direct, 1963, 193
Übergeordnetes Werk:	volume:193

DOI / URN:	10.1016/j.ijengsci.2023.103916

Katalog-ID:	ELV065441524

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245	1	0	\|a A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage
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520			\|a A new spectral representation of the strain energy function for linear anisotropic elasticity is proposed in the form of a sum of 6 scalar eigen-stiffnesses times the squares of their associated scalar eigen-strains. Since this new representation is general, it is no less or more general than the standard representation. However, the spectral form reveals fundamental coupled eigen-modes of deformation and energy associated with general anisotropic response. Specifically, each eigen-strain is the inner product of the strain tensor with its symmetric eigen-tensor. The 6 eigen-strains are linearly independent and the 6 eigen-tensors are also linearly independent. Moreover, unlike the eigenvectors of a symmetric matrix, distinct pairs of eigen-tensors are not all orthogonal. The 15 constants that define the eigen-tensors together with the 6 eigen-stiffnesses form 21 independent material constants that characterize the fundamental physics of material anisotropy. These 21 constants are invariant to the orientation of the base vectors fixed in the material. This spectral representation also simplifies the restrictions on these material constants which ensure that the strain energy is a positive-definite function of strain. In addition, a simple damage model is proposed based on this spectral representation and a generalization for finite deformations is briefly discussed.
650		4	\|a Compliance tensor
650		4	\|a Anisotropic elasticity
650		4	\|a Invariants
650		4	\|a Spectral representation
650		4	\|a Stiffness tensor
650		4	\|a Damage
773	0	8	\|i Enthalten in \|t International journal of engineering science \|d New York, NY [u.a.] : Science Direct, 1963 \|g 193 \|h Online-Ressource \|w (DE-627)301511217 \|w (DE-600)1484471-0 \|w (DE-576)096806389 \|7 nnns
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912			\|a GBV_ILN_32
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
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912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
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912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
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author_variant	m r mr
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hierarchy_sort_str	2023
bklnumber	50.00
publishDate	2023
allfields	10.1016/j.ijengsci.2023.103916 doi (DE-627)ELV065441524 (ELSEVIER)S0020-7225(23)00107-6 DE-627 ger DE-627 rda eng 600 VZ 50.00 bkl Rubin, M.B. verfasserin aut A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A new spectral representation of the strain energy function for linear anisotropic elasticity is proposed in the form of a sum of 6 scalar eigen-stiffnesses times the squares of their associated scalar eigen-strains. Since this new representation is general, it is no less or more general than the standard representation. However, the spectral form reveals fundamental coupled eigen-modes of deformation and energy associated with general anisotropic response. Specifically, each eigen-strain is the inner product of the strain tensor with its symmetric eigen-tensor. The 6 eigen-strains are linearly independent and the 6 eigen-tensors are also linearly independent. Moreover, unlike the eigenvectors of a symmetric matrix, distinct pairs of eigen-tensors are not all orthogonal. The 15 constants that define the eigen-tensors together with the 6 eigen-stiffnesses form 21 independent material constants that characterize the fundamental physics of material anisotropy. These 21 constants are invariant to the orientation of the base vectors fixed in the material. This spectral representation also simplifies the restrictions on these material constants which ensure that the strain energy is a positive-definite function of strain. In addition, a simple damage model is proposed based on this spectral representation and a generalization for finite deformations is briefly discussed. Compliance tensor Anisotropic elasticity Invariants Spectral representation Stiffness tensor Damage Enthalten in International journal of engineering science New York, NY [u.a.] : Science Direct, 1963 193 Online-Ressource (DE-627)301511217 (DE-600)1484471-0 (DE-576)096806389 nnns volume:193 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.00 Technik allgemein: Allgemeines VZ AR 193
spelling	10.1016/j.ijengsci.2023.103916 doi (DE-627)ELV065441524 (ELSEVIER)S0020-7225(23)00107-6 DE-627 ger DE-627 rda eng 600 VZ 50.00 bkl Rubin, M.B. verfasserin aut A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A new spectral representation of the strain energy function for linear anisotropic elasticity is proposed in the form of a sum of 6 scalar eigen-stiffnesses times the squares of their associated scalar eigen-strains. Since this new representation is general, it is no less or more general than the standard representation. However, the spectral form reveals fundamental coupled eigen-modes of deformation and energy associated with general anisotropic response. Specifically, each eigen-strain is the inner product of the strain tensor with its symmetric eigen-tensor. The 6 eigen-strains are linearly independent and the 6 eigen-tensors are also linearly independent. Moreover, unlike the eigenvectors of a symmetric matrix, distinct pairs of eigen-tensors are not all orthogonal. The 15 constants that define the eigen-tensors together with the 6 eigen-stiffnesses form 21 independent material constants that characterize the fundamental physics of material anisotropy. These 21 constants are invariant to the orientation of the base vectors fixed in the material. This spectral representation also simplifies the restrictions on these material constants which ensure that the strain energy is a positive-definite function of strain. In addition, a simple damage model is proposed based on this spectral representation and a generalization for finite deformations is briefly discussed. Compliance tensor Anisotropic elasticity Invariants Spectral representation Stiffness tensor Damage Enthalten in International journal of engineering science New York, NY [u.a.] : Science Direct, 1963 193 Online-Ressource (DE-627)301511217 (DE-600)1484471-0 (DE-576)096806389 nnns volume:193 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.00 Technik allgemein: Allgemeines VZ AR 193
allfields_unstemmed	10.1016/j.ijengsci.2023.103916 doi (DE-627)ELV065441524 (ELSEVIER)S0020-7225(23)00107-6 DE-627 ger DE-627 rda eng 600 VZ 50.00 bkl Rubin, M.B. verfasserin aut A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A new spectral representation of the strain energy function for linear anisotropic elasticity is proposed in the form of a sum of 6 scalar eigen-stiffnesses times the squares of their associated scalar eigen-strains. Since this new representation is general, it is no less or more general than the standard representation. However, the spectral form reveals fundamental coupled eigen-modes of deformation and energy associated with general anisotropic response. Specifically, each eigen-strain is the inner product of the strain tensor with its symmetric eigen-tensor. The 6 eigen-strains are linearly independent and the 6 eigen-tensors are also linearly independent. Moreover, unlike the eigenvectors of a symmetric matrix, distinct pairs of eigen-tensors are not all orthogonal. The 15 constants that define the eigen-tensors together with the 6 eigen-stiffnesses form 21 independent material constants that characterize the fundamental physics of material anisotropy. These 21 constants are invariant to the orientation of the base vectors fixed in the material. This spectral representation also simplifies the restrictions on these material constants which ensure that the strain energy is a positive-definite function of strain. In addition, a simple damage model is proposed based on this spectral representation and a generalization for finite deformations is briefly discussed. Compliance tensor Anisotropic elasticity Invariants Spectral representation Stiffness tensor Damage Enthalten in International journal of engineering science New York, NY [u.a.] : Science Direct, 1963 193 Online-Ressource (DE-627)301511217 (DE-600)1484471-0 (DE-576)096806389 nnns volume:193 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.00 Technik allgemein: Allgemeines VZ AR 193
allfieldsGer	10.1016/j.ijengsci.2023.103916 doi (DE-627)ELV065441524 (ELSEVIER)S0020-7225(23)00107-6 DE-627 ger DE-627 rda eng 600 VZ 50.00 bkl Rubin, M.B. verfasserin aut A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A new spectral representation of the strain energy function for linear anisotropic elasticity is proposed in the form of a sum of 6 scalar eigen-stiffnesses times the squares of their associated scalar eigen-strains. Since this new representation is general, it is no less or more general than the standard representation. However, the spectral form reveals fundamental coupled eigen-modes of deformation and energy associated with general anisotropic response. Specifically, each eigen-strain is the inner product of the strain tensor with its symmetric eigen-tensor. The 6 eigen-strains are linearly independent and the 6 eigen-tensors are also linearly independent. Moreover, unlike the eigenvectors of a symmetric matrix, distinct pairs of eigen-tensors are not all orthogonal. The 15 constants that define the eigen-tensors together with the 6 eigen-stiffnesses form 21 independent material constants that characterize the fundamental physics of material anisotropy. These 21 constants are invariant to the orientation of the base vectors fixed in the material. This spectral representation also simplifies the restrictions on these material constants which ensure that the strain energy is a positive-definite function of strain. In addition, a simple damage model is proposed based on this spectral representation and a generalization for finite deformations is briefly discussed. Compliance tensor Anisotropic elasticity Invariants Spectral representation Stiffness tensor Damage Enthalten in International journal of engineering science New York, NY [u.a.] : Science Direct, 1963 193 Online-Ressource (DE-627)301511217 (DE-600)1484471-0 (DE-576)096806389 nnns volume:193 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.00 Technik allgemein: Allgemeines VZ AR 193
allfieldsSound	10.1016/j.ijengsci.2023.103916 doi (DE-627)ELV065441524 (ELSEVIER)S0020-7225(23)00107-6 DE-627 ger DE-627 rda eng 600 VZ 50.00 bkl Rubin, M.B. verfasserin aut A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A new spectral representation of the strain energy function for linear anisotropic elasticity is proposed in the form of a sum of 6 scalar eigen-stiffnesses times the squares of their associated scalar eigen-strains. Since this new representation is general, it is no less or more general than the standard representation. However, the spectral form reveals fundamental coupled eigen-modes of deformation and energy associated with general anisotropic response. Specifically, each eigen-strain is the inner product of the strain tensor with its symmetric eigen-tensor. The 6 eigen-strains are linearly independent and the 6 eigen-tensors are also linearly independent. Moreover, unlike the eigenvectors of a symmetric matrix, distinct pairs of eigen-tensors are not all orthogonal. The 15 constants that define the eigen-tensors together with the 6 eigen-stiffnesses form 21 independent material constants that characterize the fundamental physics of material anisotropy. These 21 constants are invariant to the orientation of the base vectors fixed in the material. This spectral representation also simplifies the restrictions on these material constants which ensure that the strain energy is a positive-definite function of strain. In addition, a simple damage model is proposed based on this spectral representation and a generalization for finite deformations is briefly discussed. Compliance tensor Anisotropic elasticity Invariants Spectral representation Stiffness tensor Damage Enthalten in International journal of engineering science New York, NY [u.a.] : Science Direct, 1963 193 Online-Ressource (DE-627)301511217 (DE-600)1484471-0 (DE-576)096806389 nnns volume:193 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.00 Technik allgemein: Allgemeines VZ AR 193
language	English
source	Enthalten in International journal of engineering science 193 volume:193
sourceStr	Enthalten in International journal of engineering science 193 volume:193
format_phy_str_mv	Article
bklname	Technik allgemein: Allgemeines
institution	findex.gbv.de
topic_facet	Compliance tensor Anisotropic elasticity Invariants Spectral representation Stiffness tensor Damage
dewey-raw	600
isfreeaccess_bool	false
container_title	International journal of engineering science
authorswithroles_txt_mv	Rubin, M.B. @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
hierarchy_top_id	301511217
dewey-sort	3600
id	ELV065441524
language_de	englisch
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author	Rubin, M.B.
spellingShingle	Rubin, M.B. ddc 600 bkl 50.00 misc Compliance tensor misc Anisotropic elasticity misc Invariants misc Spectral representation misc Stiffness tensor misc Damage A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage
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topic_title	600 VZ 50.00 bkl A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage Compliance tensor Anisotropic elasticity Invariants Spectral representation Stiffness tensor Damage
topic	ddc 600 bkl 50.00 misc Compliance tensor misc Anisotropic elasticity misc Invariants misc Spectral representation misc Stiffness tensor misc Damage
topic_unstemmed	ddc 600 bkl 50.00 misc Compliance tensor misc Anisotropic elasticity misc Invariants misc Spectral representation misc Stiffness tensor misc Damage
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title	A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage
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title_full	A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage
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title_sort	a new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage
title_auth	A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage
abstract	A new spectral representation of the strain energy function for linear anisotropic elasticity is proposed in the form of a sum of 6 scalar eigen-stiffnesses times the squares of their associated scalar eigen-strains. Since this new representation is general, it is no less or more general than the standard representation. However, the spectral form reveals fundamental coupled eigen-modes of deformation and energy associated with general anisotropic response. Specifically, each eigen-strain is the inner product of the strain tensor with its symmetric eigen-tensor. The 6 eigen-strains are linearly independent and the 6 eigen-tensors are also linearly independent. Moreover, unlike the eigenvectors of a symmetric matrix, distinct pairs of eigen-tensors are not all orthogonal. The 15 constants that define the eigen-tensors together with the 6 eigen-stiffnesses form 21 independent material constants that characterize the fundamental physics of material anisotropy. These 21 constants are invariant to the orientation of the base vectors fixed in the material. This spectral representation also simplifies the restrictions on these material constants which ensure that the strain energy is a positive-definite function of strain. In addition, a simple damage model is proposed based on this spectral representation and a generalization for finite deformations is briefly discussed.
abstractGer	A new spectral representation of the strain energy function for linear anisotropic elasticity is proposed in the form of a sum of 6 scalar eigen-stiffnesses times the squares of their associated scalar eigen-strains. Since this new representation is general, it is no less or more general than the standard representation. However, the spectral form reveals fundamental coupled eigen-modes of deformation and energy associated with general anisotropic response. Specifically, each eigen-strain is the inner product of the strain tensor with its symmetric eigen-tensor. The 6 eigen-strains are linearly independent and the 6 eigen-tensors are also linearly independent. Moreover, unlike the eigenvectors of a symmetric matrix, distinct pairs of eigen-tensors are not all orthogonal. The 15 constants that define the eigen-tensors together with the 6 eigen-stiffnesses form 21 independent material constants that characterize the fundamental physics of material anisotropy. These 21 constants are invariant to the orientation of the base vectors fixed in the material. This spectral representation also simplifies the restrictions on these material constants which ensure that the strain energy is a positive-definite function of strain. In addition, a simple damage model is proposed based on this spectral representation and a generalization for finite deformations is briefly discussed.
abstract_unstemmed	A new spectral representation of the strain energy function for linear anisotropic elasticity is proposed in the form of a sum of 6 scalar eigen-stiffnesses times the squares of their associated scalar eigen-strains. Since this new representation is general, it is no less or more general than the standard representation. However, the spectral form reveals fundamental coupled eigen-modes of deformation and energy associated with general anisotropic response. Specifically, each eigen-strain is the inner product of the strain tensor with its symmetric eigen-tensor. The 6 eigen-strains are linearly independent and the 6 eigen-tensors are also linearly independent. Moreover, unlike the eigenvectors of a symmetric matrix, distinct pairs of eigen-tensors are not all orthogonal. The 15 constants that define the eigen-tensors together with the 6 eigen-stiffnesses form 21 independent material constants that characterize the fundamental physics of material anisotropy. These 21 constants are invariant to the orientation of the base vectors fixed in the material. This spectral representation also simplifies the restrictions on these material constants which ensure that the strain energy is a positive-definite function of strain. In addition, a simple damage model is proposed based on this spectral representation and a generalization for finite deformations is briefly discussed.
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title_short	A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage
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A new spectral representation of the strain energy function for linear anisotropic elasticity with a generalization for damage

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